516 Past Exams

COST-BENEFIT ANALYSIS ECONOMICS 516

SPRING 2010

FINAL EXAM Answer all parts of each of the following eight questions. Each question is worth 10 points. This examination accounts for 40% of your final grade on this course. Time allowed: 175 minutes. This examination paper has seven pages. INTRODUCTION The City of Victoria must decide whether or not to grant approval to a proposed new marina for the inner harbour. The marina will be built and operated by a local private firm, called Marinas-for-the-Rich-and-Famous (MRAF); the city has no direct financial interest in the proposed marina. The marina will be designed to attract so-called “mega-yachts”. These are very large boats owned by rich and famous people, none of whom are residents of Victoria. Construction will take one year and cost $20 million. The markets for the labour and materials to be used in construction are undistorted, and the project is too small to influence prices in either market. The marina will last forever. Proponents of the marina argue that it will attract free-spending visitors to the city (aboard the mega-yachts), who will boost demand for tourist services and for yacht-maintenance services. Opponents argue that it will create congestion in the harbour (with an increase in the risk of collisions between boats and float planes), and that it will ruin the water views of some waterfront homes near the proposed site. The City staff must conduct a CBA of the project to determine whether it is in the interests of the City as a whole to approve the project. Thus, the referent group for the CBA is the City. (Note that MRAF is a local firm, and thus, part of the referent group). Assume that there are 365 days in every year (ignore leap years). 1. PROFITS FOR MRAF The marina will have 48 berths. MRAF will charge $500 per night for each occupied berth. MRAF estimates that, on average, 50% of berths will be occupied on any given night. It will cost MRAF $200,000 per year to maintain the marina (once construction is complete). MRAF will also have to pay property taxes to the City, in the amount of $20,000 per year (once construction is complete). (a) Calculate the expected NPV of the marina investment from the perspective of MRAF,

using a discount rate of 5%.

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(b) How should this NPV be treated in the CBA? Explain your answer. (c) How should the consumer surplus to mega-yacht owners be treated in the CBA?

Explain your answer. 2. THE IMPACT ON VIEWS AND HOUSE PRICES The area adjacent to the proposed marina site has some high-priced condominiums, whose views will be adversely affected by the marina. This will translate into reduced values for these homes, all of which are locally owned. There are fifty homes that will be most affected. Real estate experts have estimated that the loss of market value to these homes will be about $50,000 each. This impact will be felt as soon as construction begins. (a) How should the loss of market value be treated in the CBA? Is this a one-time cost or

an annual cost? Explain your answer. (b) Briefly explain how you would estimate the loss of market value using house price

data. Include an explanation of why you would include a constant term in any regressions you might run.

3. DEMAND FOR RESTAURANT SERVICES Demand for a variety of tourist services may be boosted by the presence of the mega- yachts but we will restrict attention to restaurant services. There are currently 600 restaurants meals served in the City, on average, on any given night. Half of these meals are served to City residents; the remaining meals are served to visitors to the City. The restaurant service market is perfectly competitive. Existing supply and demand conditions are illustrated in Figure 1. Both supply and demand are linear. Restaurants are locally owned and operated. It is expected that a yacht berthed at the marina will add 2 meals to the existing demand for every night it is berthed. (That is, if there are 10 yachts berthed on any given night then there will be 20 additional meals demanded that night). This additional demand for meals is insensitive to price (because mega-yacht owners are really rich). (a) Using the information from Figure 1, derive equations for the existing supply and

demand curves. Confirm that your equations yield the existing equilibrium price and quantity.

(b) Illustrate the new demand curve on Figure 1, and write down the new equation for

demand. Calculate the new equilibrium price and quantity. Explain why equilibrium quantity has not risen by the full amount to which the marina has added to demand.

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(c) Calculate the change in producer surplus. How should this be treated in the CBA?

Explain your answer. (d) Calculate the change in consumer surplus for existing consumers. How should this be

treated in the CBA? Explain your answer (and include a discussion of any assumptions you need to make).

(e) Calculate the consumer surplus captured by the restaurant customers from the mega-

yachts. (Hint: Think before you do any calculations). How should this be treated in the CBA? Explain your answer.

4. YACHT-MAINTENANCE SERVICES Mega-yacht maintenance services are currently provided by a locally-owned, profit-maximizing monopoly, called HOPE Shipyards (HOPE). This firm has constant marginal costs: one yacht service costs $6000. The existing demand for these services is from non-residents of Victoria. The marina will boost this demand. The old and new annual (inverse) demands are given by (4.1) qp 2000300000 −= (4.2) qp 1000400001 −= respectively. These are illustrated in Figure 2. (a) What is the current price charged for a yacht service? What is the current annual profit

made by HOPE? (b) What is the new price charged for a yacht service? What is the new annual profit

made by HOPE? How should the change in profit be treated in the CBA? Explain your answer.

(c) How should the change in consumer surplus for existing maintenance customers be

treated in the CBA? Explain your answer. How should the deadweight loss from the monopoly be treated in the CBA? Explain your answer.

5. HARBOUR CONGESTION AND SAFETY The increased risk of a collision between a boat and a floatplane is uncertain. Experts have estimated the current risk at 1 in 20,000 on an annual basis. It is thought that the added congestion associated with the marina will double that risk. The consequences of a collision – should one occur – are also uncertain. However, it is expected that a collision

4

would lead to a loss of 2 lives on average. (Assume that these would be local lives). The value of a statistical life is $4m. (a) What is the expected annual cost of lives lost if the marina proceeds? How should this

be treated in the CBA? Explain your answer. (b) Briefly explain the meaning of “the value of a statistical life”. (c) Briefly explain how you would deal with uncertainty in general in a CBA. 6. GOVERNMENT FINANCES AND THE COST OF FUNDS (a) Construct a table summarizing outlays and receipts for the City. (b) Suppose the marginal cost of funds is 1.1. Briefly explain what this means and the

economic reasoning behind it. (c) Calculate the cost of funds for each period of the project. 7. NET PRESENT VALUE (a) Construct a table summarizing all costs and benefits for the project. (b) Explain how you have treated the property taxes in your compilation of costs and

benefits. (c) Suppose the PSDR is 5%. Calculate the NPV of the project. Hint: the present value of

a $1 perpetuity discounted at rate r is

rr

rrr+

=⎥⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

(d) Briefly outline two reasons why net present value is a better measure of the project

than the benefit-cost ratio. 8. THE DISTRIBUTION OF COST AND BENEFITS (a) Calculate the NPV of the impacts on each of the following groups: • MRAF • HOPE • Suppliers of restaurant services • Consumers of restaurant services • Waterfront-home owners

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• Float plane/boat users • Taxpayers

(b) Explain the relationship between your answers to part (a) and Question 7(c) above.

6

p

600

200

0D

meals

50

0S

FIGURE 1

Name: ____________________________

7

p

40000

0D

yachtsserviced

30000

15

1D

40

FIGURE 2

8

COST-BENEFIT ANALYSIS ECONOMICS 516

SPRING 2010

FINAL EXAM ANSWER GUIDE

1. PROFITS FOR MRAF (a) Annual revenue (MRAF expects to fill 24 berths per night for 365 nights @ $500 per

berth): 000,380,4$500$*365*24 =

Annual costs (incl. property taxes):

000,220$000,20$000,200$ =+

Annual net revenue: 000,160,4$000,220$000,380,4$ =−

NPV of investment @ 5% ($m):

2.6305.1

05.005.116.4

20 =⎟⎠⎞

⎜⎝⎛

+−=NPV

(b) This is a benefit of the project because MRAF is a local firm (within the referent

group). It accrues in year 1 (since we have already calculated the NPV). (c) Consumer surplus to mega-yacht owners is neither a cost nor a benefit because these

owners are outside the referent group. 2. THE IMPACT ON VIEWS AND HOUSE PRICES (a) The loss of market value is a cost of the project since it reflects the value of the lost

views. It is a one-time cost of $2.5m because the ongoing loss of views is capitalized into the reduced house prices. It accrues in year 1.

(b) An hedonic price study (see notes). The constant term is included to capture fixed

factors that affect all Victoria house prices (such as climate).

9

3. DEMAND FOR RESTAURANT SERVICES (a) The demand curve is pq D 48000 −=

The supply curve is pqS 12=

Equilibrium: pp 124800 =−

Solve for p: 500 =p

Then from supply (or demand): 60050*120 ==q (b) Expected additional meals per night: 482*24 = . This additional demand is

insensitive to price, so the shift in demand is parallel below 200=p . Above 200=p , the new demand curve is perfectly inelastic (though this is not relevant for

the equilibrium).1 See Figure 1A.

The new demand curve is pq D 48481 −=

The supply curve is pqS 12=

Equilibrium: pp 124848 =−

Solve for p:

1 If the new demand is perfectly inelastic, why don’t restaurants price discriminate and charge these new customers an infinite price? Because the market is competitive, and price is driven down to marginal cost for all customers.

10

531 =p

Then from supply (or demand): 63653*121 ==q The price increase has crowded-out some existing consumers. How many? 12)48636(600 =−− (c) On a daily basis:

854,1$)36*3(21600*3 =+=ΔPS

On an annual basis: mPS 677.0$854,1$*365 ==Δ

This is a benefit of the project (because restaurants are locally owned). It accrues in year 2 and each year thereafter.

(d) On a daily basis:

782,1$)12*3(21588*3 −=+−=ΔCS

On an annual basis:

mCS 65.0$782,1$*365 −=−=Δ

Part of this loss accrues to visitors from outside the city (recall that only half of the existing meals are served to city residents), and that part is not a cost of the project. We cannot distinguish these two groups in the demand curve, so assume the two groups have the same valuations on average. Thus, we include 50% of the CSΔ as a cost of the project m325.0$(− ). This accrues in year 2 and each year thereafter.

(e) The consumer surplus captured by the restaurant customers from the mega-yachts is

infinite (since they were willing to pay infinity but only had to pay $53). In any case, it doesn’t count as a benefit because they are outside the referent group.

4. YACHT-MAINTENANCE SERVICES (a) HOPE is a monopoly, and will maximize profits by setting MCMR =0 . Revenue is

11

qqR )200030000(0 −= So MCMR =0 yields 60004000030000 =− q

which solves for 60 =q

Price is then set to clear this quantity (from the demand curve): 000,18$6*2000300000 =−=p Annual profit is 000,72$6*)000,6000,18$(0 =−=π (b) HOPE is still a monopoly, and will now maximize profits by setting MCMR =1 .

Revenue is now qqR )100040000(1 −= So MCMR =1 yields 6000200040000 =− q

which solves for 171 =q

Price is then set to clear this quantity (from the new demand curve): 000,23$17*1000400001 =−=p

Annual profit is 000,289$17*)6000000,23$(1 =−=π

The change in annual profit is m217.0$000,72$000,289$ =−=Δπ

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This is a benefit of the project because HOPE is a local firm. It accrues in year 2 and each year thereafter.

(c) The change in consumer surplus for existing maintenance customers is neither a cost

nor a benefit because these customers are outside the referent group. The DWL of monopoly is also irrelevant because it is not caused by the project. (You cannot lose what you never had).

5. HARBOUR CONGESTION AND SAFETY (a) The expected annual cost of lives lost if the marina proceeds is

[prob(collision)]*[cost of a collision] = mm 0008.0$4$*220000

2=⎟

⎠⎞

⎜⎝⎛

The relevant figure for inclusion in the CBA is the change in expected cost. The probability of a collision has doubled. Hence, the change in expected cost is $0.0004m. This accrues in year 2 and each year thereafter.

(b) See notes. (c) See notes. 6. GOVERNMENT FINANCES AND THE COST OF FUNDS (a)

Table 1

Year 1Year 2(+)

Outlays 0 0 Receipts Property taxes 0.02 Net Outlays 0 -0.02 Cost of Funds 0 -0.002

(b) See notes. (c) See Table 1.

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7. NET PRESENT VALUE (a)

Table 2 Year 1 Year 2(+) Benefits Profits for MRAF (NPV) 63.2 Property taxes 0.0200 PS gain for restaurant service suppliers 0.6770 Profit increase for HOPE 0.2170 Total Benefits 63.2 0.914 Costs Loss of house values 2.5 CS loss for local restaurant customers 0.3250 Increase in expected collision costs 0.0004 Cost of funds -0.002 Total Costs 2.5 0.3234 Net Benefits 60.7 0.5906

(b) Property taxes are entered as a benefit because we deducted them from the profits of

MRAF. Hence, they have no net effect on the NPV (since they are a transfer) other than through the impact on the COF.

(c) 512.7205.1

05.005.15906.0

7.60 =⎟⎠⎞

⎜⎝⎛

+=NPV

(d) See notes.

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8. THE DISTRIBUTION OF COST AND BENEFITS (a)

Table 3

PV at 5%

Winners MRAF 63.20HOPE 4.34Restaurant service suppliers 13.54Taxpayers 0.44 81.52 Losers Waterfront-home owners 2.50Local restaurant customers 6.50Float plane & boat deaths 0.008 9.008 Net Benefits 72.51

(b) They are equal. What a remarkable coincidence!

15

p

600

200

0D

meals

50

800 848

53

636

1D

0S

588

FIGURE 1A

1

Economics 516 Spring 2010

Second Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1.(a) A public construction project will hire 5000 workers from an undistorted labour market. The

government claims that the project will create 5000 new jobs. Explain why the government is probably wrong.

(b) Suppose the breakdown of tickets sales for the 2010 Olympic Games in Vancouver is as follows: BC residents 70% Non-BC Canadians 20% Non-Canadians 10%

How should the revenue from these ticket sales be treated in a CBA of the Games? Explain your answer.

(c) Discuss the following claim: “Market failure is a necessary condition for policy intervention”.

2.(a) A project will hire 10 workers at the existing market wage of $25. The workers are currently

unemployed. What is the financial outlay associated with this hiring? What is the economic cost associated with this hiring?

(b) “Roads are congested because road use is under-priced”. Comment.

(c) Agent A undertakes an activity z that bestows an external cost on agent B. Explain why the private optimum for agent A does not maximize social surplus. Support your answer with an appropriate diagram. Is the private optimum for agent A Pareto efficient? Explain your answer.

3.(a) Explain the problem of “moral hazard” and why it can lead to inefficiency.

(b) A policy is expected to create a price change in a market in which the elasticity of supply at the current price is 0η . Describe how you would approximate the associated change in producer surplus.

(c) A recent law introduced in Britain sets a minimum price for alcohol served in pubs. The purpose of the law is to reduce public drunkenness and its associated problems on the streets. Discuss the impact of this policy on social surplus in this market. Support your answer with an appropriate diagram.

2

Answer Guide 1.(a) Note that the market is undistorted; there is no existing unemployment. The augmentation of labour demand will cause the wage to rise and thereby crowd-out some existing employers. Thus, the 5000 workers on the project will be drawn partly from new supply (workers enticed into the market because wages have risen) and partly from existing employment. As a consequence, fewer than 5000 jobs will be created. See Figure 1. There will be 5000 new jobs only if the supply curve is perfectly elastic. This is a highly unlikely scenario. Thus, the government claim is probably wrong. (b) Revenue that remains within the referent group should be treated as transfers. Revenue that flows into the referent group should treated as a benefit to the referent group. Revenue that flows out of the referent group should be treated as a cost to the referent group. Thus, there are three possible scenarios to consider: (i) Suppose the referent group is BC and BC collects the revenue. Then 70% of the ticket revenue collected is a transfer within BC; 30% of the revenue is a benefit to BC (an inflow of wealth). (ii) Suppose the referent group is BC and the federal government collects the revenue. Then there is an outflow of wealth from BC equal to 70% of the ticket revenue, and this is a cost to BC. (iii) Suppose the referent group is Canada. Then it does not matter who collects the revenue (BC or the federal government). There is a transfer equal to 90% of ticket revenue, and a benefit to Canada equal to 10% of revenue (a wealth inflow from non-Canadians). (c) First, note the difference between a necessary condition and a sufficient condition. An answer that substitutes “sufficient condition” for “necessary condition” here cannot be correct. Market failure is not a necessary condition for intervention. Intervention is motivated by market failure and/or redistribution. Even in the absence of market failure, redistribution alone can motivate intervention. 2.(a) The financial outlay is simply equal to $25 * 10 = $250. The economic cost is the social opportunity cost of the labour (SOCL). This comprises the private opportunity cost (POCL) to the worker plus any external cost (which could be negative if the unemployed workers are engaged in socially damaging activity). The POCL is somewhere between 0 and $25, since the unemployed labour must be drawn from that part of the supply curve, but we cannot say anything more than this. An estimate can be made by assuming the newly hired workers are drawn randomly from the [0,25] interval, in which case they have an average OCL equal to 25/2.

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(b) There are two distinct issues with respect to roads. First, roads tend not to be provided efficiently by the market because they are an impure public good. Thus, non-contributors to their provision may be able to free-ride once the road is provided, if exclusion costs are high. This means that a road provider may not be able to capture the full social benefit of the road. Thus, the social benefit of provision could exceed the social cost of provision but the road is still not provided. Hence, the possibility of inefficiency in provision. Second, if a road is provided (whether by government or by private provider) then it may become congested. Congestion is a negative externality imposed upon users of an impure public good (like a road) by other users of that good. The exam question relates to this second issue, and so too should a good answer. We can describe the congestion externality in the context of a standard scenario in which MSC of an activity (road use) exceeds the MPC of that activity. The equilibrium road use will be too high because road users ignore the external cost (congestion) they impose on other road users. If road use can be priced via a toll (that is, if exclusion for non-payers is possible) then the price can be set equal to the MEC at the optimum. This will internalize the congestion externality. Critically, note that congestion may not be eliminated entirely; the external cost is typically not driven down to zero at the social optimum. Thus, some congestion will persist even when road use is priced optimally. (c) This is a standard negative externality question. Note that you are asked to “Explain why the private optimum for agent A does not maximize social surplus.” Answer: the source agent does not take into account the external cost imposed on others when choosing his private optimum. 3.(a) See notes, and note especially why moral hazard leads to inefficiency. (It is not enough o explain what moral hazard is). It leads to inefficiency because agents in the trade (or contract) could be better off if the risk averse agent could obtain a lower risk contract by undertaking an unobservable action. However, that surplus goes uncaptured because the contract cannot be made contingent on the (unobservable) action. (b) See notes. (c) There are three stakeholders in this market: alcohol consumers, alcohol servers (pubs), and the external agents impacted by the public drunkenness. The problem should be framed as a negative externality problem: alcohol consumers impose an external cost on other members of society. A price floor (a minimum price) on alcohol is an attempt to internalize that externality. See Figures 2a – 2d for a breakdown of the surplus changes. Note that I have illustrated the case where the price floor is set to implement the social optimum (where MSBMSC = ). I have also simplified the PS change calculation by assuming that suppliers with lowest MC are those that actually supply at the mew price. We cannot be sure of this, since there is now an excess supply problem, and all suppliers with pMC < would be willing to supply. (Exercise: calculate the change in PS if rationing at p is random). For comparison purposes, Figures 3a – 3d illustrate an optimal excise tax on alcohol as an alternative policy. (Not required for a perfect answer). Note that the change in social surplus is the same – given the simplified calculation of PSΔ – but the distributional impacts are different (and tax-payers become a stakeholder).

4

q

w

0w

S

D0

GqD +0

q0 q1

1w

2q

5000

new jobs < 5000

Figure 1

5

q

p

MSCS ≡

MSB

MPBD ≡

q 0q

0p

p

surplus gained by external agents

Figure 2a

6

q

p

MSCS ≡

MSB

MPBD ≡

q 0q

0p

p

surplus lost by alcohol consumers

Figure 2b

7

q

p

MSCS ≡

MSB

MPBD ≡

q 0q

0p

p

surplus gained by alcohol servers

+ve-ve

Figure 2c

8

q

p

MSCS ≡

MSB

MPBD ≡

q 0q

0p

p

social surplus gained

Figure 2d

9

q

p

MSCS ≡

MSB

MPBD ≡

1q 0q

0p1p

surplus gained by external agents

Sp

t

Figure 3a

10

q

p

MSCS ≡

MSB

MPBD ≡

1q 0q

0p1p

surplus lost by consumers

Sp

t

Figure 3b

11

q

p

MSCS ≡

MSB

MPBD ≡

1q 0q

0p1p

surplus lost by alcohol servers

Sp

t

Figure 3c

12

q

p

MSCS ≡

MSB

MPBD ≡

1q 0q

0p1p

tax revenue collected

Sp

t

Figure 3d

1


First Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1. (a) What are the nine main steps of a cost-benefit analysis? (b) The 2009 recession in Canada led to an increase in unemployment despite a variety of

macroeconomic stimulus policies by government. Does this mean that these policies failed in their goal of stimulating employment?

(c) The city of Kuching is situated on the banks of the Sarawak River at its mouth on the South China

Sea. Parts of the city are occasionally subject to tidal flooding but no major damage has ever occurred. The government is now proposing the construction of extensive sea walls and earth filling at the most vulnerable parts of the city. The cost of the project will far exceed the cost of all previous floods combined. Explain the importance of the base case in assessing this project.

2. (a) The cost-benefit analysis of a proposed new ferry service in northern BC lists “Fare Revenue” of

$1.5m as a benefit of the project. An accompanying financial analysis of the same proposed service includes “Fare Revenue” of $2.5m. Has someone made a mistake?

(b) The city of Victoria is considering a project to refurbish or replace the “blue bridge” that links east

and west Victoria. If the bridge is refurbished then the construction cost of $100m will be borne entirely by the city. If the bridge is replaced with a new bridge, the construction cost will be $150m but the Federal Government will contribute $80m towards that cost. Suppose the benefits to Victoria residents, and all other costs, are identical for the two project options. (i) As an analyst for the city, which option would you recommend? Briefly explain your answer. (ii) As an analyst for the Federal Government, would you make a different recommendation?

Explain your answer. (c) Cars fitted with modern pollution-control equipment produce far fewer emissions than older cars.

With this in mind, the State of California has recently proposed a policy whereby any car built before 1980 must be fitted with modern pollution-control equipment before it can be sold to a new owner. Existing owners are not required to have the equipment installed provided they do not wish to sell the car. A group of economists have argued that this policy could in fact have a perverse effect on emissions. Are those economists correct? Explain your answer.

3. (a) Explain the difference between a Pareto improvement and a potential Pareto improvement. (b) (i) Two individuals enter into a trade. The WTP of the buyer exceeds the WTA of the seller. Does the

trade improve social welfare? Explain your answer. (ii) A public policy will create winners and losers. The WTP of the winners exceeds the WTA of the

losers. Does the policy improve social welfare? Explain your answer with reference to your answer to part (i) above.

(c) Explain the trade-off between wealth creation and wealth redistribution.

1

Cost-Benefit Analysis Economics 516

Spring 2009

Final Exam Answer all parts of each of the following eight questions. Each part of each question is worth 5 points. This examination accounts for 40% of your final grade on this course. Time allowed: 175 minutes. This examination paper has seven pages. Introduction The City of Victoria is considering a project to extend the main runway at its airport. The extended runway would allow international flights to land and depart. This would make it easier for Victoria residents to take long distance flights; they currently have to fly to Vancouver and then depart from that airport. The capacity to accommodate long distance flights will also mean that some foreign tourists who currently arrive in Canada via Vancouver will arrive via Victoria. These tourists will then spend time in Victoria whereas currently they do not visit the city. The referent group for the CBA is the province. 1. Construction Construction of the expanded runway will take one year and cost $20 million. The construction cost will be shared 50/50 between the province (BC) and the federal government. The new runway will last forever. The expansion will require use of land currently owned by the province. This land was purchased ten years ago for $500,000 in anticipation of expanding the runway at some future date. The land cannot be used for any other purpose due to its proximity to the existing runway. (a) What is the cost of construction (from the perspective of the referent group)? Explain your answer. (b) Explain how the new land use should be treated in the CBA. 2. Short Distance Travelers There are currently two groups of BC-resident travelers using the airport: short distance travelers and long distance travelers. Both groups have the option to take the ferry to Vancouver and take their flight from there. Thus, both groups are sensitive to services and prices at the Victoria airport. To help finance the runway expansion the airport will levy a departure fee on all passengers departing from the airport, beginning in year 2. The fee will be $10. Suppose the demand for airport departures for short distance travelers is as illustrated in Figure 1, where the departure fee is depicted on the price axis. Note that there are currently 200,000 departures. (a) Derive the demand curve and calculate the post-project number of departures. (b) Calculate the change in consumer surplus for short distance travelers and illustrate this change on a

reproduction of Figure 1. (c) How should this change in consumer surplus be treated in the CBA? 3. Long Distance Travelers

2

The new runway will cause a parallel shift of 10,000 in the demand for departures from long distance travelers because long distance travel is now more convenient than it was. The existing and anticipated new demand curves are illustrated in Figure 2. Note that there are currently 50,000 departures. (a) Derive the existing demand curve ( 0D ). (b) Derive the new demand curve ( 1D ) and the new number of departures. (c) Calculate the change in consumer surplus. How this be treated in the CBA? 4. Foreign Tourists The runway upgrade will cause 20,000 foreign tourists who would have arrived directly in Vancouver to arrive in Canada via Victoria instead. These tourists would not otherwise have visited Victoria but will now extend their stay in Canada to spend some time in Victoria before flying to Vancouver. While visiting Victoria, these new tourists will utilize various tourist services provided by Victoria firms. The associated parallel shift in demand for tourist services in Victoria is illustrated in Figure 3. The figure also illustrates the supply curve for tourist services. The existing quantity and price are 200,000 and $100 respectively. (a) Derive the existing demand curve. (b) Derive the new demand curve, the new price and the new equilibrium quantity. (c) Illustrate in Figure 3 the consumer surplus enjoyed by the new foreign tourists. How should this CS be

treated in the CBA? (d) Calculate the reduction in tourist services demanded from existing users in response to the price rise.

Calculate the change in consumer surplus for this group and illustrate this change in Figure 3. (e) The composition of existing tourist service users is 50% BC residents and 50% non-BC residents. How

should the consumer surplus change calculated in (d) be treated in the CBA?

Note: assume that existing non-BC resident users of tourist services do not arrive in Victoria by plane. (Otherwise you would need to calculate the new airport fees collected from this group).

(f) Calculate the change in producer surplus for tourist service suppliers. How should this be treated in the

CBA? 5. Noise Approximately 300 homes near the airport will experience an increase in noise exposure as a consequence of the runway expansion. The average price of these homes is currently $500,000. Estimates based on an existing study suggest that the increased noise exposure will reduce the value of these homes by 10%. Explain how the house price effect should be treated in the CBA. 6. Government Finances and the Cost of Funds (a) Construct a table summarizing outlays and receipts for the BC government. (b) Suppose the marginal cost of funds is 1.1. Briefly explain what this means and the economic reasoning

behind it. (c) Calculate the cost of funds for each period of the project.

3

7. Net Present Value (a) Construct a table summarizing all costs and benefits for the project. (b) Explain how you have treated airport user fees in your compilation of costs and benefits. (c) Suppose the PSDR is 5%. Calculate the NPV of the project. Hint: the present value of a $1 perpetuity

discounted at rate r is

rr

rrr+

=⎥⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

(d) Briefly outline two reasons why net present value is a better measure of the project than the benefit-cost

ratio. 8. The Distribution of Cost and Benefits (a) Calculate the NPV of the impacts on each of the following groups: • Long distance travelers • Short distance travelers • Consumers of tourist services • Suppliers of tourist services • Local home owners • Taxpayers

(b) Explain the relationship between your answers to part (a) and Question 7(c) above.

4

p

200,000

200

D

departures

10

FIGURE 1

5

p

120

0D

departures

10

FIGURE 2

100

50,000

1D

6

p

0D

tourist service users

100

FIGURE 3

200

400,000

1D

S

200,000 420,000

7


Spring 2009

Final Exam Answer Guide Answer all parts of each of the following eight questions. Each part of each question is worth 5 points. This examination accounts for 40% of your final grade on this course. Time allowed: 175 minutes. This examination paper has seven pages. Introduction The City of Victoria is considering a project to extend the main runway at its airport. The extended runway would allow international flights to land and depart. This would make it easier for Victoria residents to take long distance flights; they currently have to fly to Vancouver and then depart from that airport. The capacity to accommodate long distance flights will also mean that some foreign tourists who currently arrive in Canada via Vancouver will arrive via Victoria. These tourists will then spend time in Victoria whereas currently they do not visit the city. The referent group for the CBA is the province. 1. Construction Construction of the expanded runway will take one year and cost $20 million. The construction cost will be shared 50/50 between the province (BC) and the federal government. The new runway will last forever. The expansion will require use of land currently owned by the province. This land was purchased ten years ago for $500,000 in anticipation of expanding the runway at some future date. The land cannot be used for any other purpose due to its proximity to the existing runway. (a) What is the cost of construction from the perspective for the province? Explain your answer. Construction cost is the cost of resources used within the referent group (the province) less net inflow of wealth from the federal government:

mmm 101020 =− (b) Explain how the additional land use should be treated in the CBA. This is irrelevant to the CBA. The original cost is sunk and the land has no current opportunity cost.

8

2. Short Distance Travelers There are currently two groups of BC-resident travelers using the airport: short distance travelers and long distance travelers. Both groups have the option to take the ferry to Vancouver and take their flight from there. Thus, both groups are sensitive to services and prices at the Victoria airport. To help finance the runway expansion the airport will levy a departure fee on all passengers departing from the airport, beginning in year 2. The fee will be $10. Suppose the demand for airport departures for short distance travelers is as illustrated in Figure 1, where the departure fee is depicted on the price axis. Note that there are currently 200,000 departures. (a) Derive the demand curve and calculate the post-project number of departures.

pQ 1000000,200 −= The post-project number of trips is

000,19010*1000000,2001 =−=Q (b) Calculate the change in consumer surplus for short distance travelers and illustrate this change on a

reproduction of Figure 1.

mCS 95.12

000,10*10000,190*10 −=⎟⎠⎞

⎜⎝⎛ +−=Δ

See Figure 1A. (c) How should this change in consumer surplus be treated in the CBA? This is a cost of the project. It is incurred in year 2 and every year thereafter. 3. Long Distance Travelers The new runway will cause a parallel shift of 10,000 in the demand for departures from long distance travelers because long distance travel is now more convenient than it was. The existing and anticipated new demand curves are illustrated in Figure 2. Note that there are currently 50,000 departures. (a) Derive the existing demand curve ( 0D ). ppQ 500000,50)( 0 −=

9

(b) Derive the new demand curve ( 1D ) and the new number of departures.

ppQ 500000,60)( 1 −= The post-project number of trips is 000,5510*500000,601 =−=Q (c) Calculate the change in consumer surplus. How this be treated in the CBA?

mCSCSCS 525.02

000,50*1002

000,55*)10120(01 =⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛ −

=−=Δ

This is a benefit of the project. It accrues in year 2 and every year thereafter. 4. Foreign Tourists The runway upgrade will cause 20,000 foreign tourists who would have arrived directly in Vancouver to arrive in Canada via Victoria instead. These tourists would not otherwise have visited Victoria but will now extend their stay in Canada to spend some time in Victoria before flying to Vancouver. The associated parallel shift in demand for tourist services in Victoria is illustrated in Figure 3. The figure also illustrates the supply curve for tourist services. (Victoria firms supply these services). The existing quantity and price are 200,000 and $100 respectively. (a) Derive the existing demand curve. ppQ 2000000,400)( 0 −= (b) Derive the new demand curve, the new price and the new equilibrium quantity. The new demand curve is

ppQ 2000000,420)( 1 −= The supply curve is ppQS 2000)( = The new equilibrium price is 1p such that

)()( 111 pQpQ S= Thus, 1051 =p . The total quantity supplied at the new price is

000,210105*2000000,4201 =−=Q See Figure 3A. (c) Illustrate in Figure 3 the consumer surplus enjoyed by the new foreign tourists. How should this CS be

treated in the CBA?

10

See area A in Figure 3A. This CS is not included as a benefit of the project because foreign tourists are not part of the referent group. (d) Calculate the reduction in tourist services demanded from existing users in response to the price rise.

Calculate the change in consumer surplus for this group and illustrate this change in Figure 3. The post-project services demanded by existing users is

000,190)105(2000000,400*1 =−=Q

Thus, the change in services demanded from this group is 10,000. The change is consumer surplus for this group is

mCS 975.02

000,10*5000,190*5 −=⎟⎠⎞

⎜⎝⎛ +−=Δ

See area B in Figure 3A. (e) The composition of existing tourist service users is 50% BC residents and 50% non-BC residents. How

should the consumer surplus change calculated in (d) be treated in the CBA?

Note: assume that existing non-BC resident users of tourist services do not arrive in Victoria by plane. (Otherwise you would need to calculate the new airport fees collected from this group. Today I am in a generous mood).

Assuming that BC residents and non-BC residents have the same average WTP, then 50% of the CS loss (0.4875m) is incurred by BC residents. This is a cost of project. It is incurred in year 2 and each year thereafter. The CS loss to non-BC residents is not included as a loss because they are not part of the referent group. (f) Calculate the change in producer surplus for tourist service suppliers. How should this be treated in the

CBA?

mmmPS 025.110025.112

000,200*1002

000,210*105=−=⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=Δ

This is a benefit of the project (because suppliers are part of the referent group). It accrues in year 2 and every year thereafter. 5. Noise Approximately 300 homes near the airport will experience an increase in noise exposure as a consequence of the runway expansion. The average price of these homes is currently $500,000. Estimates based on an existing study suggest that the increased noise exposure will reduce the value of these homes by 10%. The total loss of house values is

m15000,50*300 = This is a one-time cost of the project incurred in year 2. Note that anticipation of the increased noise level may cause market values to fall ahead of the actual increase in noise. However, the actual loss in housing

11

services (due to the increased noise) does not occur until year 2. It is this cost that is of interest for the CBA. 6. Government Finances and the Cost of Funds (a) Construct a table summarizing outlays and receipts for the BC government.

Table 1 Year 1 Year 2(+) Outlays Construction 10 Receipts Airport users fees 2.65 Net Outlays 10 -2.65

Note that fees are collected from all airport users, beginning in year 2. Thus, total fee receipts are m65.2)000,20000,55000,190(*10 =++ (b) Suppose the marginal cost of funds is 1.1. Briefly explain what this means and the

economic reasoning behind it. See course notes. (c) Calculate the cost of funds for each period of the project. The COF is 1m in year 1 and m265.0− in year 2 and each year thereafter. 7. Net Present Value (a) Construct a table summarizing all costs and benefits for the project Table 2 Year 1 Year 2 Year 3(+) Benefits CS gain for long distance BC travelers 0.5250 0.5250 PS gain for tourist service suppliers 1.0250 1.0250 Airport user fees 2.6500 2.6500 Total Benefits 0 4.2 4.2 Costs Construction 10 CS loss for short-distance BC travelers 1.9500 1.9500 CS loss for BC tourist service users 0.4875 0.4875

12

Increased noise exposure 15 Cost of funds 1 -0.265 -0.265 Total Costs 11 17.1725 2.1725 Net Benefits -11 -12.9725 2.0275 (b) Explain how you have treated airport user fees in your compilation of costs and benefits. Since we have included costs and benefits to BC travelers in terms of CS surplus (rather than the value of reduced trips), user fees collected from them must be included as a benefit. Had we included only the social value of the changes in BC-resident departures then fees collected from BC-residents would not be included since they are just a transfer. However, user fees collected from foreign tourists constitute an inflow of wealth and are therefore a benefit of the project.

13

(c) Suppose the PSDR is 5%. Calculate the NPV of the project. Hint: the present value of a $1 perpetuity discounted at rate r is

rr

rrr+

=⎥⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

2)1(

10275.2

19725.1211

rr

r

rNPV

+

⎟⎠⎞

⎜⎝⎛ +

++

−−=

At 05.0=r , mNPV 264.15= . (d) Briefly outline two reasons why net present value is a better measure of the project than the benefit-cost

ratio. See course notes. 8. The Distribution of Cost and Benefits (a) Calculate the NPV of the impacts on each of the following groups: • Long distance travelers:

mNPVLDT 5.1005.0525.0

==

• Short distance travelers:

mNPVSDT 3905.095.1

−=−=

• Consumers of tourist services:

mNPVCTS 75.905.0

4875.0−=−=

• Suppliers of tourist services:

mNPVSTS 5.2005.0

025.1==

14

• Local home owners:

mNPVLHO 286.1405.1

15−=−=

• Taxpayers:

mNPVT 3.4705.0915.211 =+−=

(b) Explain the relationship between your answers to part (a) and Question 7(c) above. The NPV for the project as a whole must equal the sum of the NPVs of the impacts on each of the identified groups. Recall that the NPV measures the social surplus created by the project, which is by definition equal to the gains to the winners net of the losses to the losers.

15

p

200,000

200

D

departures

10

FIGURE 1

16

p

200,000

200

D

departures

10

FIGURE 1

190,000

17

p

120

0D

departures

10

FIGURE 2

100

50,000

1D

18

p

0D


100

FIGURE 3

200

400,000

1D

S

200,000 420,000

19

p

0D


100

FIGURE 3

200

400,000

1D

S

200,000190,000

105

210,000 420,000

210

A

B

20


Second Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1.(a) The Province of BC has announced a plan to install 140 red light cameras across the province. (Red

light cameras take a photograph of a car’s license plate if the car enters an intersection against a red light). There are currently 900 accidents per year caused by red light violations at the intersections where the cameras are to be installed. The red light cameras are expected to reduce that number by 25%. Explain how you would specify the base case for this policy against which costs and benefits should be measured.

(b) The Province of BC is considering the provision of camping facilities at Gordon Campbell Provincial Park. A fee of $20 per night will be charged for a camping site. The expected breakdown of users is as follows: BC residents 70% Non-BC Canadians 20% Non-Canadians 10%

How should the camping fees be treated in the CBA for this project? Explain your answer.

(c) Discuss the following claim: “Market failure is a sufficient condition for policy intervention”.

2.(a) Explain why there can arise a conflict between equity and efficiency in the pursuit of wealth

redistribution. What is the primary role of economic analysis in redistribution policy?

(b) What is the “tragedy of the commons” and why does it arise?

(c) Agent A undertakes an activity z that bestows an external benefit on agent B. Explain why the private optimum for agent A does not maximize social surplus. Support your answer with an appropriate diagram. Is the private optimum for agent A Pareto efficient? Explain your answer.

3.(a) Explain the problem of “adverse selection” and why it can lead to inefficiency.

(b) A policy is expected to create a price change in a market in which the elasticity of demand at the current price is 0ε . Describe how you would approximate the associated change in consumer surplus.

(c) Consider Figure 1. It depicts a policy-imposed price ceiling in an otherwise competitive market. This policy prohibits suppliers from raising their price above p . Discuss the impact of this policy on social surplus in this market. Support your answer with an appropriate diagram.

21


First Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1. (a) What are the nine main steps of a cost-benefit analysis? (b) The forestry industry in BC has experienced a sharp contraction in recent years, and many

former forestry workers are currently unemployed. These former workers currently receive welfare payments from the Province. Payments to a former worker will continue until he or she finds a new job or retires at age 67, at which time he or she will receive retirement benefits from the Canada Pension Plan. The age distribution of these former workers is approximately normal. The province is considering a re-training program for these former forestry workers. Describe how you would construct the base case for this project.

(c) Suppose a CBA for a particular project yields a negative NPV. Would you necessarily

recommend against the project? Explain your answer. 2. (a) Lead is a neurotoxin; it retards brain development in children. Lead was banned as an

additive to gasoline in the US in the 1970s. A more expensive additive (to boost the octane of the fuel) is now used instead. The CBA conducted at the time of the ban showed without doubt that the benefits of the ban outweighed the costs by a wide margin. Lead was not banned in Cambodia until the 1990s. Does this necessarily indicate a failure of public policy in Cambodia? Explain your answer.

(b) The Canadian Federal Government funds unemployment insurance payments to

unemployed workers for a maximum of 50 weeks. An infrastructure project is currently being considered for BC that will employ some currently unemployed residents of BC. An analysis of the project includes the associated reduction in unemployment payments as a benefit of the project. Comment.

(c) California has some of the worst air quality problems in the US. The state is currently

pressing the US (Federal) Environmental Protection Agency (EPA) to allow the state regulator to impose stricter vehicle emission standards on cars sold in California than currently apply at the national level. These tighter standards would add about $1200 to the cost of a new car. The California market is so large – about 20% of the entire US market – and economies of scale in vehicle production so strong that vehicle manufactures will likely choose to adopt the tighter standards for all cars sold in the US if forced to adopt the tighter standards for the California market. Analysis by the state of California indicates that the benefits of the tighter standards will be about $1500 for every new car sold in the state (since each new car displaces an older car). The state has based its case for the tighter standards on this analysis. Suppose you are an analyst for the EPA. Do the California numbers constitute a compelling case for its proposal? Explain your answer.

3. (a) Consider again the California vehicle emissions proposal from Question 2(c). On average over the past five years, there have been 2m new vehicles sold per year in California. The

22

state has therefore calculated that the annual net benefits of its proposal will be $600m, calculated as

$(1500 – 1200)*2m = $600m

You have recently been hired as an analyst for the state of California. Identify two problems with this net benefit calculation.

(b) A proposed construction project will use $20,000 worth of steel. Does the economic cost of

the steel depend on whether it is supplied from within the referent group or imported from another jurisdiction? Explain your answer.

(c) (i) Two individuals enter into a trade. The WTP of the buyer exceeds the WTA of the seller.

Does the trade improve social welfare? Explain your answer.

(ii) A public policy will create winners and losers. The WTP of the winners exceeds the WTA of the losers. Does the policy improve social welfare? Explain your answer with reference to your answer to part (i) above.

23

Answer Guide 1. (a) See course notes.

(b) There are two key issues to address in the construction of a base case here. First, some of the older former workers will soon enter retirement, so the benefits of re-training will be short-lived for those people. We can construct an age-based survivor function to reflect this dynamic element using the normality of the age distribution. Second, some of the former workers may find re-employment – either in the forestry sector if it recovers, or in some other field – without re-training. This too can be modeled with a survivor function relationship. Because the probability of a former worker finding a new job (without re-training) is likely to be related to age, the two key issues are interconnected, so a joint survivor function that takes account of that correlation is needed.

(c) No. The recommendation is based on the NPV, and on the sensitivity testing results and the

distributional analysis. 2. (a) No. Cambodia is a poor country (with a per capita GDP equal to about 3% of that of the

US). Thus, the costs and benefits of banning lead are likely to be very different from those in the US. The net benefit of banning lead for Cambodia in the 1970s may have been correctly assessed to be negative. The net benefit may have become positive in the 1990s due to rising wealth over the intervening period time, and the falling costs of the lead-substitute.

(b) The treatment of the reduced unemployment payments depends on critically whether the

referent group is Canada or BC. Suppose it is Canada. Then the reduced unemployment payments are simply the termination of a transfer. This is not a benefit of the project. Now suppose the referent group is BC. The reduced unemployment benefits are a cost of the project (the termination of an inflow of wealth from outside BC). Of course, that inflow of wealth would have been terminated eventually (due to the 50 week payment limit) so the base case would need to take account of that.

(c) The key issue here is that the California numbers are not based on a federal referent group,

and EPA is a national regulator. In particular, the benefits of the tighter emissions standards might be much lower in other areas of the country that do not have the same current air quality problems as California (due to differences in population density or geography, for example). The cost of the tighter standards may outweigh the benefits in those areas. Even if the vehicle manufactures do not adopt nationwide standards in response to the California rules, the loss of some scale economies will drive up vehicle costs in other parts of the country. A thorough EPA assessment should take a national perspective in calculating costs and benefits.

24

3. (a) The issues raised in Question 2(c) relate to costs and benefits beyond California. In contrast, as an analyst for California, your focus would likely be on California. However, even from this perspective there are (at least) two problems with the numbers. First, current economic conditions in the US mean that car sales over the next two years (and possibly beyond) will be much lower than the annual average over the past five years. Second, the higher cost of producing a vehicle to meet the new standards will likely drive up the price of a new car, and the quantity demanded will fall accordingly. Thus, the number of new vehicles that will enter the fleet has likely been over-estimated.

Note that the price effect could even be perverse. In particular, some consumers who would have bought a less-polluting car will now hold on to their old – and more polluting – car for longer (because the price has risen). Thus, the tighter regulations could actually cause emissions to rise – relative to where they would have been – in the short run at least.

There may, of course, be other problems beyond the two identified here.

(b) Yes. The economic cost is the cost of resources used within the referent group plus any net

outflow of wealth. If internal steel is used then resources are used within the referent group. If the steel is imported then the payment for the steel is an outflow of wealth. Whether or not these values are equal depends on a number of factors. Consider first the simplest possible setting in which supply costs are the same everywhere and the market for steel is undistorted. In that case the market value of steel is a correct measure of the value of the resources used internally, and a correct measure of the outflow of wealth if the steel is imported. Either way, the cost is the same. However, if the steel can be produced more cheaply outside the referent group then the cost of internal and imported steel will be different. In addition, if the market is distorted then the market price of steel may not be an accurate measure of the cost of the resources used to produce it. Thus, the cost of imported steel – the market price – may be different from the cost of internal steel.

(c) (i) Yes. The trading price is bounded by WTP and WTA ( WTPpWTA ≤≤ ) since only then

will both parties be willing to conduct the trade. Since WTAWTP > , at least one party must be strictly better off, and the other party cannot be worse off. Thus, we have a Pareto improvement. Welfare must rise.

(ii) Not necessarily. We can only judge the impact on social surplus. Since the gains

exceed the losses (in the sense that WTP for the winners exceeds the WTA of the losers), social surplus rises; we have a potential Pareto improvement. However, we cannot judge the impact on social welfare when some agents win and others lose. The impossibility theorem prevents us from ranking the pre- and post-policy allocations according to any social choice rule constructed from individual preferences.

25


Spring 2007

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 40% of your final grade on this course. Time allowed: 175 minutes. This examination paper has eight pages. Introduction The City of Victor Harbour currently discharges its untreated sewage directly into the ocean about 3km off-shore via a pipeline. Recent population growth has led to an increased volume of sewage and concerns have been raised about possible environmental damage associated with the oceanic discharge. There is also some concern about a loss of tourism to the city because of its poor environmental image. The city is now is considering building a sewage treatment plant. Construction of the treatment plant will take one year and cost $1.2 billion. The construction cost will be shared 50/50 between the city and the province. The plant will last forever. On-going maintenance will cost $20m per year once the plant is operational The referent group for the CBA is the city. 1. The Price of Plankton A scientific study has concluded that heavy tidal action of the ocean near the point of sewage discharge quickly dilutes and dissipates most of the discharged organic material. However, there is some damage to sea life in the immediate vicinity of the pipeline outlet. Outline the main steps of the non-market valuation technique that you think would be most appropriate for placing a monetary value on the environmental damage caused by the sewage discharge, from the perspective of the city residents. Henceforth assume that the estimated annual environmental damage caused by the untreated sewage discharge is $5m. 2. The Value of a Clean Image The city currently attracts about 1 million tourists (from outside the city) per year. The average tourist spends about $200 on “visitor services” (such as accommodation, restaurants, and visits to the local tourist attractions) per visit to the city. We can think of this expenditure as the current “price” of a visit. Visitor services are provided by a competitive tourist industry whose linear supply curve is illustrated in Figure 1. Visitor services are currently subject to a $20 excise tax collected by the city. The current demand for visitor services (labeled 0D ) and the existing market equilibrium are illustrated in Figure 1. The supply and demand curves are linear. (a) Calculate the annual producer surplus, consumer surplus to tourists, and tax revenue collected in the

existing equilibrium. The tourism industry believes that demand would be higher if the city improved its image by installing sewage treatment. The estimated higher demand 1D (with sewage treatment in place) and the associated equilibrium is illustrated in Figure 2.

26

(b) Calculate the expected change in the annual producer surplus, consumer surplus to tourists, and tax revenue collected if the sewage treatment plant is built. How should these items be treated in the CBA?

3. Not in My Backyard The proposed site of the sewage treatment plant is on vacant ocean-front land (owned by the city) next to an established residential neighborhood. An hedonic price study conducted in a similar city indicates that houses located within a half-kilometer radius from a sewage treatment plant (called Zone 1) are on average 20% less valuable than comparable houses located elsewhere, and that houses located within a radius between a half-kilometer and one-kilometer (Zone 2) are 10% less valuable. Houses more than one kilometer from the plant suffer no loss in value. These results are summarized in Figure 3. In the City of Victor Harbour there are 100 houses in Zone 1 and 300 houses in Zone 2. The current average house price in these zones is $500,000 and $400,000 respectively. (a) Briefly outline the main steps associated with an hedonic price study designed to measure the affect of

proximity to a sewage treatment plant. (b) Based on the estimated impacts derived from the existing hedonic price study, calculate the expected

total loss of house values in Zones 1 and 2 respectively. (c) Explain how this loss should be treated in the CBA. (Hint: the price of a house is in principle equal to

the discounted sum of housing services provided by the house). (d) The vacant land on which the sewage plant would be built could sell for $25m (for housing

development) if the plant is not built. How should this fact be treated in the CBA?

27

4. Money for Nothing The sludge collected from the treated sewage will be sold by the city as fertilizer. The existing local market for fertilizer (supplied by local dairy farms) is perfectly competitive. The existing equilibrium is illustrated in Figure 4. The supply and demand curves are linear. The treatment plant will generate 10,000 tonnes of fertilizer per year; it will be sold on the local market at the market-clearing price. (a) Reproduce Figure 4 and illustrate the impact of the treatment plant fertilizer on the fertilizer market.

What is the new equilibrium price and quantity supplied by the private suppliers? (Hint: you need to write down the equations for private supply and demand and then calculate the new equilibrium price when 10,000 tonnes is added to the market).

(b) Calculate the changes in consumer and producer surpluses in the fertilizer market. How much revenue

is collected by the city for the sale of the treatment plant fertilizer? 5. The Cost of Funds (a) Construct a table listing all financial outlays and receipts for the city government in each year of the

project. (b) Suppose the existing marginal cost of funds for the city is 1.1. Calculate the cost of funds in each year

of the project. 6. Net Present Value (a) Construct a table listing all benefits and costs in each year of the project. (b) Assume the discount rate is 3%. Calculate the net present value of the project. Hint: the present value of

a $1 perpetuity discounted at rate r is

rr

rrr+

=⎥⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

(c) Briefly outline two reasons why net present value is a better measure of the project than the benefit-cost

ratio.

28

7. The Distribution of Benefits and Costs (a) Construct a table detailing the present value of net benefits (at 3%) accruing to each of the following

impact groups: • people concerned about environmental damage • house owners in the area of the proposed treatment plant • suppliers of visitor services • fertilizer producers • fertilizer consumers • tax-payers

(b) Explain the relationship between your answer to 6(b) and your answer to 7(a).

29


Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1. (a) Explain the relationship between EV, CV and the change in consumer surplus as measures of welfare

change for a price rise for an inferior good. Support your answer with appropriate diagrams. (b) Australia recently announced that it is going to ban the sale of incandescent light bulbs to force a shift

towards more energy-efficient fluorescent lighting. (Incandescent light bulbs produce a great deal of heat and therefore use much more energy to produce light than do fluorescent light tubes). Currently, about 100 million incandescent light bulbs are purchased each year in Australia. Explain how you would construct the base case against which the light-bulb-ban policy should be assessed.

(c) Suppose a public project will use an input drawn from an undistorted market with an upward-sloping

supply curve. Suppose also that the project is large enough to have an impact on the market price of the input. Explain how the cost of the input should be calculated, and explain the logic behind that calculation. Support your answer with an appropriate diagram.

2. Consider the following mining project. There are 100m tonnes of copper available for extraction from

the mining site. The current (2007) price of copper is $2 per tonne. Extraction costs are $1 per tonne. Site preparation must be undertaken in the first year of the project, and will cost $60m. All extraction will take place in the second year. There are no other costs or benefits associated with project. The discount rate is 10%.

(a) Based on NPV, should this project be undertaken? Explain your answer. (b) Suppose the project begins and site preparation is completed. The cost of extraction in 2008 then

rises to $1.50 per tonne. If none of the site preparation costs can be recovered, should the project be continued? Explain your answer.

(c) Now suppose instead that the cost of extraction rises to $c per tonne (rather than $1.50 per tonne) in

2008. If 50% of the site preparation costs can be recovered if the project is terminated, what is the critical value of c at which the project should be terminated? Explain your answer.

3. (a) Use an appropriate diagram to illustrate the gain in social surplus associated with a shift from the

private optimum to the social optimum in the presence of a negative externality. Does this shift constitute a Pareto improvement? Explain your answer. Illustrate the Pigouvian tax that would be applied as a corrective measure against this externality.

(b) What is the “marginal cost of funds” and why is it typically greater than one? Support your answer

with an appropriate diagram illustrating an excise tax. (c) What are the nine main steps of a cost-benefit analysis?

30


Spring 2006

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. This examination paper has four pages. Introduction1 The proposed Bear Bones Gravel Project is located near Port McNeill on northern Vancouver Island. It is a partnership between a Vancouver-based company – Solomon Minerals Corporation – and the local community. It will extract gravel in an open-pit mining operation. The extracted gravel will be transported 2.5km via a giant conveyor to a ship loading facility to be built nearby. Ships will then transport the gravel for sale in California. A special port facility will be built in San Francisco to unload the gravel. The conveyor will cross the feeding grounds of Roosevelt elk (big deer-like animals). To moderate the impact on the elk, special elk crossings will be installed over the conveyor. Some important information about the project: • Construction of the conveyor and elk crossing, the loading facility, the San Francisco port facility, and

other site infrastructure will occur in 2006. • The project will produce 6 million tonnes of gravel annually for 25 years, beginning in 2007. • The price of gravel (in the California market) is $14 per tonne. • Shipping costs are $3 per tonne. • A royalty of $5 per tonne will be paid to the BC government. • Construction costs are

• $15m for the loading facility; • $5m for the conveyor; • $10m for other site infrastructure; • $65m for the port facility in San Francisco; and • $5m for the elk crossing

• The BC government will fund 50% of the cost of the loading facility; the federal government will fund the remaining 50%.

• The local community will fund construction of the elk crossing. • The other construction costs will be funded by Solomon. • The project will employ 50 full-time workers in each year of operation, beginning in 2007. These

workers will each be paid the market wage for gravel-pit workers, which is $40,000 per year. • Under an agreement with the local community, 50% of the workers will be drawn from local people

who are currently unemployed. The remaining workers will be drawn from existing mining employment elsewhere in the province.

• The workers who are currently unemployed will lose existing support payments of $12,000 per year paid by the federal government. The activities in which they are currently engaged have no social or private value.

• All financial operating costs – labour, shipping and royalties – will be paid by Solomon. • The local community will receive a 15% share of annual net operating revenue (calculated as the

market value of the gravel less financial operating costs). • BC is the referent group. • The BC government faces a marginal cost of funds of 1.2. • The PSDR is 5%. 1 This is based on an actual project but most of the information has been invented.

31

• The value of a 25 year annuity is

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+

−+

=+

+++

++

+25

252 1111

)1(1........

)1(1

)1(11

rrr

rrr

32

1. The Wisdom of Solomon (a) What will Solomon pay in wages annually? (b) What is the annual net operating revenue for Solomon? (c) What is the NPV of this investment for Solomon (assuming a discount rate of 5%)? 2. Benefits to the Community (a) What is the annual net operating revenue for the local community? (b) What are the net financial receipts from employment for the local community? What is the value of

producer surplus from that employment? (c) What is the NPV of this investment for the local community (assuming a discount rate of 5%)? 3. Taxpayer on the Take (a) Explain the meaning of the “marginal cost of funds” and why it is greater than one. Support your

answer with an appropriate diagram. (b) Construct a table of financial outlays and receipts for the BC government. (c) Calculate the cost of funds for BC in each year of the project. (d) Calculate the NPV of this investment for BC taxpayers. 4. Nothing’s as Precious as a Hole in the Ground (a) Construct a table of economic benefits and costs (with BC as the referent group). Number your listed

items consecutively and then explain the calculation of each item. (b) Calculate the NPV of the project. (c) Explain the relationship between the four NPV results you have derived. (d) Calculate the benefit-cost ratio (BCR) for the project. Give two reasons why the BCR should not be

used as a project evaluation criterion.

33

5. What’s an Elk Worth Anyway? (a) Provide a brief outline of how a referendum format contingent valuation might be

conducted in order to place a value on the loss of an elk population. (b) For this particular project, what is the minimum annual cost of disrupting the elk that would make

building the elk crossing worthwhile? 6. Too Good to be True Suppose the project begins and all construction is completed. Then in 2007 the California economy goes into a deep recession and the market price of gravel falls. (a) What is the lowest price of gravel at which Solomon would continue to mine and ship gravel if all

construction costs are sunk? (b) What is the lowest price of gravel at which Solomon would continue to mine and ship gravel if the San

Francisco port facility could be sold for $50m? (c) What is the lowest price of gravel at which the community would want Solomon to continue to mine

and ship gravel if all construction costs are sunk? Why is this price different from your answer to part (a)?

7. The Optimal Royalty Suppose the price of gravel falls to $4 per tonne, and all construction costs are sunk. At what value should the BC government set the royalty if it wishes to maximize net benefits to the Province? Hint: this is not a difficult question. Bonus Question Name the Midnight Oil song from which the title of Question 4 is taken. This question carries no points but a correct answer confers considerable bragging rights.

34


Spring 2006

Final Exam Answer Guide

1. The Wisdom of Solomon (a) What will Solomon pay in wages annually? Wage payments = 2)04.0(50 = (b) What is the annual net operating revenue for Solomon? Net operating revenue for Solomon = 9.2834)85.0(]2))53(14(6)[85.0( ==−+− (c) What is the NPV of this investment for Solomon (assuming a discount rate of 5%)?

2.327)09.14(9.288005.111

05.09.2880

25

=+−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−=SNPV

2. Benefits to the Community (a) What is the annual net operating revenue for the local community? Net operating revenue for community = 1.534)15.0( = (b) What are the net financial receipts from employment for the local community? What is the value of

producer surplus gained from that employment? Net employment receipts = 7.0)012.004.0(25 =− Producer surplus is equal to financial receipts since the opportunity cost of labour is zero. (c) What is the NPV of this investment for the local community (assuming a discount rate of 5%)?

72.76)09.14(8.5505.111

05.08.55

25

=+−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−=CNPV

3. Taxpayer on the Take (a) Explain the meaning of the “marginal cost of funds” and why it is greater than one. Support your

answer with an appropriate diagram. See Course Notes. (b) Construct a table of financial outlays and receipts for the BC government.

35

BC Government Outlays and Receipts (in $m)

Year 1 Year 2+Outlays Share of loading facility construction 7.50

Receipts Royalties 30.00

Net Outlays 7.50 -30.00

Cost of Funds 1.50 -6.00 (c) Calculate the cost of funds for BC in each year of the project. See Table above. (d) Calculate the NPV of this investment for BC taxpayers.

24.498)09.14(36905.111

05.0369

25

=+−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−=TNPV

36

4. Nothing’s as Precious as a Hole in the Ground (a) Construct a table of economic benefits and costs (with BC as the referent group). Number your listed

items consecutively and then explain the calculation of each item.

Economic Benefits and Costs (in $m)

Year 1 Year 2+Benefits Value of gravel 84.00

Total benefits 84.00

Costs Loading facility 7.50Conveyor 5.00Other site infrastructure 10.00Port facility 65.00Elk crossing 5.00Labour costs 1.00Shipping costs 18.00Loss of federal funds 0.30Cost of funds 1.50 -6.00

Total costs 94.00 13.30

Net benefit -94.00 70.70

(b) Calculate the NPV of the project.

16.902)09.14(7.709405.111

05.07.7094

25

=+−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−=BCNPV

(c) Explain the relationship between the four NPV results you have derived. TCSBC NPVNPVNPVNPV ++= The sum of the net benefits to each of the groups within the referent group must always equal the net

benefits to the referent group as a whole.

37

(d) Calculate the benefit-cost ratio (BCR) for the project. Give two reasons why the BCR should not be used as a project evaluation criterion.

2.4)09.14(30.1394

)09.14(84=

+=BCR

See Course Notes for a critique of the BCR.

5. What’s an Elk Worth Anyway? (a) Provide a brief outline of how a referendum format contingent valuation might be

conducted in order to place a value on the loss of an elk population.

See Course Notes. (b) For this particular project, what is the minimum annual cost of disrupting the elk that would make

building the elk crossing worthwhile?

The NPV of the investment in the elk crossing is

)09.14(505.111

05.05

25

xxNPVELK +−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−+−=

Setting this NPV equal to zero and solving for x yields

35.0=MINx If the cost is less than this then investment in the elk crossings is not worthwhile.

38

6. Too Good to be True Suppose the project begins and all construction is completed. Then in 2007 the California economy goes into a deep recession and the market price of gravel falls. (a) What is the lowest price of gravel at which Solomon would continue to mine and ship gravel if all

construction costs are sunk?

Let p denote the price of gravel. Then the annual continuation payoff for Solomon (its annual net operating revenue) is

Annual continuation payoff = 5.421.5]2))53((6)[85.0( −=−+− pp

Setting this payoff equal to zero and solving for p yields

33.81 =Sp

(b) What is the lowest price of gravel at which Solomon would continue to mine and ship gravel if the San

Francisco port facility could be sold for $50m? The continuation payoff must now be specified in terms of NPV. It is

58.62845.755005.111

05.0)05.1)(5.421.5(50

25

−+−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−

−+−= ppNPVS


99.82 =Sp

(c) What is the lowest price of gravel at which the community would want Solomon to continue to mine

and ship gravel if all construction costs are sunk? Why is this price different from your answer to part (a)?

The community receives a share of net operating revenues plus employment income. Thus, the continuation payoff its perspective is

Annual continuation payoff = 8.69.07.0]2))53((6)[15.0( −=+−+− pp


56.7=Cp

7. The Optimal Royalty Suppose the price of gravel falls to $4 per tonne, and all construction costs are sunk. At what value should the BC government set the royalty if it wishes to maximize net benefits to the Province? The NPV for BC as a whole is increasing monotonically in the royalty over the entire range for which Solomon is willing to continue operations. Thus, we simply need to find the highest royalty such that Solomon is willing to participate. Let R denote the royalty. Then the continuation payoff for Solomon is

39

Annual continuation payoff = ]2))3(4(6)[85.0( −+− R Setting this payoff equal to zero and solving for R yields 67.0* =R Bonus Question Name the Midnight Oil song from which the title of Question 4 is taken. This question carries no points but a correct answer confers considerable bragging rights. “Blue Sky Mine”, from the album Blue Sky Mining (1990).

The song refers to the Wittenoom asbestos mine in Western Australia where blue asbestos was mined between 1947 and 1966. The once-thriving town is now a ghost town. Hundreds – likely thousands – of the men who mined asbestos there have died or will die from asbestos related diseases. (See next page for the complete lyrics).

40

Blue Sky Mine Midnight Oil

My gut is wrenched out it is crunched up and broken My life that is lived is no more than a token

Who'll strike the flint upon the stone and tell me why? If I yell out at night there's a reply of blue silence

The screen is no comfort I can't speak my sentence They blew the lights at heaven's gate and I don't know why

But if I work all day on the blue sky mine (There'll be food on the table tonight)

Still I walk up and down on the blue sky mine (There'll be pay in your pocket tonight)

The candy store paupers lie to the shareholders They're crossing their fingers they pay the truth makers

The balance sheet is breaking up the sky So I'm caught at the junction still waiting for medicine

The sweat of my brow keeps on feeding the engine Hope the crumbs in my pocket can keep me for another night

And if you blue sky mining company won't come to my rescue If the sugar refining company won't save me

Who's gonna save me? But if I work all day on the blue sky mine (There'll be food on the table tonight)

And if I walk up and down on the blue sky mine (There'll be pay in your pocket tonight)

And some have sailed from a distant shore And the company takes what the company wants

And nothing's as precious As a hole in the ground Who's gonna save me?

I pray that sense and reason brings us in Who's gonna save me?

We've got nothing to fear In the end the rain comes down

Washes clean the streets of a blue sky mine

41


Spring 2006

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1. (a) Suppose a project will improve local air quality. Should we use EV or CV to measure the

welfare gain? Explain your answer. (b) Air bags have been shown to reduce the risk of death in car accidents but cars built before

1992 did not have airbags. A proposed policy will require all cars built before 1992 to be retrofitted with air bags. How would you construct the base case for such a policy?

(c) A project will draw labour from a pool of currently unemployed workers. How would you

calculate the cost of that labour? 2. (a) The City of Victoria is contemplating building a waste water treatment plant, at a cost of

$300m using materials and labour drawn from Victoria through undistorted markets. The Government of British Columbia will contribute $100m to the project and the Government of Canada will contribute $150m. The remaining $50m will be financed by residents of Victoria.

What is the cost of the project if (i) the referent group is the City of Victoria? (ii) the referent group is British Columbia? (iii) the referent group is Canada?

(b) Use an appropriate diagram to illustrate the gain in social surplus associated with a shift

from the private optimum to the social optimum in the presence of a positive externality. Provide an example of such an externality. Illustrate the Pigouvian subsidy required to implement the social optimum. Is this social optimum unique? Explain your answer.

(c) Explain the meaning of “moral hazard” and explain why it may lead to inefficiency in

unregulated market outcomes. 3. (a) What is the role of CBA in the assessment of wealth redistribution policies? (b) What is the marginal cost of funds and why is it typically greater than one? Support your

answer with an appropriate diagram illustrating an ad valorem tax. (c) What are the nine main steps of a cost-benefit analysis?

42


Spring 2006

Midterm Exam Partial Answer Guide

1.(a) This depends on the implicit assignment of property rights:

• if the local citizens are deemed to have a right to the cleaner air then the appropriate measure is WTA to forgo the gain. This means using EV since it takes the new utility (with the improved air quality) as the reference point.

• if the local citizens are deemed to have no right to the cleaner air then the appropriate measure is WTP to obtain the gain. This means using CV since it takes the current utility (with the lower air quality) as the reference point.

2.(a) In all cases the cost is calculated as the value of the resources used within the

referent group plus any net outflow of wealth. Thus

(i) 300 – (100 +150) = 50 (ii) 300 – 150 = 150 (iii) 300

43


Spring 2005

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 45% of your final grade on this course. Time allowed: 175 minutes. This examination paper has seven pages. Introduction2 In late 2004 the Government of British Columbia announced the planned construction of the “Pacific Marine Circle Route”. This is a road construction project that will connect Port Renfrew to Lake Cowichan, thereby forming a “circular route”: Victoria – Port Renfrew – Lake Cowichan – Victoria. (See the map on p.7). Port Renfrew is currently connected to Lake Cowichan by an active logging road. Part of the road is owned by the Province and part of it is owned by Timberwest, a local forestry company. The project involves the purchase of the Timberwest portion of the road, plus the upgrading of the entire Port Renfrew – Lake Cowichan connection to make it suitable for two-wheel drive traffic. The new road will last forever. Some important information about the project: • The provincial government will purchase the Timberwest portion of the road for $2.5m. This will

occur in 2005. Timberwest will in turn spend $1.5m in 2005 to upgrade an alternative road to carry its logging trucks. This alternative logging road will be equally useful as the old road for Timberwest.

• The provincial government will fund the upgrading of the entire Port Renfrew – Lake Cowichan connection at a cost of $3m. This work will be undertaken in 2005 and the new road will open in 2006.

• Currently 20,000 tourists per year make the Victoria – Port Renfrew return trip. Of these tourists, 10,000 are expected to return via the circle route once it is constructed while the others will continue to return via the existing route. We refer to those who switch routes as “switchers” and to those who do not switch routes as “non-switchers”.

• 10,000 additional tourists are expected to visit Port Renfrew using the circle route once it is completed. (The expected increase in visitors reflects the fact that a trip to Port Renfrew will be more interesting for tourists when the return to Victoria can be made via a different route). We refer to these additional tourists as “new visitors”.

• 50% of all current tourists are BC residents and the rest are non-residents. That percentage breakdown of tourists is expected to remain unchanged when the new route is open. Resident and non-resident tourists are otherwise the same in all respects.

• The main attraction in the Port Renfrew area is Botanical Beach; it is visited by all tourists who make the trip. The provincial government currently charges $5 per visit but this fee will rise to $10 per visit post-project.

• Switchers and non-switchers currently value a visit to Botanical Beach at $20 (net of travel costs). That value will rise to $40 (net of travel costs) for switchers once the new circle route is complete, and will remain unchanged for non-switchers.

• New visitors are expected to value a visit to Botanical Beach at $30 (net of travel costs). • Many of the tourists who make the trip to Port Renfrew eat lunch at the locally owned Lighthouse

Restaurant; it is the only place in town to eat. The value that tourists place on lunch is in addition to the above-mentioned value from visiting Botanical Beach.

2 This is based on an actual project but most of the data have been invented. It should not be interpreted as a factual accounting of the Pacific Marine Circle Route costs and benefits.

44

• The existing lunch demand schedule is illustrated in Figure 1. Also illustrated is the marginal cost curve for the restaurant and it’s current pricing strategy.

• Demand will expand to that illustrated in Figure 2 once the road project is complete. The restaurant owner will invest $500,000 in 2005 to expand the restaurant to accommodate the expected increase in customers but the marginal cost of providing lunch will remain unchanged.

• The existing Port Renfrew – Victoria road is narrow and winding. On average there is currently one death per year on the road. No changes will be made to this road. The value of a statistical life is $3m.

• The new Port Renfrew – Lake Cowichan road will pass through a working forest area. Cigarette butts cast from cars are expected to pose an annual fire risk of one fire for every one million tourists traveling on the road. Given the current capacity of the fire department in Lake Cowichan, an average fire would cost Timberwest $500,000 in lost timber export profits, and would cost the provincial government $100,000 in lost royalties on that timber.

• The fire department in Lake Cowichan has requested $75,000 in 2006 for new equipment to deal with the increased risk of fire due to the new road. They estimate that the new equipment would allow them to reduce the expected loss of timber in the event of a fire by 30%. This equipment would last forever.

• The Province of British Columbia is the referent group. • The provincial government faces a marginal cost of funds of 1.2. • The PSDR is 5%. • The value of a perpetuity is

rr

rrr+

=+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

45


Spring 2005

Final Exam Question 1: No Free Lunch (a) Show that current annual consumer surplus from lunch consumption is

250,56$0 =CS and that current annual profit for the Lighthouse Restaurant is

500,112$0 =π (b) Show that post-project annual consumer surplus from lunch consumption is

375,84$1 =CS and that post-project annual profit for the Lighthouse Restaurant is

750,168$1 =π (c) What is the annual welfare loss due to the restaurant monopoly in the post-project scenario? Question 2: Life is a Beach (a) Assume that the valuations of a Botanical Beach visit stated above are WTP measures. What is the

implicit property rights assumption underlying the use of these values in the CBA of the road project? (b) In view of your answer to part (a), would you use CV or EV to measure the change in welfare for

current visitors when the government raises the Botanical Beach visitor fee? Which of these welfare measures would you expect to be larger (in absolute value)? Explain your answer.

(c) What is the current total value of trips to Botanical Beach? What is the post-project total value of trips

to Botanical Beach? Question 3: Death on the Highway (a) What is the current rate of deaths per 1000 trips on the Victoria – Port Renfrew road? (Note that every

tourist who currently visits Port Renfrew must make two trips along the road: there and back). (b) What is the expected post-project number of deaths on the Victoria – Port Renfrew road? What is the

economic cost of these deaths? Question 4: Up In Smoke (a) If there is no additional investment in fire fighting equipment, what is the annual expected cost of fires

due to the new road?

46

(b) Should the province invest in the new equipment if the road is built? Explain your answer. Note: Regardless of your answer to this question, assume henceforth that the government does invest

in the new equipment in 2006 if the road is built. Question 5: Money for Nothing? (a) Construct a table of government financial outlays and receipts. Number your listed items consecutively

and then explain the calculation of each item. Use the following example as a guide (where the number of items listed is not necessarily correct):

Financial Outlays and Receipts (in $000s)

Year 1 Year 2+ Item Outlays

1 Road purchase 2500 2 3 4 Total outlays Receipts

5 6 7 8

Total receipts Net outlays

Item 1: Road purchase The government pays Timberwest $2.5m in 2005 (year 1).

(b) Explain the meaning of the “marginal cost of funds” and why it is greater than one. Support your

answer with an appropriate diagram. (c) Calculate the cost of funds in each year of the project.

47

Question 6: To Build or Not to Build? (a) Construct a table of economic benefits and costs. Number your listed items consecutively and then

explain the calculation of each item. Use the following example as a guide (where the number of items listed is not necessarily correct):

Economic Benefits and Costs (in $000s)

Year 1 Year 2+ Item Benefits

1 2 3 4 Total benefit Costs

5 Fire equipment 75 6 7 8

Total cost Net benefit

Item 5: Fire equipment Fire fighting equipment is acquired at a cost of $75,000

(b) Calculate the NPV of the project. (c) Calculate the benefit-cost ratio (BCR) for the project. Give two reasons why the BCR should not be

used as a project evaluation criterion. Question 7: A Road to Heaven or a Road to Hell? Construct a table of winners and losers in the referent group for each year of the project, based on the following groups:

• Tourists − Switchers − Non-switchers − New visitors

• Lighthouse Restaurant • Timberwest • Taxpayers

48

q

$

10

40

25

MC

0D

20 (000s)7.5

0MR

Figure 1

q

$

10

40

MC

1D

30 (000s)

Figure 2

49

Map of the Project Region

VICTORIA

PORTRENFREW

LAKECOWICHAN N

50


Spring 2005


Question 1 (a) Refer to Figure 1

562502

)7500(150 ==CS

112500)7500(150 ==π

(b) Refer to Figure 2. The monopoly pricing strategy is to equate MR with MC:

103ˆ840 =−q

which solves for 25ˆ =p and correspondingly, 25.11ˆ =q . Then

843752

)11250(151 ==CS

168750)11250(151 ==π (c) See Figure 3. The welfare loss (or “deadweight loss”) due to monopoly in the post-

project scenario is

843752

)11250(151 ==DWL

Question 2 (a) Tourists have no right to visit the beach. (b) EV. It is not possible to rank the magnitude of EV and CV without more information on preferences. (c) Current value to all tourists = 20,000(20) = 400,000

Current value to BC resident tourists = 0.5(400,000) = 200,000 Post-project value to all tourists = 10,000(20) + 10,000(40) + 10,000(30) = 900,000 Post-project value to BC resident tourists = 0.5(900,000) = 450,000

51

Question 3 (a) Currently there are 40,000 trips and one death per year. Thus, the death rate per 1000 trips is 0.025. (b) Post-project there will still be 40,000 trips per year, and hence one death per year on average. Only 50%

of these will BC residents. The cost of a death is $3m so the economic cost is $1.5m. Note that there is no change in this value relative to the base case. Thus, we need not consider highway deaths any further.

Question 4 (a) The risk of fire is one in one million trips and there will be 20,000 trips. Thus, the

expected number of fires is

02.01000000

20000=

The cost of a fire is at most 600,000 since lost exports represent a foregone inflow of wealth (Timberwest is a local company). Note that the 100,000 in lost royalties is included since Timberwest would have to export 600,000 worth of timber to make 500,000 in profit after paying the royalty. Why at most 600,000? The resources that would have been used to harvest the timber had it not been lost to fire would be saved. We know nothing about harvesting costs so we need to make an assumption. Assumption: harvesting costs are zero. Thus, the expected economic cost of fire is 0.02(600,000) = 12,000 per year.

(b) The expected present value of lost timber values if no equipment is purchased is

25200005.005.1120000 ==LTV

There is also a cost of funds (since royalties are foregone) which has a present value:

840005.005.1)100000)(02.0(2.00 ==COF

Thus, the expected present value of fire costs if no equipment is purchased is 26040084002520000 =+=PVC If the fire equipment is purchased then these costs will be reduced by 30%, which means a saving (or benefit) of 78120)(3.0 0 == PVCB In comparison, the cost of the equipment (inclusive of the cost of funds) is 90000)75000(2.1 ==C Since CB < , the equipment should not be purchased.

52

Question 5 (a)

Financial Outlays and Receipts (in $000s)

Year 1 Year 2 Year 3+ Item Outlays

1 Road purchase 2500 2 Road upgrade 3000 3 Fire equipment 75 Total outlays 5500 75 Receipts 4 Beach visitor fees 200 200 5 Foregone timber royalties - 1.4 - 1.4

Total receipts 198.6 198.6 Net outlays 5500 - 123.6 - 198.6

1. The government pays Timberwest $2.5 million in year 1 (2005). 2. The government must pay $3m for the road upgrade in year 1. 3. Fire equipment is purchased in year 2 for $75,000 4. Beach visitor fee receipts in the base case are 5(20000) = 100,000. Post-project

receipts are 10(30000) = 300,000. Thus, additional receipts equal 200,000. These additional receipts occur in year 2 and each year thereafter.

5. The probability of a fire is 0.02. The cost of a fire in terms of lost royalties is

0.7(100000) = 70,000, given that the new equipment is purchased. Thus, the expected loss in royalties is 0.02(70000) = 1400.

(b) See course notes. (c) The cost of funds Year 1: (0.2)5,500,000 = 1,100,000 Year 2: - (0.2)123,600 = - 24,720 Year 3+: - (0.2)198,600 = - 39,720

53

Question 6 (a)

Economic Benefits and Costs (in $000s)

Year 1 Year 2 Year 3+ Item Benefits

1 Beach visit values 250.00 250.00 2 Lunch consumer surplus 14.06 14.06 3 Lunch profit 56.25 56.25 4 Fees from non-residents 100.00 100.00

Total benefit 420.31 420.31 Costs

5 Road upgrade 3000.00 6 Logging road upgrade 1500.00 7 Restaurant expansion 500.00 8 Expected fire damage 8.40 8.40 9 Fire equipment 75.00

10 Cost of funds 1100.00 -24.72 -39.72 Total cost 6100.00 58.68 -31.32 Net benefit -6100.00 361.63 451.63

1. From question 2(c): change in total values for BC residents = $450,000 – $200,000 = $250,000. This accrues in year 2 and every year thereafter.

2. From question 1: change in consumer surplus from lunch = $28,125. Only 50% of this accrues to

BC residents. It accrues in year 2 and every year thereafter.

Note that agents may have derived surplus from eating lunch somewhere else had they not taken the trip but this is included as part of the opportunity cost of making the trip. Similarly, the demand curve for lunch at the Lighthouse reflects WTP for the restaurant lunch relative to the next best lunch alternative on the trip. See Figure 4. For example, for pre-project Port Renfrew visitors:

surplus] lunch restaurant520[011 +−=−VV if they eat lunch at the restaurant

]520[010 −=−VV if they do not eat lunch at the restaurant

3. From question 1: change in profit = $56,250. This accrues in year 2 and every year thereafter. 4. Current fees from non-residents = 5(10,000) = 50,000. Post-project fees from non-residents =

10(15,0000) = 150,000. Thus, the increased is $100,000. 5. Cost of the road upgrade = $3m.

54

6. The cost of the logging road upgrade = $1.5m. Note that $2.5 paid to Timberwest by the government is just a transfer.

7. The restaurant expansion cost = $500,000. Even though this expansion is not part of the project

itself, it is a direct impact of the project.

8. Given that new fire equipment is purchase, damage from a fire is 0.7(600,000) = 420,000. This occurs with probability 0.02. Thus, the expected cost (in year 2 and every thereafter) is $8,400.

9. The cost of the fire equipment in 2006 is $75,000

10. The cost of funds in each year as calculated in question 5(c).

(b) rr

rr

PVB 31.4201

131.420=

+

+

=

)1(32.31)68.58(6100

)1(

132.31

168.586100 2 rr

rr

rr

rPVC

+−

+=+

+

−+

+=

PVCPVBNPV −=

At 05.0=r : 886,846,2$=NPV

(c) PVCPVBBCR =

At 5%: 51.1=BCR See course notes for a discussion of the shortcomings of the BCR.

55

Question 7

Year 1 Year 2 Year 3+ npvBC Tourists

Non-switchers Increase in visit fees -25.00 -25.00 -25.00 -25.00 -500.00 Switchers Increase in visit values 100.00 100.00 Increase in visit fees -25.00 -25.00 75.00 75.00 1500.00 New visitors Visit values 150.00 150.00 Visit fees -50.00 -50.00 Lunch surplus 14.06 14.06 114.06 114.06 2281.20

Lighthouse Increased profits 56.25 56.25 Expansion cost -500.00 -500.00 56.25 56.25 625.00

Timberwest Road sale 2500.00 Upgrade cost -1500.00 Expected fire costs -7.00 -7.00 1000.00 -7.00 -7.00 860.00

Taxpayers From the financial analysis -5500.00 123.60 198.60 Cost of funds -1100.00 24.72 39.72 -6600.00 148.32 238.32 -1919.31

Total -6100.00 361.63 451.63 2846.89

56

q

$

10

40

25

MC

0D

20 (000s)7.5

0MR

0CS

0π

Figure 1

q

$

10

40

25

MC

1D

15 30 (000s)11.25

1MR

1CS

1π

Figure 2

57

q

$

10

40

25

MC

1D

15 30 (000s)11.25

1MR

DWL

22.5

Figure 3

Travelto Port Renfrew

Do Not Travelto Port Renfrew

Eat atLighthouse

Do Not Eat atLighthouse

≡0V value of next best alternative

11V

10V

Figure 4

58


Spring 2005

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 25% of your final grade on this course. Time allowed: 75 minutes. This examination paper has two pages. 1. (a) Using an appropriate diagram in },{ 21 xx space, illustrate and compare the EV and CV for a

price rise for an income-neutral good. Suppose the agent is deemed to have a right to the lower price. Which is the appropriate measure of welfare change?

(b) Consider a welfare-to-work training program which subsidizes education for welfare

recipients in order to improve their employment prospects. An analysis of the project found that within two years of completing training, 100% of the welfare recipients covered by the program had moved off welfare into employment. The government claimed that the project had therefore been a great success. Is this a valid claim?

(c) If there exist no Pareto improvements then social surplus must be maximized. True of false?

Explain your answer and provide an example. 2. (a) Suppose a departure tax is levied on passengers departing from the Port of Victoria. The

Government of Canada will collect the tax and distribute 50% of the revenue to the City of Victoria. The composition of passengers departing from the port is

Residents of Victoria: 10% Residents of British Columbia from outside Victoria: 30% Residents of Canada from outside British Columbia: 40% US tourists: 20%

How should the tax revenue be treated in the CBA if (i) the referent group is the City of Victoria? (ii) the referent group is British Columbia? (iii) the referent group is Canada?

(b) Use an appropriate diagram to illustrate the gain in social surplus associated with a shift

from the private optimum to the social optimum in the presence of a negative externality. (c) Explain how the problem of second best might mean that the surplus gain you have

illustrated in 2(b) above could overstate the true net benefit of correcting the externality. How can an over-estimation of this type be avoided?

59

3. (a) What is the role of CBA in the assessment of wealth redistribution policies? (b) Explain why moral hazard can lead to market outcomes in which agents cannot purchase

full insurance. Why is this a market failure? (c) What are the nine main steps of a cost-benefit analysis?

60


Spring 2005

Midterm Exam Answer Guide

1. (a) See Figure 1. EVCV = for income-neutral goods (due to the symmetry of the Slutsky

substitution matrix). Note that '11

~ xx = in the figure; this reflects the absence of an income effect. Since the agent is deemed to have a right to the lower price, CV is the appropriate measure (though in this case, EVCV = , so the choice between the two is immaterial).

(b) There are two problems with this claim. First, the success of the program must be judged

against the base case. In particular, how many welfare recipients would have moved off welfare even in the absence of the program? Second, even if the program is effective (when measured against the base case), “success” would require that the benefits outweigh the costs.

(c) False. Social surplus maximization means that there exist no potential Pareto

improvements. Pareto improvements may not exist even when social surplus is not maximized. For example, in the case of monopoly, social surplus is typically not maximized but any departure from the monopoly outcome will make the monopolist worse off and so cannot be a Pareto improvement.

x1

x2

x0

′x

~x

SE

CV

EV

Figure 1

61

2. (a) Let T denote the total tax collected. Then (i) Victoria residents pay T1.0 but Victoria gains T5.0 (from the Government of Canada).

The net benefit to Victoria is T4.0 . (ii) BC residents pay T)3.01.0( + but BC gains T5.0 . The net benefit to BC is T1.0 .

Within the referent group, there is a transfer of TT 15.0)3.0(5.0 = from non-Victoria residents of BC to Victoria.

(iii) The net benefit to Canada = inflow of wealth from US = T2.0 . Within the referent group, there is a net transfer of TT 3.0)1.04.03.0(5.0 =−+ from non-Victoria residents of Canada to Victoria.

These calculations are illustrated in Figures 2 – 4 (for scenarios (i) – (iii) respectively) for the case where 100=T .

(b) See Figure 5. (c) If other markets are distorted then the shift of resources out of the policy-targeted activity

(the shift from z to *z ) into another activity in a distorted market could cause a loss of surplus in that market. Thus, the shaded area in figure 5 could overstate the true net benefit of the policy. This over-estimation can be avoided if the policy is assessed in a general equilibrium framework, which would trace the flow of resources into other markets and examine the associated impacts in those markets.

z

$

MPCMPB MSB≡

$zz*

a

b

c

d

MSC

Figure 5

62

3. (a) The role of CBA is to identify and calculate the costs of redistribution (most importantly, through the distortionary effects of redistributive taxation), to assess the effectiveness of different redistribution policies and to identify least-cost ways of meeting redistribution goals.

(b) Moral hazard (asymmetry of information about actions) means that insurance contracts

cannot be made contingent on precautionary activity by the insured agent. This means that full insurance eliminates any incentive for the insured agent to take precautionary action, even when the first-best solution requires that some precautionary action be taken. Thus, the risk of loss is increased beyond the optimum when full insurance is offered. To reduce risk by eliciting precautionary action, the insurer must offer less than full insurance. However, a risk averse agent is always better off with (actuarially fair) full insurance. Thus, the market outcome provides a sub-optimal solution. It is in this sense that the market fails.

(c) See the lecture notes.

63

VICTORIA

$10

NET BENEFIT TO VICTORIA = $40

$5 + $15 + $20 + $10 = $50

FIGURE 2

VICTORIA

$10

NET BENEFIT TO BC = $10NET TRANSFER WITHIN BC TO VICTORIA = $15

BC

$30

$5 + $15 + $20 + $10 = $50

FIGURE 3

64

VICTORIA

$10

NET BENEFIT TO CANADA = $20NET TRANSFER WITHIN CANADA

TO VICTORIA = $30

CANADA

$20

$5 + $15 + $20 + $10 = $50

FIGURE 4

65


Fall 2003

Final Exam Answer all parts of each of the following six questions. All questions are of equal value. This examination accounts for 45% of your final grade on this course. Time allowed: 175 minutes. This examination paper has three pages. Introduction The Municipality of Oak Bay is considering an energy efficiency upgrade on its recreation centre. (Oak Bay is one of the municipalities that make up the Victoria urban area). The upgrade project has two distinct parts: (i) the replacement of incandescent lighting with more energy-efficient fluorescent lighting; and (ii) improved ceiling insulation. Thus, there are three different project options:

A: the lighting upgrade only B: the insulation upgrade only C: both the lighting and insulation upgrades

There are currently 100 incandescent lighting fixtures in the building. Switching to fluorescent lighting would cost $100 per fixture (including labour and materials). The total area of the ceiling to be insulated is 1000 2m , at a cost of $10 per square meter (including labour and materials). There is some chance that the building has asbestos in the existing insulation, and this would have to be removed through a special procedure before the new insulation could be installed. (Asbestos is fibrous material used commonly in the 1960s and 1970s but is now linked to lung disease). The removal costs would be $100 per square meter. Based on building practices used at the time of construction, engineering experts believe there is a 50% chance that asbestos will be found. If no asbestos is found then the building can remain open while the upgrades are done. If asbestos is found, the building would have to be closed to users for 10 days while the work is undertaken. On average, the recreation centre serves 500 users per day, each of whom pays $2 per visit. These users are all Oak Bay residents. Current yearly electricity usage in the building is 50,000 kWh (kilowatt hours) for lighting and 500,000 kWh for heating. The lighting upgrade is expected to reduce lighting usage by 50%, while the insulation upgrade is expected to reduce heating usage by 20%. The price of electricity is $0.05 per kWh, equal to the marginal cost of electricity production. Energy-efficiency projects may receive a provincial grant equal to 50% of upgrade costs. A project must reduce electricity usage by at least 50,000 kWh per year to qualify. (The costs associated with asbestos removal would not be covered). This subsidy program is motivated by concerns over environmental impacts from electricity generation, which are estimated to cost $0.005 per kWh to BC residents located near the generation facilities. This cost is not included in the aforementioned marginal cost of electricity production. These environmental costs are not incurred by Oak Bay residents.

66

The recreation building is scheduled to be demolished and replaced after sixteen more years of operation regardless of whether or not the energy-efficiency upgrades are undertaken. The replacement building has an estimated cost of $5m. The upgrades on the existing building would be completed within two weeks of commencement. Assume that the referent group is the Municipality of Oak Bay. Ignore any consideration of the cost of funds until Question 3. Question 1: The Insulation Upgrade (a) What is the economic benefit of the insulation upgrade? (b) Suppose no asbestos is found. What is the financial cost of the insulation upgrade to the municipal

government? Assuming there are no distortions in the labour or materials markets, what is the economic cost of the insulation upgrade?

(c) Suppose asbestos is found. What is the financial cost of the insulation upgrade to the municipal

government? Assuming there are no distortions in the labour or materials markets, what is the lower bound on the economic cost of the insulation upgrade? Explain why you can only calculate a lower bound. (Henceforth, use this lower bound as the actual cost).

(d) What is the expected financial cost of the insulation upgrade to the municipal government? What is the

expected economic cost? Question 2: The Lighting Upgrade (a) What is the economic benefit of the lighting upgrade? (b) Suppose the insulation upgrade is not undertaken. What is the financial cost of the lighting upgrade to

the municipal government? Assuming there are no distortions in the labour or materials markets, what is the economic cost of the lighting upgrade?

(c) Suppose the insulation upgrade is undertaken. What is the financial cost of the lighting upgrade to the

municipal government? Assuming there are no distortions in the labour or materials markets, what is the economic cost of the lighting upgrade?

Question 3: The Cost Funds Construct three different tables illustrating the expected financial receipts and outlays for the municipal government under the three different project options. Calculate the cost of funds in each case. Question 4: Net Present Value (a) Construct three different tables illustrating the expected benefits and costs under the three different

project options. (b) Assume a discount rate of 5%. What is the expected NPV of each option?

Hint: ∑ = − =16

2 1 38.10)05.1(

1t t

(c) Based on expected NPV, which option should the municipality choose? (d) Comment on the NPV of option C compared to the sum of the NPVs for options A & B. What role

does the grant – and the qualification rules in particular – play in this relationship?

67

Question 5: Dealing with Uncertainty Identify “best case” and “worst case” scenarios for project option C. Calculate the critical probability of finding asbestos at which the expected NPV of project C becomes negative. Question 6: The Province as Referent Group Now suppose that the province is the referent group. (a) For each project option, construct a table summarizing all financial outlays and receipts for government

(municipal and provincial combined). (b) For each project option, construct a table summarizing all costs and benefits of the project and calculate

the NPV. (c) Recall that the provincial grant program is motivated by concerns over environmental impacts. Does

the grant program make economic sense in the context of this particular upgrade project? Explain your answer with reference to a comparison of the NPVs from a provincial perspective versus the NPVs from a municipal perspective.

Question 7: An Alternative Grant Scheme Now consider an alternative grant scheme whereby the municipality is offered a payment of $0.005 for every kWh of electricity reduced. (a) Based on NPV, rank the options from the perspective of the municipality. Compare this ranking with

your answer to question 6(b) above. (b) Explain how and why this alternative grant scheme is superior to the original one.

68


Fall 2003


Question 1 (a) Reduction in electricity use for heating: 0.2 * 500,000 kWh = 100,000 kWh

Valued at its price (the relevant value to Oak Bay): 100,000 * $0.05 = $5000 in years 1 – 16 (b) Note that the electricity reduction is large enough to qualify for the grant. Thus, Financial cost = 0.5 * 10000 * $10 = $5000 in year 1

Economic cost = financial cost = $5000 in year 1 (c) Financial cost = $5000 + [1000 * $100] + [10 * 500 * $2] = $115,000 in year 1

The value of visits to users must be at least $2. Thus, this puts a lower bound on the cost of lost use. Assuming this lower bound as the cost: Economic cost = financial cost = $115,000 in year 1

(d) Expected financial cost = [0.5 * $5000] + [0.5 * $115,000] = $60,000 in year 1

Expected economic cost = expected financial cost = $60,000 in year 1 Question 2 (a) Reduction in electricity use for lighting: 0.5 * 50,000 kWh = 25,000 kWh

Valued at its price (the relevant value to Oak Bay): 25,000 * $0.05 = $1250 in years 1 – 16 (b) The lighting upgrade project alone is not large enough to qualify for the provincial grant. Thus,

Financial cost = 100 * $100 = $10000 in year 1 Economic cost = financial cost = $10000 in year 1

69

(c) If the insulation upgrade is also undertaken then the combined project qualifies for the provincial grant. Thus,

Financial cost = 0.5 * $10000 = $5000 in year 1 Economic cost = financial cost = $5000 in year 1

Question 3

Project A Year 1 Year 2+

Outlays Lighting upgrade 10000

Receipts Reduced electricity bill 1250 1250

Net outlays 8750 -1250

Cost of funds 1750 -250

Project B Year 1 Year 2+

Outlays Insulation upgrade 10000 Expected asbestos removal 50000Expected lost user revenue 5000

65000

Receipts Grant 5000Reduced electricity bill 5000 5000 10000 5000



70

Project C

Year 1 Year 2+ Outlays Insulation upgrade 10000Lighting upgrade 10000Expected asbestos removal 50000Expected lost user revenue 5000

75000

Receipts Grant 10000Reduced electricity bill 6250 6250

16250 6250


Cost of funds 11750 -1250 Question 4 (a)

Project A Year 1 Year 2+

Benefits Electricity savings 1250 1250

Costs Lighting upgrade 10000Cost of funds 1750 -250

11750 -250

Net benefits -10500 1500

NPV = -$10500 + 10.38 * $1500 = $5070

71

Project B

Year 1 Year 2+ Benefits Electricity savings 5000 5000

Costs Insulation upgrade 10000Expected asbestos removal 50000Expected loss of use 5000Grant -5000Cost of funds 11000 -1000

71000 -1000


NPV = -$66000 + 10.38 * $6000 = -$3720

Project C Year 1 Year 2+

Benefits Electricity savings (light) 1250 1250Electricity savings (heat) 5000 5000

6250 6250

Costs Lighting upgrade 10000Insulation upgrade 10000Expected asbestos removal 50000Expected loss of use 5000Grant -10000Cost of funds 11750 -1250

76750 -1250

Net benefits -70500 7500 NPV = -$70500 + 10.38 * $7500 = $7350

72

(c) Based on expected NPV alone, the municipality would choose option C. (d) 7350$=CNPV . In comparison, 1350$=+ BA NPVNPV . These projects are fundamentally

independent, so the sum of their NPVs taken individually should equal the NPV of the combination project. A distortion arises here because of the qualification rules for the grant. These rules make option B more valuable when taken in combination with option A because it allows qualification for the grant. The saving for the municipality from accessing the grant on the lighting upgrade is $5000 (50% of the upgrade cost) plus the associated cost of funds, for a total saving of $6000. This accounts for the difference between CNPV and BA NPVNPV + .

Question 5

Project C: Best Case Scenario Year 1 Year 2+

Outlays & Receipts Outlays Insulation upgrade 10000Lighting upgrade 10000

20000


16250 6250



Benefits & Costs Benefits Electricity savings (light) 1250 1250Electricity savings (heat) 5000 5000

6250 6250

Costs Lighting upgrade 10000Insulation upgrade 10000Grant -10000Cost of funds 750 -1250

10750 -1250


BESTNPV = -$4500 + 10.38 * $7500 = $73350

73

Project C: Worst Case Scenario

Year 1 Year 2+ Outlays & Receipts Outlays Insulation upgrade 10000Lighting upgrade 10000Asbestos removal 100000Lost user revenue 10000

130000


16250 6250



Benefits & Costs Benefits Electricity savings (light) 1250 1250Electricity savings (heat) 5000 5000

6250 6250

Costs Lighting upgrade 10000Insulation upgrade 10000Asbestos removal 100000Loss of use 10000Grant -10000Cost of funds 22750 -1250

142750 -1250


WORSTNPV = -$136500 + 10.38 * $7500 = - $58650 The threshold probability is given by π such that:

0NPV)1(NPV BESTWORST =−+ ππ Solution: 56.0ˆ =π

74

Question 6 (a) & (b)

Project A: The Province as Referent Group Year 1 Year 2+

Outlays & Receipts Outlays Lighting upgrade 10000




Benefits & Costs Benefits Electricity savings (light) 1250 1250 Reduced environmental damage 125 125

1375 1375

Costs Lighting upgrade 10000 Cost of funds 1750 -250

11750 -250


NPV = -$10375 + 10.38 * $1625 = $6493

75

Project B: The Province as Referent Group

Year 1 Year 2+ Outlays & Receipts Outlays Insulation upgrade 10000 Expected asbestos removal 50000 Expected lost user revenue 5000

65000




Benefits & Costs Benefits Electricity savings (heat) 5000 5000 Reduced environmental damage 500 500

5500 5500

Costs Insulation upgrade 10000 Expected asbestos removal 50000 Expected loss of use 5000 Cost of funds 12000 -1000

77000 -1000


NPV = -$71500 + 10.38 * $6500 = - $4030

76

Project C: The Province as Referent Group

Year 1 Year 2+ Outlays & Receipts Outlays Insulation upgrade 10000 Lighting upgrade 10000 Expected asbestos removal 50000 Expected lost user revenue 5000

75000




Benefits & Costs Benefits Electricity savings (light) 1250 1250 Electricity savings (heat) 5000 5000 Reduced environmental damage 625 625

6875 6875

Costs Lighting upgrade 10000 Insulation upgrade 10000 Expected asbestos removal 50000 Expected loss of use 5000 Cost of funds 13750 -1250

88750 -1250


NPV = -$81875 + 10.38 * $8125 = $2463

Note that BAC NPVNPVNPV += . (c) The grant makes some rough economic sense. The municipality has no incentive to take account of the

external benefits associated with reducing its electricity use; namely, the reduction in environmental impacts that occur outside the municipal referent group. Thus, there is a role for policy to correct for the externality in some way. However, the grant is a badly designed incentive scheme, for two reasons. First, the qualification rules are distorting. In particular, the rules induce the municipality to pursue option C, even though option A is best from the perspective of the province, because this allows the municipality to meet the grant threshold. Second, the grant is tied to upgrade costs but the externality is related to electricity use. This means that a grant scheme based on the external costs avoided would be better; see the answer to Question 7.

77

Question 7 (a)

Project A: Alternative Grant Scheme Year 1 Year 2+

Outlays & Receipts Outlays Lighting upgrade 10000

Receipts Grant 125 125 Reduced electricity bill 1250 1250

1375 1375



Benefits & Costs Benefits Electricity savings (light) 1250 1250

Costs Lighting upgrade 10000 Grant -125 -125 Cost of funds 1725 -275

11600 -400


NPV = -$10350 + 10.38 * $1650 = $6777

78

Project B: Alternative Grant Scheme

Year 1 Year 2+ Outlays & Receipts Outlays Insulation upgrade 10000 Expected asbestos removal 50000 Expected lost user revenue 5000

65000

Receipts Reduced electricity bill 5000 5000 Grant 500 500

5500 5500



Benefits & Costs Benefits Electricity savings (heat) 5000 5000

Costs Insulation upgrade 10000 Expected asbestos removal 50000 Expected loss of use 5000 Grant -500 -500 Cost of funds 11900 -1100

76400 -1600


NPV = -$71400 + 10.38 * $6600 = -$2892

79

Project C: Alternative Grant Scheme

Year 1 Year 2+ Outlays & Receipts Outlays Insulation upgrade 10000 Lighting upgrade 10000 Expected asbestos removal 50000 Expected lost user revenue 5000

75000

Receipts Reduced electricity bill 6250 6250 Grant 625 625

6875 6875



Benefits & Costs Benefits Electricity savings (light) 1250 1250 Electricity savings (heat) 5000 5000

6250 6250

Costs Lighting upgrade 10000 Insulation upgrade 10000 Expected asbestos removal 50000 Expected loss of use 5000 Grant -625 -625 Cost of funds 13625 -1375

88000 -2000


NPV = -$81750 + 10.38 * $8250 = $3885

The ranking of projects is now the same as that when the province is the referent group. Note also that

BAC NPVNPVNPV += , as expected for independent projects. (b) The alternative grant scheme is superior because it yields the correct ranking of projects from a

provincial perspective. Its superiority stems from the fact that the grant is based on the actual externality; it works as a Pigouvian subsidy. (Moreover, it does not have a threshold qualification rule). Note however, that the actual NPVs under this scheme are different from those under the provincial perspective. The difference is due to the cost of funds, which is lower for the municipality because of the grant. Thus, the municipality receives a greater benefit from the grant (when the effect on the cost of funds is included) than the true externality warrants. This difference could in principle be enough to distort the decisions; that is, subsidized projects may make sense from the perspective of the

80

municipality even if they yield a negative NPV for the province as a whole. The true optimal subsidy should ideally adjust for the cost of funds distortion.

81


Fall 2003

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 25% of your final grade on this course. Time allowed: 75 minutes. This examination paper has 1 page1. 1. (a) What are the nine main steps of a CBA? (b) Consider a seismic upgrade project for local schools (a seismic upgrade project involves the

reinforcement of buildings to improve their ability to withstand an earthquake). How would you specify the base case in this situation?

(c) What is the “potential Pareto improvement” criterion and how does it relate to the notion of

maximizing social surplus? Does social surplus maximization maximize social welfare? Explain your answer.

2. (a) Why is there often a conflict between efficiency and equity in public policy? (b) Use an appropriate diagram to illustrate how privately optimal levels of basic education are

likely to be sub-optimal from a social perspective. Why might a subsidy for basic education be an appropriate policy response?

(c) Explain the meaning of “adverse selection” and explain why it may lead to inefficiency in

unregulated market outcomes. 3. (a) Using an appropriate diagram(s), illustrate and compare the EV, CV and CSΔ for a price

rise for an inferior good. Which is the appropriate measure of welfare change? (b) Why might the social opportunity cost of labour be negative? (c) A proposed job-training project is designed to provide BC welfare recipients with

marketable skills. Training will cost $1000 per person and the program will cover 100 people currently on welfare. It is expected that the project will successfully move 60% of the trainees off welfare into an undistorted labour market, where they will earn $10 per hour. The BC government will save $10,000 per year in welfare payments for the successful trainees. Identify the costs and benefits of the project.

82


Fall 2002

Final Exam Answer all parts of each of the following five questions. All questions are of equal value. This examination accounts for 45% of your final grade on this course. Time allowed: 175 minutes. This examination paper has five pages. Introduction The Government of Canada is considering constructing a lighthouse on a reef at the entrance to Portville harbour. (“Portville” is a fictional coastal city). A large number of ships currently enter the harbour each year to use the port facilities. On average, five ships per thousand run aground on the reef. Construction of the lighthouse is expected to reduce that number to one per thousand. Significant costs are incurred when a ship runs aground. The ship owners incur the cost of ship damage, cargo losses, time costs, etc. The Government of Canada incurs the cost of rescue services. Often there are also environmental costs (from fuel leakage and dumping to lighten the load) associated with a grounding. On average, rescue costs are estimated to be $0.5m per grounding. In addition, it costs $5m per year to maintain the rescue service regardless of how many groundings there are. On average, environmental costs are estimated to be $1.5m per grounding; of this total, $0.5m is for clean-up services (incurred by the Government of Canada) and $1m is environmental damage (a non-financial cost). The Portville Port Authority (wholly owned by the Government of Canada) regulates shipping in the harbour and currently charges $10,000 per ship for use of the port facilities. The Port Authority will raise the port facility fee to $15,000 per ship once the lighthouse is installed. Any revenue earned by the Port Authority is returned to the Government and added to general revenue. The estimated current demand for use of port facilities is illustrated as 0D in Figure 1. The increased

safety associated with the lighthouse installation is expected to shift that demand to 1D in Figure 1. (This shift in demand reflects the expected cost savings to ship owners from fewer groundings). On average, 75% of the ships entering the harbour are foreign-owned, and this is not expected to change. Construction of the lighthouse will take one year and cost $50m. Once completed, it is expected to last forever. Annual operation and maintenance costs are estimated to be $0.5m per year. These costs will be incurred every year following the construction year. These costs will be financed by the Government. The estimated marginal cost of funds for Canada is 1.2. Canada is the referent group for the cost-benefit analysis. In your answers, delay any consideration of the cost of funds until Question 4.

83

Question 1: Market Failure (a) The lighthouse is a public good. Explain what this means, and why public goods tend to be under-

provided in the absence of government intervention. (b) Briefly discuss one other type of “market failure” that can justify government intervention on efficiency

grounds, and provide a real world example. (c) In general, why is there often a conflict between government’s efficiency goals and its distributional

goals? Question 2: Consumer Surplus (a) What is the gain in consumer surplus for ship owners from the project? Estimate the consumer surplus

gain to foreign ship owners and the consumer surplus gain to domestic ship owners. (b) The shift in demand reflects a reduction in the expected cost of using Portville Harbour, due to the

lower probability of a grounding. From the information contained in Figure 1, it is therefore possible to calculate the cost (on average) to ship owners from a grounding. What is that cost?

(c) Should the CBA include the values from (a) and (b)? Explain your answer. Question 3: Rescue and Environmental Costs Avoided (a) What is the expected number of groundings avoided per year due to the project? (b) What is the expected value of rescue costs avoided? How should the fixed costs of maintaining the

rescue service be treated in the CBA? (c) What is the expected value of environmental costs avoided? Question 4: Government Finances and the Cost of Funds (a) How should the change in revenue from port facility fees be treated in the CBA? (b) Explain what is meant by “the marginal cost of funds is 1.2”. (c) Construct a table like the one below that summarizes the financial costs to the referent government.

(The number of rows in the sample table is not necessarily correct).

$m year 1 year 2 (+)Outlays

Total outlays Receipts

Total receipts

Net outlay

84

(d) Calculate the cost of funds in year 1 and year 2 (+). Question 5: Net Present Value (a) Summarize all costs and benefits in a table like the one below. (The number of rows in the sample table

is not necessarily correct).

$m year 1 year 2(+)Benefits

Total benefits

Costs

Total costs

Net benefits (b) Calculate the NPV. Assume the PSDR is 10%.

Hint: r

rrrr

+=⎥

⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

(c) How would your answer to (b) be different if we took a global perspective?

85

$

ships per year2700

0D

2000

10,000

1D

15,000

1000 1200

Figure 1

86


Fall 2002


Question 1: Market Failure See Course Notes Question 2: Consumer Surplus (a) Consider Figure 1A. The gain in consumer surplus is area [A+B] – [B+C] = [A – C].

That is, CSΔ = 7.2m – 5m = 2.2m

The gain to foreign ship owners is 0.75*2.2m = 1.65m; the gain to domestic ship owners is 0.25*2.2m = 0.55m

(b) See Figure 1A. Ship owners are now willing to pay $7000 more per visit. That is,

they are WTP $7000 for a reduction in the risk of a grounding by 4 one-thousandths. The implied expected cost of a grounding (assuming risk neutrality) is

75.1

10004

7000=

⎥⎦⎤

⎢⎣⎡

m

(c) No. There are two equivalent but mutually exclusive ways to include the net gain to the ship owners

(both weighted by the domestic ownership share): the change in CS = 2.2m; or

[the reduction in expected total grounding costs to existing users] – [fee increases for existing users] +

[net benefit to new users3] = [(5 – 1)*1.75m] – [(15000 – 10000)*1000] + [2000*200* ½] = 2.2m

Including both items would double-count the benefits. Question 3: Rescue and Environmental Costs Avoided (a) Pre-project groundings: (5/1000)*1000 = 5; post-project groundings: (1/1000)*1200 =

1.2. Thus, there will be (on average), 3.8 fewer groundings per year (year 2 +). (b) Expected rescue costs avoided per year (year 2 +): 3.8*0.5m = 1.9m. The fixed costs

are irrelevant since are incurred in the base case and under the project.

3 The net benefit to new users is the shaded area in Figure 1A.

87

(c) Expected clean-up costs avoided per year (year 2 +): 3.8*0.5m = $1.9m; expected environmental damage avoided per year (beginning in year 2): 3.8*1m = $3.8m.

Question 4: Government Finances and the Cost of Funds (a) The change in port fee revenue is (15,000*1200) – (10,000*1000) = $8m per year (beginning in year 2)

This change in revenue enters as an economic benefit (captured by taxpayers). a receipt for government (for the calculation of the cost of funds).

(b) See course notes. (c)

$m year 1 year 2 (+)Outlays Construction 50.00Operation & Maintenance 0.50Total outlays 50.00 0.50 Receipts Port fees 8.00Rescues avoided 1.90Clean-up avoided 1.90Total receipts 0.0 11.80

Net outlay 50.00 -11.3 (d) The cost of funds in year 1:

0.2*$50m = $10m

The cost of funds in year 2(+): - 0.2*$11.3 = $2.26

88

Question 5: Net Present Value (a)

Canadian Perspective $m year 1 year 2(+)Benefits Domestic consumer surplus 0.55Foreign consumer surplus Port fees 8.00Rescue costs avoided 1.90Clean-up costs avoided 1.90Environmental damage avoided 3.80Total benefits 0.0 16.15

Costs Construction 50.00Operation & maintenance 0.50Cost of funds 10.00 -2.26Total costs 60.00 -1.76

Net benefits -60.00 17.91

(b) rr

r

NPV+

⎥⎦⎤

⎢⎣⎡ +

+−=1

191.1760

At 10%: NPV = $119.1m

(c) Differences from the Canadian referent group case are highlighted in grey:

Global Perspective $m year 1 year 2(+)Benefits Domestic consumer surplus 0.55Foreign consumer surplus 1.65Port fees 8.00Rescue costs avoided 1.90Clean-up costs avoided 1.90Environmental damage avoided 3.80Total benefits 0.0 17.80

Costs Construction 50.00Operation & maintenance 0.50Cost of funds 10.00 -2.26Total costs 60.00 -1.76

Net benefits -60.00 19.56

89

rr

r

NPV+

⎥⎦⎤

⎢⎣⎡ +

+−=1

156.1960

At 10%: NPV = $135.6m

$

ships per year2700

0D

2000

10,000

1D

15,000

1000 1200

27,000

20,000

Figure 1A

90


Fall 2002

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 25% of your final grade on this course. Time allowed: 75 minutes. This examination paper has 2 pages. 1. (a) What are the nine main steps of a CBA? (b) Explain why the base case for a CBA is not necessarily the status quo. Support your

answer with an example. (c) What is the “potential Pareto improvement” criterion and how does it relate to the notion of


2. (a) Suppose an airport improvement levy of $5 is to be imposed on all travelers using Victoria

airport. The government of British Columbia will collect the tax. There are expected to be 1,000,000 travelers using the airport annually, with the following composition:

Residents of British Columbia: 60% Non-British Columbian Canadians: 20% Foreign tourists: 20%

How should the tax revenue be treated in the CBA if (i) the referent group is British Columbia? (ii) the referent group is Canada?

(b) Explain why the cost of air pollution, as measured by WTA, is likely to be lower in a poor

country than in a wealthy country. How would justify the use of such cost numbers in CBA when faced with accusations from critics that the basic methodology is inequitable?

(c) Using appropriate diagrams, illustrate and compare the EV, CV and CSΔ for a price fall for

an inferior good. Which is the appropriate measure of welfare change if the affected agents are deemed to have a right to the lower price?

91


Fall 2001

Final Exam Answer all parts of each of the following six questions. All questions are of equal value. This examination accounts for 45% of your final grade on this course. Time allowed: 175 minutes. This examination paper has five pages. Introduction The Province of British Columbia is considering building an irrigation project. The proposed project involves flooding a valley by constructing a dam on the Piper River. The new reservoir would supply irrigation water to fruit growers downstream from the dam. The discharge of water would also be used to generate electricity. The project will destroy the recreational fishing on the downstream river and will flood existing grazing land upstream from the dam. The local town draws its water from an existing lake on the river and the project will degrade that water; a filtration system will be built to restore the water quality. Details of the project are as follows: Construction will take place in year 1. Non-labour construction costs are expected to be $22m, of

which $12m will be spent to import rock fill from the United States. The project will require 100 workers for 2000 hours each during construction. These workers will be

drawn from the local area, where they are currently unemployed. Their current activities are estimated to have no social value. The workers will be paid $10 per hour. During the year in which they are employed by the project they will loose $10,000 in unemployment benefits (currently paid by the Provincial government) and will have to pay 10% of their earnings in Federal income taxes.

The project will begin providing irrigation benefits in year 2; these will continue forever. The

irrigation services will boost the productivity of the fruit growers, shifting their aggregate supply curve from 0S to 1S in Figure 1. Price will fall from $200 per tonne to $180 per tonne. Annual production will rise from 100,000 tonnes per year to 120,000 tonnes per year.

The project will generate 3000 MWh (megawatt-hours) of electricity every year, beginning in year 2.

This electricity will be sold to BC Hydro (the provincial electricity utility) at the prevailing (competitive) market price of $100 per MWh. BC Hydro will then export twenty percent of this electricity to the United States (at $100 per MWh).

Based on travel cost studies conducted elsewhere, the value of the existing recreational fishing is

estimated to be $500,000 per year. Twenty percent of this value accrues to tourists from the United States. The fishing will be permanently lost, beginning in year 2.

The grazing land to be flooded is owned by the Province and is currently leased to a private firm for

$200,000 per year. This land will be permanently flooded in year 2 and the lease will be cancelled. The water filtration plant will be built in year 1 by a local private firm. The estimated cost of

construction is $1m. There are no ongoing operating costs. The plant will be leased back to the government for $100,000 per year in perpetuity, beginning year 2.

The Federal government will contribute an infrastructure grant of $5m in year 1.

92

The marginal cost funds is 1.2.

The Province of British Columbia is the referent group.

In your answers, delay any consideration of the cost of funds until Question 5. Question 1: Construction Costs (a) What is the economic cost of labour (inclusive of any tax outflows). Explain your answer. (Hint:

remember to measure cost relative to the base case). (b) What is the financial cost of labour (to the referent government)? (c) What is the economic cost of non-labour construction? How would your answer be different if the rock

fill was purchased in British Columbia (at the same price)? Explain your answer. Question 2: Consumer and Producer Surplus (a) What is the change in producer surplus for fruit farmers? (b) What is the change in consumer surplus for fruit buyers? (c) If instead we used compensating variation to measure the welfare change for consumers, would it be

greater or smaller than the change in consumer surplus? Explain your answer. Question 3: Electricity and Fishing (a) What is the economic benefit of the electricity generation? How would your answer be different if all

the electricity was exported to the United States? (b) What is the economic cost of the lost recreational fishing? Does it matter that some of the fishers are

tourists from the United States? (c) Briefly outline the main steps of a travel cost study? How useful is the travel cost method for

measuring passive use values? Question 4: Grazing Land and Water Quality (a) Explain why you do not have enough information to determine the true economic cost of the lost

grazing land. What is the lower bound on this cost? (For the remainder of the analysis assume this lower bound is the true cost).

(b) What is the economic cost of the filtration plant? Explain your answer. (c) Explain how you would conduct a referendum format contingent valuation study to determine whether

or not construction of the filtration system makes economic sense. Question 5: The Cost of Funds (a) Explain why the marginal cost of funds is greater than one. (b) Construct a table like the one below that summarizes the financial costs to the referent government.

(The number of rows in the sample table is not necessarily correct).

93

$m year 1 year 2 (+)Outlays

Total outlays Receipts

Total receipts

Net outlay (c) Calculate the cost of funds in year 1 and year 2 (+). Question 6: Net Present Value (a) Summarize all costs and benefits in a table like the one below. (The number of rows in the sample table

is not necessarily correct).

$m year 1 year 2(+)Benefits

Total benefits

Costs

Total costs

Net benefits (b) Calculate the NPV. Assume the PSDR is 10%.

Hint: r

rrrr

+=⎥

⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

(c) Based on NPV, should the project proceed? How would your answer be different if we took a national

perspective?

94

$

FIGURE 1

tonnes120,000

200

0S 1S

100,000

180

300

95


Fall 2001


Question 1: Construction Costs (a) Economic cost is the opportunity cost of resources used within the referent group plus any net outflow

of wealth. Opportunity cost is $0. The net outflow of wealth in Federal taxes is $2000 per worker. Thus: 100*$2000=$200,000.

(b) Financial cost = wages paid - unemployment payments saved = $(2 – 1)m = $1m. (c) Economic cost is $22m. It would make no difference unless the market in BC is distorted such that

price does not reflect true social cost. Question 2: Consumer and Producer Surplus (a) mmmPS 8.0108.10 =−=Δ . See Figure A1-1: ABPS −=Δ (b) mmmCS 2.252.7 =−=Δ . See Figure A1-2: CCS =Δ (c) It depends on whether fruit is a normal good. If it is normal for all consumers, then CSCV Δ< . The

converse is true if fruit is inferior for all consumers. If it is normal for some consumers and inferior for others then we cannot rank aggregate CV and aggregate .CSΔ

Question 3: Electricity and Fishing (a) Economic benefit: 3000*$100 = $300,000 per year. It is irrelevant how much is exported to the US. (b) The economic cost to the referent group is $400,000 per year. The losses incurred by US tourists are

not counted as costs. They would be included if a global perspective was taken for the analysis. (c) See notes. Question 4: Grazing Land and Water Quality (a) The leaseholder is willing to pay $200,000 per year, so the value of the grazing land must be worth at

least that much. Thus, $200,000 is a lower bound on cost. We would need information on the leaseholder’s revenues to determine the true producer surplus foregone.

(b) Economic cost is $1m (assuming an undistorted market for construction). The financial cost to the

government is $100,000 per year forever. (c) See notes. Note that a CVM would measure typically measure WTP. If it is deemed by the referent

government that the town has a right to the existing water quality, then WTA would be the correct measure of cost. If aggregate WTP (or aggregate WTA) is less than $1m then the filtration system should not be built.

96

Question 5: The Cost of Funds (a) See notes. (b)

$m year 1 year 2 (+)Outlays Construction

non-labour 22.0labour 1.0

Foregone grazing lease 0.2Filtration plant lease 0.1Total outlays 23.0 0.3 Receipts Federal grant 5.0Electricity sales 0.3Total receipts 5.0 0.3

Net outlay 18.0 0 (c) Cost of funds in each year is $0.2*net outlay. Question 6: Net Present Value (a)

$m year 1 year 2(+)Benefits Producer surplus 0.8Consumer surplus 2.2Electricity production** 0.1Federal grant 5.0Total benefits 5.0 3.1

Costs Construction

labour 0.2non-labour 22.0

Foregone recreation 0.4Foregone grazing land 0.2Filtration plant 1.0Cost of funds 3.6Total costs 26.80 0.60

Net benefits -21.8 2.5 ** This should be 0.3 (as in Q3(a) above). (b)

2.35.28.211

15.28.21 =+−=

+

⎟⎠⎞

⎜⎝⎛ +

+−=rr

rr

NPV

97

(c) Proceed, since 0>NPV . From a national perspective, the Federal grant and Federal taxes are

transfers. The new tables are:

$m year 1 year 2 (+)Outlays Construction

non-labour 22.0Labour** 0.0

Foregone grazing lease

0.2

Filtration plant lease 0.1Total outlays 22.0 0.3 Receipts Federal grant Electricity sales 0.3Total receipts 0.0 0.3

Net outlay 22.0 0 ** This should be 1.0 (as in Q5 above)

$m year 1 year 2(+)Benefits Producer surplus 0.8Consumer surplus 2.2Electricity production 0.1Federal grant Total benefits 0.0 3.1

Costs Construction

labour 0.0non-labour 22.0

Foregone recreation 0.4Foregone grazing land 0.2Filtration plant 1.0Cost of funds 4.4Total costs 27.40 0.60

Net benefits -27.4 2.5 The revised NPV is:

4.25.24.271

15.24.27 −=+−=

+

⎟⎠⎞

⎜⎝⎛ +

+−=rr

rr

NPV

98

$

tonnes120,000

200

0S 1S

100,000

180

300

A

B

Figure A1-1

99

$

tonnes120,000

200

0S 1S

100,000

180

300

C

Figure A1-2

100


Fall 2001

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 25% of your final grade on this course. Time allowed: 75 minutes. This examination paper has 2 pages. 1. (a) What are the nine main steps of a CBA? (b) A local city government is considering building a waste-water treatment plant, with an

expected life of 20 years. On average, each city resident produces 7000 litres of waste-water per year. Explain how you would specify the base case for the volume of wastewater.

(c) What is the “potential Pareto improvement” criterion and how does it relate to the notion of


2. (a) A tax of $10 per guest per night is to be imposed on all British Columbia hotel

accommodation. The government of British Columbia will collect the tax. There are expected to be 2,000,000 guest-nights per year, with the following guest composition:


How should the tax revenue be treated in the CBA if (i) the referent group is British Columbia? (ii) the referent group is Canada?

(b) Explain why there can be a conflict between efficiency and distributional goals in

government policy. Provide an example to illustrate your answer. What is the role of CBA in assessing alternative redistribution policies?

(c) Using appropriate diagrams, illustrate and compare the EV, CV and CSΔ for a price rise

for a normal good. Which is the appropriate measure of welfare change if the affected agents are deemed to have a right to the existing price?

101

3. (a) Explain the term “adverse selection”, and explain why it can cause market failure. Provide an example to support your answer.

(b) Using an appropriate diagram, illustrate the effect of a negative externality associated with

some activity z. On your diagram, illustrate the private optimum, the “social optimum”, and the surplus changes that would accrue to winners and losers if a policy measure forced a switch – without compensation – from the private optimum to the “social optimum”. Is the “social optimum” unique?

(c) Explain the “problem of second best”. Is the problem of second best necessarily an

obstacle to conducting policy analysis in a partial equilibrium framework? Explain your answer.

102


Fall 2000

Final Exam Answer all parts of each of the following five questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. This examination paper has four pages. Introduction The City of Trashville is facing a garbage crisis. At current usage levels, its existing landfill will have reached capacity after 2 more years. At that time the City will have to switch to an incineration facility. It is currently considering an aggressive curbside recycling program that would divert some waste away from garbage collection; this would extend the life of the existing landfill. Your task is to perform a cost-benefit analysis on the recycling program, in terms of whether or not it should be introduced, and if so, when. You are not required to undertake a distributional analysis nor any sensitivity testing. The City is the referent group. Assume a discount rate of 5%. The City has provided you with the following information about waste volumes and financial costs: • 10,000 tons of garbage are currently sent to the landfill each year. That number is expected to remain

unchanged unless a recycling program is introduced. • the remaining capacity of the existing landfill is 20,000 tons. • garbage is collected and transported to the landfill at a cost of $20 per ton. • there is a fixed cost of $500,000 per year to operate the landfill (independent of how much garbage is

dumped) • closure of the landfill will require a one-time decommissioning cost of $1m incurred in the final year

of operation. • installation of the incinerator will cost $10m in the year prior to its first year of operation; the province

will pay 50% of this cost. • operating costs for the incinerator are $40 per ton. • the incinerator is expected to last forever. • the cost of garbage collection and transportation to the incineration site is expected to be $30 per ton. • the recycling program is expected to reduce the amount of garbage collected by 50%; thus, there will

be 5,000 tons of garbage and 5,000 tons of recyclables collected. • the recycling program will require a one-time cost of $500,000 in the first year of operation (for the

provision of collection boxes and instructions to households). • collection costs for the recycling program will be $25 per ton of recyclable material. • the recyclable material collected will be sold on the market for $5 per ton. There is no reason to believe that any of the markets relating to the above costs are distorted. You also have the following additional information: • incineration causes local air pollution, the estimated social cost of which is $10 per ton of garbage

incinerated. • construction of the landfill 10 years ago destroyed a lake, the foregone recreational value of which has

been estimated at $10,000 per year. • time costs for households for sorting and preparing recyclable material is estimated to be $20 per ton

of recycling material. • the marginal cost of funds is 1.2

103

Questions 1. Begin by examining waste management costs in the absence of the recycling program. (a) Prepare a table of costs organized in the following way (explain any calculations used to obtain the table

entries): Costs: No Recycling

year 1 year 2 year 3 year 4 year 5+1. Landfill Related Costs (a) (b) etc. 2. Incineration Related Costs (a) (b) etc. 3. Cost of Funds

Total (b) Calculate the present value of waste management costs in the absence of the recycling program. (See

Calculation Hints on page 4). (c) Explain the meaning of the “marginal cost of funds”. 2. Examine waste management costs under a recycling program introduced in year 1. (a) Prepare a table of costs organized in the following way (explain any calculations used to obtain the table

entries): Costs: Recycling

year 1 year 2 year 3 year 4 year 5+1. Landfill Related Costs (a) (b) etc. 2. Recycling Related Costs (a) (b) etc. 3. Incineration Related Costs (a) (b) etc. 4. Cost of Funds Total

104

(b) Calculate the present value of waste management costs under a recycling program introduced in year 1. (See Calculation Hints on page 4).

(c) Briefly describe how the averting behaviour method could be used to estimate the costs of pollution

associated with incineration. 3. The NPV of the recycling program is the difference in the present value of waste management costs with

and without the program. (a) Based on NPV, should the recycling program be introduced in year 1? Explain your answer. [Hint: this

is not a trivial question]. (b) Would your answer to part (a) change if the Province is taken as the referent group? 4. (a) Explain why the presence of taxes and other capital market imperfections make it difficult to define

the public sector discount rate.

(b) In general, why is the NPV rule better than the BCR rule? 5. There are costs imposed on residents living by the landfill and incinerator that have not been included in

the analysis. Outline how you would conduct an hedonic house price study to determine these costs. Calculation Hints

952.005.11

=

907.0)05.1(

12 =

864.0)05.1(

13 =

823.0)05.1(

14 =

2005.01

=

rr

rrr+

=⎥⎦

⎤⎢⎣

⎡+

+++

++

+ ∞

1)1(

1........ )1(

1)1(

11 2

105


Fall 2000


Base Case: No Recycling

year 1 year 2 year 3 year 4 year 5+ PVCLandfill Related Costs Collection Costs 0.20 0.20 Operating Costs 0.50 0.50 Closure 1.00 Cost of Funds 0.14 0.34

Incineration Related Costs Collection Costs 0.30 0.30 0.30Operating Costs 0.40 0.40 0.40Installation 5.00 Cost of Funds 1.00 0.14 0.14 0.14

Pollution Costs 0.10 0.10 0.10

Total 0.84 8.04 0.94 0.94 0.94 26.40

106

Recycling: Introduction Year 1

year 1 year 2 year 3 year 4 year 5+ PVCLandfill Related Costs Collection Costs 0.10 0.10 0.10 0.10 Operating Costs 0.50 0.50 0.50 0.50 Closure 1.00 Cost of Funds 0.12 0.12 0.12 0.32

Recycling Related Costs Set-Up Costs 0.50 Net Collection Costs 0.10 0.10 0.10 0.10 0.10Cost of Funds 0.12 0.02 0.02 0.02 0.02

Household Sorting Costs 0.10 0.10 0.10 0.10 0.10

Incineration Related Costs Collection Costs 0.15Operating Costs 0.20Installation 5.00 Cost of Funds 1.00 0.07

Pollution Costs 0.05

Total 1.54 0.94 0.94 8.14 0.69 22.24

NPV of Recylcing in Year 1 4.16

107


year 1 year 2 year 3 year 4 year 5+ PVCLandfill Related Costs Collection Costs 0.20 0.10 0.10 Operating Costs 0.50 0.50 0.50 Closure 1 Cost of Funds 0.14 0.12 0.32

Recycling Related Costs Set-Up Costs 0.50 Net Collection Costs 0.10 0.10 0.10 0.10Cost of Funds 0.12 0.02 0.02 0.02

Household Sorting Costs 0.10 0.10 0.10 0.10

Incineration Related Costs Collection Costs 0.15 0.15Operating Costs 0.20 0.20Installation 5.00 Cost of Funds 1.00 0.07 0.07

Pollution Costs 0.05 0.05

Total 0.84 1.54 8.14 0.69 0.69 22.21


108

Recycling: Introduction Year 3 year 1 year 2 year 3 year 4 year 5+ PVC

Landfill Related Costs Collection Costs 0.20 0.20 Operating Costs 0.50 0.50 Closure 1.00 Cost of Funds 0.14 0.34

Recycling Related Costs Set-Up Costs 0.50 Net Collection Costs 0.10 0.10 0.10Cost of Funds 0.12 0.02 0.02

Household Sorting Costs 0.10 0.10 0.10



Total 0.84 8.04 1.29 0.69 0.69 22.18


109


year 1 year 2 year 3 year 4 year 5+ PVCLandfill Related Costs Collection Costs 0.20 0.20 Operating Costs 0.50 0.50 Closure 1.00 Cost of Funds 0.14 0.34

Recycling Related Costs Set-Up Costs 0.50 Net Collection Costs 0.10 0.10Cost of Funds 0.12 0.02

Household Sorting Costs 0.10 0.10



Total 0.84 8.04 0.94 1.29 0.69 22.39


110


Fall 2000

Midterm Exam

Answer all parts of each of the following two questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 50 minutes. 1. (a) What are the nine main steps of a CBA? What is the meaning of the “base case”? (b) Explain the meaning of “Pareto efficiency” with respect to the allocation of resources. Under what

conditions will a competitive equilibrium yield a Pareto efficient allocation? (c) A toll of $5 is to be imposed on a proposed new highway. There are expected to be 1,000,000 trips

per year on the highway, with the following composition: Residents of British Columbia: 70% Non-British Columbian Canadians: 20% Foreign tourists: 10%

How should the toll revenue be treated in the CBA? 2.(a) Using an appropriate diagram, illustrate the effect of a negative externality associated with some

activity z. On your diagram, illustrate the private optimum, the “social optimum”, and the surplus changes that would accrue to winners and losers if a policy measure forced a switch – without compensation – from the private optimum to the “social optimum”. Is the “social optimum” unique?

(b) Use a series of appropriate diagrams to illustrate the CV and EV associated with a price fall for an

inferior good. (c) A proposed natural gas power station will cause a reduction in air quality for surrounding residents.

The CBA for the project uses an EV measure for the associated cost. What is the implied assignment of property rights? Explain your answer.

111


Fall 1999

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1.(a) Explain the meaning of “Pareto efficiency” with respect to an allocation of resources.

Explain the limitations of the “Pareto improvement” criterion for assessing the merits of a policy or project.

(b) What is the “potential Pareto improvement (PPI)” criterion? Comment on the sensitivity of

the PPI-based “social optimum” to the distribution of wealth. (c) Provide a brief defense against the following critique of economic value: “Willingness-to-pay (WTP) and willingness-to-accept (WTA) are functions of preferences

and wealth. Since the existing distribution of wealth is unfair, notions of value based on WTP and WTA are flawed and should not be used.”

2.(a) Using an appropriate diagram, illustrate the effect of a positive externality associated with

some activity z. On your diagram, illustrate the private optimum, the “social optimum”, and the surplus changes that would accrue to winners and losers if a policy measure forced a switch – without compensation – from the private optimum to the “social optimum”. Provide a policy-relevant example of a positive externality.

(b) In what sense is the “social optimum” identified in your diagram a social optimum? Would

that “social optimum” be different if the distribution of wealth was changed? Explain your answer.

(c) Why might actual compensation not be made after a policy-induced reallocation that

produces winners and losers? Support your answer with an appropriate policy example. 3. (a) Explain the term “moral hazard”, and explain why it can cause market failure. Provide a

policy-relevant example to support your answer. (b) Consider the following wealth redistribution policy proposal. A welfare payment will be

paid to each person of age 65 or older who has an income of less than $10,000 per year. The welfare payment is $0.5 for every $1 by which income falls below the threshold level of $10,000. Thus, a person with an income of $10,000 receives $0; a person with an income of $5000 receives $2500; a person with an income of $0 receives $5000; etc. Discuss the “Samaritan’s dilemma” in the context of this candidate policy.

(c) Explain the “problem of second best”. Is the problem of second best necessarily an obstacle

to conducting policy analysis in a partial equilibrium framework? Explain your answer.

112

Economics 516 Fall 1999


1.(a) An allocation of resources is Pareto efficient if it is not possible to reallocate those resources in a way

that makes at least one individual better-off and no individual worse-off.

The Pareto improvement criterion is limited because most policies create winners and losers; very few policies actually pass the Pareto improvement test. For example, a policy that reduced the wealth of agent A by $1 and raised the wealth of agent B by $1 billion would not pass the Pareto improvement test, yet one could reasonably argue that this is a good policy.

(b) A reallocation is a potential Pareto improvement if the winners could in principle compensate the

losers and still be better-off.

The PPI-based social optimum is that which maximizes social surplus, as measured by willingness-to-pay (WTP) or willingness-to-accept (WTP). However, WTP and WTA are both functions of wealth; a redistribution of wealth will generally change WTP and WTA measures. Thus, the PPI-based social optimum is not independent of the initial distribution of wealth.

(c) One can reasonably argue that the existing distribution of wealth is “unfair”, according to some definition of “fair”. However, abandoning WTP and WTA as measures of value can lead to unexploited gains from trade; that is, it can prevent resource reallocations that would make all parties better-off, given the existing distribution of wealth. Concerns over the distribution of wealth should be addressed separately from the issue of using WTA and WTP as value measures.

2.(a) See course notes. (b) The “social optimum” is that which maximizes surplus (where gains and losses are simply

aggregated). It has no claim to the “best” allocation in any wider sense. A redistribution of wealth would cause the MSC and MSB schedules to shift; this would in turn imply a different “social optimum”.

(c) Two main reasons:

• compensation is costly because it generally requires the use of distortionary instruments to raise revenue, like taxes; and

• the implicit reassignment of property rights associated with an uncompensated change may be a deliberate element of the policy.

3.(a) Moral hazard refers to the distortion of incentives associated with the unobservability of actions. An important example is the reduced incentive to take precautionary action against an accident when an agent purchases full insurance against loss.

(b) The Samaritan’s dilemma here is the following: by attempting to improve the welfare of poor older

people, incentives to save are distorted. A young agent will recognize that the amount she receives from the government when old will be reduced if she saves for her own old age; she therefore has an increased incentive to spend when young rather than save.

(c) The problem of second best is the following. Correcting one type of market distortion while other

distortions remain uncorrected could actually make the situation worse than if no corrections were made (that is, social surplus could be reduced). The only way to ensure that a single correction would improve welfare is to conduct a complete general equilibrium analysis that traces all linkages

113

in the economy. However, the problem of second best does not pose an insurmountable obstacle to the use of partial equilibrium analysis if the size and scope of the policy intervention is relatively small.

114


Fall 1999

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. All questions relate to the cost-benefit analysis of an increase in the level of public transit service in a city. All of the information you need to address each question is contained within the question, or within the questions that precede it. Therefore, be sure to answer the questions in the order in which they appear. General Information The City of Troy is considering an increase in the frequency of bus service during rush hours. This enhanced service is henceforth referred to as “the project”. There is an excess demand for bus travel at the existing level of service and commuters routinely have to wait in line to get a ride. The project is expected to reduce those waiting times. The project will require the purchase of additional buses and will require the employment of additional drivers. The City is the referent group. Defer any consideration of the cost of funds until question 5. 1. Bus Purchases The project will require the purchase of 5 additional buses in year 1 of the project. These have a purchase price of $200,000 each. The purchase is exempt from provincial sales tax but is subject to a federal sales tax of 10%. The provincial government will pay a subsidy of $50,000 for each bus. There are no other distortions in this market. (a) What is the financial cost of the bus purchase? (b) What is the economic cost of the bus purchase? 2. Labour and Training The project will require hiring 5 additional part-time drivers. These future drivers will be drawn from the ranks of the existing unemployed and trained specifically as part of the project. The drivers currently spend their time in leisure. The drivers will lose 80% of the unemployment assistance they currently receive from the federal government; the amount they currently receive is $100 per week. They will be paid a salary of $200 per week (in each of 52 weeks per year), from which they will have to pay 20% in federal income tax and 10% in provincial income tax. The drivers are hired in year 1 of the project and employed in each year thereafter. It will cost $2000 to train each driver but the province will pay 50% of that cost; the city will pay the rest. These costs are incurred in year 1 and the training is conducted by a school based outside the city. (a) Show that the private value of a future driver’s leisure must be no greater than $60 if he or she is to

accept employment in the project. Henceforth assume that value is zero. (b) What is the financial cost of the training? What is the economic cost? Does it matter that the school is

based outside the city?

115

(c) What is the on-going financial cost of employing the drivers (per year)? What is the economic cost (per

year)? 3. Value of the Improved Service The demand for bus travel, together with existing and planned levels of service ( 0q and 1q respectively), are illustrated in Figure 1. The price of a bus trip is fixed at p , both before and after the expansion in service. (a) Provide an interpretation of the “effective price” of a trip, depicted on the vertical axis of Figure 1,

before and after the project. (b) Illustrate the increase in consumer surplus associated with the project as a shaded area in Figure 1.

Provide an explanation of the area you have shaded. (c) If we could estimate a CV or EV measure instead of the consumer surplus measure, which measure, EV

or CV, would be appropriate? Explain your answer. Assume the following values in Figure 1: • 2=p

• 30 =τ

• 11 =τ

• 5000 =q trips per week

• 7001 =q trips per week (d) What is the change in consumer surplus (per year)? (e) What are the bus fare totals collected before and after the project (per year)? How should this change in

fares collected be treated in the CBA? 4. Reduced Private Car Use The improved service will cause some commuters to switch from private car use to the bus. This reduced demand for private car trips is illustrated in Figure 2 as a shift from 0D

to 1D . (a) Provide an interpretation of Figure 2. (b) Illustrate the change in consumer surplus for car commuters as a shaded area in Figure 2. (Hint:

previous car users who have switched to the bus do not enjoy an increase in surplus from reduced car trip costs).

(c) What is the numerical value of the consumer surplus change you have illustrated in Figure 2? 5.The Cost of Funds Assume the marginal cost of funds is 1.2 (a) Explain what this means.

116

(b) Explain in general how a cost-benefit analysis should account for the cost of funds. (c) Prepare a table like the following to indicate all the financial costs and receipts to the city. (The number

of rows indicated is not necessarily correct). Briefly explain each entry; if an entry is drawn from a previous question, simply state “from question X(y)” as your explanation.

Item Money amount in Year 1 Year 2 and each year thereafter Total

6. Net Present Value (a) Prepare a table like the one below to summarize the economic costs and benefits derived above. (The

number of rows indicated is not necessarily correct). Briefly explain each entry; if an entry is drawn from a previous question, simply state “from question X(y)” as your explanation.

Item Cost or benefit in Year 1 Year 2 and each year thereafter Net benefit

(b) Assume a discount rate of 5%. On the basis of the information you have, calculate the NPV of the

project. Should the project proceed?

Hint: rrrr1

)1(1.........

)1(1

)1(1

2 =⎥⎦

⎤⎢⎣

⎡+

+++

++ ∞

(c) Calculate the benefit-cost ratio for this project (assuming a discount rate of 5%). (d) What are the main shortcomings of the benefit-cost ratio criterion? 7. Optimal Pricing Suppose the bus fare is raised after the service expansion to equate supply and demand. (a) At what price should the new fare be set to equate supply and demand? (b) Calculate the change in consumer surplus from the service expansion under the new pricing rule. (c) Explain the relationship between your answers to 8(b) and 3(d) with reference to the cost of wasted

time. (Hint: think about fare revenue). (d) Construct revised versions of the Tables from questions 5 and 6, and calculate a new NPV.

117

q

p

p +τ 0

p +τ1

q0 q1

D

q p( )

p

Figure 1 Name: ___________________

118

per week trips

$

54

MPC

400 600

0D

12

1D

Figure 2

Name: __________________

119


Spring 1999

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1.(a) Define Pareto efficiency and explain why this criterion generally cannot be used to identify a unique

“social optimum”. (b) Explain the relationship between “social surplus” and the “potential Pareto improvement (PPI)”

criterion. Comment on the sensitivity of the PPI-based “social optimum” to the distribution of wealth.

(c) Explain the potential conflict between the efficiency and distributional goals of policy. Illustrate your

answer with a specific policy example. 2.(a) Consider Figure 1. In what sense is $z inefficient? Is there necessarily a role for government

intervention in this situation? Explain your answer. (b) Explain why the cost of funds is positive. How should financing costs be treated in a cost-benefit

analysis? (c) A proposed entry fee to a new park in British Columbia is expected to raise $150,000 per year. The

expected composition of visitors is as follows:


How should the entry fee revenue be treated in a cost-benefits analysis if: (i) British Columbia is the referent group and the fee-collector? (ii) British Columbia is the referent group but the Federal government is the fee collector?

3(a) Explain the meaning of the “base case” in a cost-benefit analysis. Give an example of how the analysis

could be flawed if the base case is not properly specified. (b) Using an appropriate diagram(s), illustrate and compare the EV, CV and CSΔ for a price rise for an

inferior good. Which is the appropriate measure of welfare change?

120

z

$

MPCMPB MSB≡

$z

MSC

Figure 1

121


Spring 1999


1.(a) Pareto efficiency: an allocation is Pareto efficient if it is not possible to make one person better off

without making someone else worse off. Many allocations satisfy this criterion, differing according to the distribution of utility. Arrow’s impossibility theorem (and in particular, the impossibility of inter-personal utility comparisons) means that allocations differing according to the distribution of utility cannot be ranked. Thus, Pareto efficiency alone cannot identify a unique social optimum.

(b) A reallocation represents a PPI if the winners in the reallocation could in principle fully compensate

the losers and still be better off. Such a reallocation would increase social surplus. A social optimum based on the PPI criterion is sensitive to the distribution of wealth because social surplus is derived from willingness-to-trade (WTT), whether measured by WTP or WTA, and this is a joint function of preferences and wealth. Thus, a redistribution of wealth will generally change measured WTT, and so change the social surplus associated with a particular allocation. Thus, social surplus maximization cannot identify a unique social optimum independent of the distribution of wealth.

(c) Policies designed to redistribute wealth generally distort incentives, and thus generate inefficiency.

For example, income taxation distorts incentives to work. Thus, policy-makers usually face a trade-off between distributional goals and efficiency.

2.(a) $z is inefficient is the sense that social surplus is not maximized: the external agents could fully

compensate the source agent and still be better off. Note that $z is not Pareto-inefficient: any deviation from $z would make the source agent worse off. Any role for government intervention must be argued on the basis of institutional advantage in the circumstances; that is, that the transaction costs associated with a government solution are lower than those associated with allowing the market to respond to the apparent inefficiency.

(b) The cost of funds is positive because funds must be raised through taxation, and taxation is typically

distortionary in a destructive way because it erodes incentives to create wealth. The cost of funds should be included as a separate cost item, calculated as RMCF Δ− )1( , where RΔ is the aggregate net revenue loss (and thus, fund-raising requirement) for the government from the project.

(c) (i) Fees received from non-BC residents (Canadian and foreign) are a benefit. Thus, a benefit of

$60,00 p.a. Fees received from BC residents are just a transfer; neither a cost nor benefit (though they will have cost of funds implications).

(ii) Fees paid by BC residents to the Federal government ($90,000 p.a.) are a cost to BC. Fees paid by non-BC residents are of no consequence to BC.

3(a) The “base case” is the forecast of what would happen if the project does not proceed. Example:

accelerated vehicle retirement program. Assuming that the cars will remain on the road indefinitely in the absence of the program will over-estimate the benefits of the program, since those cars will eventually be retired anyway. The program only accelerates that retirement.

(b) See figure. )(abefareaCV = ; )(acdfareaEV = and )(acefareaCS =Δ .The appropriate

choice between CV and EV depends on the assignment of property rights. If the agent is assigned a

122

right to the lower price, then CV is the appropriate measure. If the agent is assumed to have no right to the lower price, then EV is the appropriate measure. CSΔ is an approximation to the EV and CV measures.

z

$

0p

1p

d

a b c

)( 0uH

)( 1uH

D

ef

123


Spring 1999

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. All questions relate to the cost-benefit analysis of a hypothetical bridge building project. All of the information you need to address each question is contained within the question, or within the questions that precede it. Therefore, be sure to answer the questions in the order in which they appear. General Information The Provincial Ministry of Transportation and Highways is considering building a bridge over a lake. The bridge will allow commuters to by-pass an existing route that goes around the lake, and thereby save on travel time. All construction will take place in year one. The bridge will open to traffic in year two and will remain open indefinitely. The Province is the referent group. Defer any consideration of the cost of funds until question 5. 1. Construction Costs Construction involves the use of labour and materials. The project will employ 30 workers for 8 hours per day for 100 days. The wage rate is $10 per hour. Workers pay 20% Federal income tax and 10% Provincial income tax. The labour market is otherwise undistorted and there is no unemployment. Materials for the project will be purchased from a distortion-free market at a cost of $100,000 plus 10% Provincial sales tax and 10% Federal sales tax. (a) What is the financial cost of construction? (b) What is the economic cost of construction? 2. Foregone Land Use The land required for the bridge construction is owned by the Province and there are no plans for any alternative use. However, the land provides nesting sites for waterfowl and is currently used by local residents of bird-watching. This activity will be permanently lost as soon as construction begins. (a) Briefly describe the steps you would take to conduct a referendum format contingent valuation exercise

to determine the value for the bird-watching. (b) Briefly comment on the main shortcomings of the contingent valuation method. Henceforth, assume that the bird-watching has an estimated value of $20,000 per year.

124

3. Travel Time Savings There 6000 commuting trips taken on the road around the lake each year, and it is expected that all of these road users will switch to the bridge. No new traffic is expected. The bridge will reduce round-trip commuting time by 30 minutes. However, during construction, it is expected that traffic disruption will add around 20 minutes to each round-trip. (a) No information is available about hourly time costs for these road users and no funds are available to do

a study. How would you choose an hourly time cost for inclusion in the cost-benefit analysis? (b) Assume a time cost of $6 per hour. What is the annual value of time cost savings from the bridge

project? Distinguish between year one and subsequent years. 4. Construction Noise Construction will impose noise costs on local residents. Based on existing hedonic price studies of airport noise, these costs have been estimated at $5,000 per year during the construction period. Briefly explain how you would conduct an hedonic price study to value airport noise. 5.The Cost of Funds Assume the marginal cost of funds is 1.2 (a) Explain what this means. (b) Explain in general how a cost-benefit analysis should account for the cost of funds. (c) Prepare a table like the following to indicate all the financial costs and receipts to the Province. (The

number of rows indicated is not necessarily correct). No explanation is needed for the items and amounts entered.

Item Money amount in Year 1 Year 2 and each year thereafter Total

6. Net Present Value (a) Prepare a table like the one below to summarize the economic costs and benefits derived above. (The

number of rows indicated is not necessarily correct). No explanation is needed for the items and amounts entered.

Item Cost or benefit in Year 1 Year 2 and each year thereafter Net benefit

(b) Assume a discount rate of 5%. On the basis of the information you have, calculate the NPV of the

bridge project. Should the project proceed?

125

Hint: )1(

1)1(

1.........)1(

1)1(

12 rrrrr +

=⎥⎦

⎤⎢⎣

⎡+

+++

++ ∞

(c) Calculate the benefit-cost ratio for this project (assuming a discount rate of 5%). (d) What are the main shortcomings of the benefit-cost ratio criterion? 7. Project Delay The project will qualify for a Federal government infrastructure grant if the entire project is delayed by one year. Under the grant scheme, the Federal government pays the Provincial government $0.25 for every $1 spent on construction. The funds are awarded during the year in which construction takes place. (a) How much will the provincial government receive if the project is delayed? (b) Should the project be delayed? Fully explain your answer.

126


Fall 1997

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 115 minutes. 1.(a) Define Pareto efficiency and explain why this criterion cannot be used to identify a

unique “social optimum”. (b) Defend the use of willingness-to-pay as a measure of value and comment on the

associated inseparability of efficiency and distribution. (c) Explain the potential conflict between the efficiency and distributional goals of

policy in the context of a specific policy example. 2.(a) Consider Figure 1. In what sense is $z inefficient? Is there necessarily a role for

government intervention in this situation? Explain your answer. (b) Suppose there is currently a three month waiting period for hip replacement surgery

for the elderly due to high demand. If policy A is implemented, the waiting period in five years time will be four months. Assume that waiting for hip replacement surgery causes suffering (and suffering is bad!). Could policy A nonetheless be a good policy? Explain your answer.

(c) Explain why the cost of funds is positive. How should financing costs be treated in a

cost-benefit analysis? 3.(a) Explain why the cessation of unemployment benefits paid to previously unemployed

workers could be a cost of the project that employs those workers. How should entry fees paid by visitors to a proposed new national park be treated in a cost-benefit analysis of the park-creation project?

(b) On figures 2a. and 2b. respectively, identify the EV and CV associated with the

illustrated price/income change. Which measure of welfare change is appropriate? Relate your answer to the assignment of property rights.

(c) Figure 3 illustrates the use of a project input that has an associated negative

externality and is subject to an excise tax. Illustrate the economic cost of the input.

127


Fall 1997

Final Exam Answer all parts of each of the following nine questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. All questions relate to the cost-benefit analysis of a hypothetical trail building project. All of the information you need to address each question is contained within the question, or within the questions that precede it. Therefore, be sure to answer the questions in the order in which they appear. General Information The Provincial Ministry of Environment, Lands and Parks is considering building a major coastal hiking trail in an area of Crown land (owned by the Province). The Province is the referent group. There is currently road access to one end of the proposed trail but not to the other. One element of the project is to construct a new access road. Construction of the road will take place in the first year. Construction of the trail will take place in year two. The first hikers will use the trail in year three and it is expected that use of the trail will then continue into the indefinite future. Defer any consideration of the cost of funds until question 6. 1. The Value of Hiking (Part 1) No data is available on the demand for hiking in the particular project area so it has been suggested that a travel cost study be conducted on a similar existing trail elsewhere on the coast. Describe the steps you would take in conducting such a study and how you would use the results to estimate a demand curve for hiking.

128

2. The Value of Hiking (Part 2) Suppose the estimated demand curve for the proposed trail is as illustrated in figure 1. The curve plots the number of users per day against a hypothetical user fee for hiking the trail. To reduce congestion and the risk of damage to the area, the Ministry has decided that the number of hikers will be restricted to 10 starters per day during 120 days over summer. The trail will be closed during the rest of the year. A $20 user fee will be charged to each hiker, and applications to hike the trail will have to be lodged in advance. Successful applicants will be chosen by lottery if demand exceeds the permitted 10 hikers per day. (a) What would be the expected demand for the trail at the $20 user fee? (b) Discuss the tradeoff between efficiency and distributional goals inherent in the

combination of the user fee and the lottery. (c) Explain why the shaded area in figure 1 does not represent the daily expected

consumer surplus from the hiking. (d) What is the correct value for the expected daily consumer surplus? (e) Suppose 20% of the hikers will be from outside the province. What is the correct

value of consumer surplus per year for inclusion as a benefit of the project? Explain your answer.

(f) How much money will the province collect per year in user fees? 3. Road Construction The road will require the permanent lease of a right-of-way through private land. That lease will cost the province $6000, to be paid in year 1. The land is owned by a foreign individual. Road construction will be contracted to a private firm in a market that is more or less competitive. The contract will be worth $900,000. Of that amount, $600,000 will be for wages, which are subject to a 20% Federal income tax, and a 15% Provincial income tax. The labour market in road construction is otherwise undistorted and the project is small relative to the market as a whole. (a) What is the financial cost of the road? Explain your answer. (b) What is the economic cost of the road? Explain your answer.

129

4. Trail Construction The trail will be constructed by students hired specifically for the task during the summer of year two. Each of 45 students will be hired for 8 hours per day for 100 days at an hourly wage of $7. The Province will pay $5 of that wage and the Federal Government will contribute the other $2 as part of a student summer employment program. The wages are subject to a 20% Federal income tax, and a 15% Provincial income tax. It is expected that the students to be employed on the project would otherwise spend the summer loitering around shopping malls harassing security guards. (a) What is the financial cost of the student labour to the Province? (b) What might be a reasonable estimate of the opportunity cost of labour per hour for

these students? Explain your answer. (c) Henceforth, assume that the opportunity cost of labour for students is zero. What is

the economic cost of the student labour? 5. Foregone Timber Harvesting Dedication of the trail will mean that valuable timber that could otherwise be harvested will be left standing. It is thought that 30,000 cubic feet of timber would be harvested from the area in year one, using the existing access road, if the trail project does not proceed. Construction of the new access road would allow an additional 80,000 cubic feet to be harvested. Both stands of timber would be harvested by a private firm under license from the Province and sold on the market for $12 per cubic foot. A royalty (“stumpage”) of $4 per cubic foot would be received by the Province. The true economic cost of harvesting in the area is estimated to be $3 per cubic foot. The quantity of timber is not enough to affect either the price of timber nor forestry-related employment in the region. (a) Explain why the 80,000 cubic foot stand of timber foregone is not a cost of the

project. Relate your answer to the importance of correctly specifying the base case. (Hint: you need to do some calculations to justify your answer).

(b) What is the financial cost to the Province of the foregone timber? (c) What is the economic cost of the foregone timber?

130

6. The Cost of Funds Assume the marginal cost of funds is 1.2 (a) Explain what this means. (b) Explain in general how a cost-benefit analysis should account for the cost of funds. (c) Prepare a table like the following to indicate all the money costs and receipts to the

Province. (The number of rows indicated is not necessarily correct). No explanation is needed for the items and amounts entered.

Item Money amount in Year 1 Year 2 Year 3 and each

year thereafter Total

7. Net Present Value (Part 1) (a) Explain why the benefit-cost ratio is not an appropriate valuation criterion. (b) What welfare criterion is implicit in the net present rule? Explain your answer. (c) Explain why discounting per se does not imply unequal treatment of current and

future generations. What is the true source of potential intergenerational inequity? 8. Net Present Value (Part 2) (a) Prepare a table like the one below to summarize the economic costs and benefits

derived above. (The number of rows indicated is not necessarily correct). No explanation is needed for the items and amounts entered.

Item Cost or benefit in Year 1 Year 2 Year 3 and each

year thereafter Net benefit

131

(b) Assume a discount rate of 5%. On the basis of the information you have, calculate the NPV of the trail project.

Hint: 1

11

11

11

12 3( ) ( ).........

( ) ( )++

++ +

+⎡

⎣⎢

⎤

⎦⎥ = +∞r r r r r

9. Re-Evaluation After Commencement (a) Suppose the project does proceed. In year 2 (after the road has been constructed), the

price of timber rises to $20 per cubic foot. Should the project continue? Explain your answer.

(b) Would your answer to part (a) change if the Province abandoned the lottery scheme

and set a higher user fee instead? What does this suggest about the wisdom of using the lottery system to implement the “equity” goal?

132


Fall 1997


1. See notes (section 6.4) 2. (a) 25 (b) Total surplus is lower than if the user fee was chosen to clear the market because

the highest value hikers are not necessarily the ones to win the lottery. However, this loss of surplus must be weighed against the distributional goal of allowing lower income hikers to use the trail.

(c) Demand exceeds supply so the lottery will be used. The 10 hikers who win the

lottery will not necessarily be the 10 hikers with the highest WTP. (d) Among the 25 hikers who would be willing to pay at least $20, the average surplus

($120-$20)*0.5 = $50. Thus, the expected surplus for the 10 who win the lottery is $500.

(e) The surplus enjoyed by the foreigners does not count as a benefit of the trail. Thus,

the daily surplus to the referent group is $400. The surplus per year is (120*$400) = $48,000.

(f) User fee revenue = (120*10*$20) = $24,000. 3. (a) Financial cost: Right-of-way lease $ 6000 Wages (less tax receipts) $510,000 Non-wage costs $300,000 $816,000 (b) Economic cost: Right-of-way lease $ 6,000 Total OCL (0.65*200,000) $390,000 Federal tax payments $120,000 Non-wage costs $300,000 $816,000

133

4. (a) The Province pays $5 per hour but receives 15% of $7 in tax revenue. Thus, the financial cost per hour is $3.95. The total financial cost is (45*8*100*$3.95) = $142,200.

Erratum: the $2 received from the Feds should be included as a negative cost. Thus, the financial cost per hour should be $1.95.

(b) Zero. The value the students derive from loitering is likely to be offset by the cost

to the security guards and shoppers. (c) Economic cost per hour: OCL $0 Federal tax payments (0.2*$5) $1 $1

Thus, total cost is (45*8*100*$1) = $36,000 5. (a) The value of the timber is $(12 - 3)*80,000 = $720,000. However, the cost of the

road is $816,000. Thus, the timber would not be harvested if the trail does not go ahead.

(b) Financial cost: ($4*30,000) = $120,000 (c) Economic cost: $(12 - 3)*30,000 = $270,000 6. (a) See notes (section 3.4) (b) See notes (section 3.4) (c) Money costs and receipts:

Item Money amount in Year 1 Year 2 Year 3 and each

year thereafter Road - 816,000 Trail - 142,200 Timber revenue

-120,000

User fees 24,000 Total - 936,000 - 142,200 24,000

135

7. (a) See notes (section 7.5) (b) The PPI criterion. See notes (section 1.8) (c) See notes (section 9.3) 8. (a) Costs and benefits:

Item Cost or benefit in Year 1 Year 2 Year 3 and each

year thereafter Road - 816,000 Trail - 36,000 User fees 24,000 Timber loss - 270,000 Hiking 48,000 Cost of funds -187,200 - 28,440 4,800 Net benefit - 1,273,200 - 64,440 76,800

(b) NPV = − − + = >1 273 20064 440

10576 800

0 05 105128 285 0, ,

,( . )

,. ( . )

,

9. (a) Since the road has been built, all of the foregone harvestable timber must be

included as a cost of continuing.

Continuation money costs and receipts:

Item Money amount in Year 2 Year 3 and each

year thereafter Trail - 142,200 Lost timber revenue

- 440,000

User fees 24,000 Total - 582,200 24,000

136

Continuation costs and benefits:

Item Cost or benefit in Year 2 Year 3 and each

year thereafter Trail - 36,000 User fees 24,000 Timber loss - 1,870,000 Hiking 48,000 Cost of funds - 116,440 4,800 Net benefit - 2,022,440 76,800

NPV ′ = − + = − <2 022 44076 800

0 05486 440 0, ,

,.

,

Thus, the project should not continue.

(b) If the user fee is set to clear the market ($80), then two things change:

• user fee revenue increases to $96,000 per year • the highest valuation hikers use the trail, and so consumer surplus to the hikers

is $400 per day, of which $320 accrues to the referent group. Check this: should it be $200 and $180?

Thus, the revised tables are:

Continuation money costs and receipts:

Item Money amount in Year 2 Year 3 and each

year thereafter Trail - 142,200 Lost timber revenue

- 440,000

User fees 96,000 Total - 582,200 96,000

137

Continuation costs and benefits:

Item Cost or benefit in Year 2 Year 3 and each

year thereafter Trail - 36,000 User fees 96,000 Timber loss - 1,870,000 Hiking 38,400 Cost of funds - 116,440 19,200 Net benefit - 2,022,440 153,600

NPV ′ = − + = >2 022 440153 600

0 051 049 560 0, ,

,.

, ,

Thus, the project would be worthwhile if the user fee was set higher. This reflects the efficiency cost of attempting to achieve distributional goals through rationing.

138


Spring 1997

Midterm Exam

Answer all parts of each of the following three questions. All questions are of equal value. This examination accounts for 20% of your final grade on this course. Time allowed: 75 minutes. 1.(a) Explain how the NPV of a project with high decommissioning costs is affected by

the choice of the public sector discount rate. (b) What rule should be used for reassessing a project that has already begun? Support

your answer with a simple numerical example. (c) If a project is expected to have a higher NPV (calculated from the commencement

date) if its commencement is delayed, when should the project commence? Explain your answer.

2.(a) Explain how projects with discretionary scales should be assessed and compared.

Provide an example to illustrate your answer. (b) Explain the shortcomings of using a benefit-cost ratio to assess and compare

projects. (c) Explain the meaning of a “potential Pareto improvement”. Relate your answer to

the use of the NPV rule in cost-benefit analysis. 3.(a) How should revenue from a user fee attached to an amenity (such as a park) be

treated in the cost-benefit analysis of providing that amenity? (b) Provide four reasons why the shadow price of an input might differ from its market

price. (c) What is the shadow price of unemployed labour used in a project?

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Spring 1997

Final Exam Answer all parts of each of the following seven questions. All questions are of equal value. This examination accounts for 35% of your final grade on this course. Time allowed: 175 minutes. All questions relate to the cost-benefit analysis of a hypothetical mining development. All of the information you need to address each question is contained within the question, or within the questions that precede it. Therefore, be sure to answer the questions in the order in which they appear. General information An area of Crown land (owned by the Province) is currently an undeveloped wilderness area. A mineral deposit is known to exist within the area. The policy problem is to decide whether or not to allow the mineral deposit to be mined. The Province is the referent group. A private sector company will construct and operate the mine. The owners of this company are residents of the Province. Construction will take one year. Once constructed, the mine will produce ore worth $3m per year over 5 years, after which it will close. A royalty of 20%, calculated on the value of the ore, is payable to Province. The wilderness value of the area will be lost completely once construction on the mine begins, and will remain lost forever if the area is not restored after the mine is closed. Assume a discount rate of 10% throughout. Defer any consideration of the cost of funds until question 6. 1. The value of the wilderness area (part 1) (a) Distinguish between use and non-use values for an environmental amenity. (b) Explain the limitations of indirect valuation methods for valuing a wilderness area. (c) Describe the key elements of a contingent valuation survey. (d) What are the main shortcomings of contingent valuation? 2. The value of the wilderness area (part 2) Outline the steps you would take to determine a value of the wilderness area using a referendum format contingent valuation.

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3. Restoration of the wilderness area Restoration of the wilderness area after the mine closure would cost $6m and would take one year. (There would be no wilderness benefits during that year). This cost would be paid by the mining company. Suppose the results of the contingent valuation indicate that the wilderness area is worth $500,000 per year. If the mine proceeds, should restoration be undertaken after its closure? Explain your answer.

Hint: xr

x rrt

t ( )( )

11

0 +=

+

=

∞

∑

4. Mine construction costs (a) A road will have to be constructed into the mine site. There are two options: (i) a

concrete road that will last the entire life of the mine, at a cost of $500,000 in the first year of construction; and (ii) a gravel road at cost of $200,000 in the first year, plus annual maintenance costs of $50,000 in subsequent years. Which is the better option? Explain your answer.

(b) Construction will require 100,000 person hours. The construction workers will be

drawn from a labour market in which there is currently no unemployment. The prevailing wage is $20 per hour, and the mine project is too small to put any upward pressure on that wage. In addition, the company will have to pay a Provincial payroll tax of 10%, and a Federal payroll tax of 10%, calculated on the total wage bill. Each construction worker will pay 10% of his or her wage in Provincial income tax, and 20% in Federal income tax.

What is the economic cost of this construction labour? Explain your answer.

5. Operating costs The only operating costs are labour costs. The mine will employ 50 miners in each year of production (no miners are employed during construction). They will each be paid $60,000 per year. In addition, the company will have to pay a Provincial payroll tax of 10%, and a Federal payroll tax of 10%, calculated on the total wage bill. Each miner will pay 10% of his or her wage in Provincial income tax, and 20% in Federal income tax. These miners are currently unemployed and are receiving Federally-funded unemployment assistance worth $25,000 per year each. They would be willing to work for $45,000 (after tax) if work was available. What is the annual economic cost of this labour? Explain your answer.

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6. The cost of funds Assume the marginal cost of funds is 1.5 (a) Explain what this means. (b) Explain in general how a cost-benefit analysis should account for the cost of funds. (c) Prepare a table like the following to indicate all the money costs and receipts to the

Province.

Item Money amount in Year 1 Years 2-6 Total

7. Net present value (a) Prepare a table like the following to calculate net benefits of the mine in each year.

Briefly explain each entry.

Item Amount in Year 1 Years 2-6 Year 7 Years 8 - Construction Operation Foregone wilderness

Restoration Ore extraction

Cost of funds Net benefit

(b) On the basis of the information you have, calculate the NPV of the mine. Should the

mine proceed? (c) Does your answer to part (b) change if you use a discount rate of 5%? Hint: review

your answer to part (a) before calculating the NPV. (d) Explain briefly what steps you would take next, before making a recommendation to a

policy-maker.

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Values for 1

1( )+ r t :

t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7 t = 8 r = 0.1 0.9090 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 r = 0.05 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768

516 Past Exams

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