Conclusion of “tools” chapters

Today: Welfare economics

Some cost-benefit analysis tools

Certainty equivalent value

Administrative issues

Crashers? I do have add codes (updated from posted lecture

slides) Talk to me after class

Administering tests If you qualify for an exception on taking any of the

tests, see syllabus for more details

Last week

Introduction to Econ 130 and public finance Read syllabus if you have not done so

Chapter 1 What is public finance?

Parts of Chapter 2 Empirical tools to test theory

Tiebout model “Voting with your feet”

Today

Conclusion of our “tools” chapters Welfare economics

Pure exchange economy Pareto improvements

Market failure Common in markets we will be examining this quarter

Cost-benefit analysis What projects should be done?

Certainty equivalent value How much money are risk-averse people willing to give

up to get a sure thing?

Before we start…

Why is trade beneficial? Econ 1 answer: Comparative advantage Another possibility

You did not get the right bundle allotted to you

Welfare economics

Begin study using Edgeworth boxes Pure exchange economy

R/G chapter 3 For an in-depth look, see also Varian’s Intermediate

Micro book, chapters 30-33

Edgeworth boxes

Simple study of distribution We will make extensive use of Edgeworth boxes,

Pareto efficiency, and Pareto improvements Edgeworth boxes are used for a two-person

economy Bottom left of Edgeworth box is origin for one person Top right of Edgeworth box is origin for other person

Edgeworth Box

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

vwu

y

x

Indifference curves in Edgeworth Box

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

A1

A2

A3

E1

E3

E2

Pareto efficiency

Nobody can be made better off without making another person worse off

In cases with “standard” indifference curves (ICs), the two ICs will be tangent to each other when Pareto efficiency is achieved

Pareto improvement

Reallocation of goods or resources that meets the following requirement At least one person is made better off without

anybody else being made worse off

Pareto efficient point: p

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

Ag

Ah

Ap

Eg

gh

p

A Pareto Efficient

Allocation

Points g and h are not optimal, since Adam can be made better off without making Eve worse off

Another efficient point: p1

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

Ag

Eg

g

p1

pEp1

A Pareto Efficient

Allocation

Here, by going from point g to point p1, Eve is being made better off without making Adam worse off

Point p2 is also Pareto efficient

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

Ag

Eg

g

p1

p

Ep2

Ap2

p2

• Pareto efficient

• Pareto improvement

Point p2 makes both Adam and Eve better off, relative to g

Starting from a different initial point

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

Ag

Eg

g

p1

p

Ep2

Ap2

p2

p3

p4

k

Contract curve

The set of all Pareto efficient points Usually goes from one person’s origin to the

other person’s origin Origin of each person is Pareto efficient

Note that efficient points may or may not be “fair” in your mind Fairness is often not a topic brought up by

economists More on “fairness” later

The Contract Curve

Edgeworth Box

Adam

Eve

0

0’

s

r

Apples per year

Fig

leav

es p

er y

ear

Ag

Eg

g

p1

p

Ep2

Ap2

p2

p3

p4

The contract curve

Moving on to production

We have found the efficient points on the consumption side

Now, let’s do the same on the production side Production possibilities curves

Production possibilities: Linear example Becky has a

given number of hours per day

Feasible bundles: t, v, w, x, y, z Point t does not

use up her time allotment

Point u is infeasible

Efficiency

Efficient points are on the line connecting (0,4) and (20,0)

Examples of efficient points: v, w, x, y, and z

Efficiency

At efficient points, increasing production of one good must result in another good having decreased production

We will typically assume efficient points are chosen No satiation assumption: More is better

New example

Apples per year

Fig

leav

es p

er y

ear

C

C0

w

y

x z

│Slope│ = marginal rate oftransformation

A more realistic example of production possibilities is a curve with increasing marginal cost

Why increasing marginal cost Let’s go from the

vertical intercept to the horizontal intercept

As the slope gets steeper, we must give up more figs for each additional apple we can consume Opportunity cost

increases as more apples are consumed

Apples per year

Fig

leav

es p

er y

ear

C

C0

w

y

x z

¦ Slope¦ = marginal rate oftransformation

A more realistic example of production possibilities is a curve with increasing marginal cost

Market failure

There are instances in which market efficiency cannot be achieved Market power

Many ways to control price Nonexistence of markets

Asymmetric information Important in health care and retirement: Chapters 9-11

Externalities: Chapter 5 Public goods: Chapter 4

Market failure due to market power How Do Firms Gain Market Power?

Exclusive control over important inputs Patents and copyrights Government licenses or franchises Economies of scale Natural monopoly Networks

Exclusive control over important inputs If a company controls a significant portion of

the important inputs to a product, it can have significant influence on price

Exclusive control over important inputs Example: De Beers

Rough diamond explorer Around 40% of world diamond production by

value Sales and marketing through the Diamond

Trading Company This company sells almost half of the world’s rough

diamonds by value(Information from http://en.wikipedia.org/wiki/De_Beers, checked Feb.

3, 2008)

De Beers

Such large control over the market makes De Beers able to act similarly to a monopolist Marketing of diamond jewelry does not have to be

brand specific "A Diamond is Forever" attempts to prevent old jewelry

from entering the market De Beers does have some control over world

prices

Patents and copyrights

Patents and copyrights prohibit others from copying private work and discoveries Example: Copying songs and movies that are

copyrighted are typically prohibited by law

Government licenses or franchises Government owned property often allows

exclusive operation of the property for various uses

This is to prevent competition that could deteriorate a natural destination

Government licenses or franchises Example: Yosemite National

Park Limited parking Tasteful hotels Most of the park is undeveloped

Most of park development is in only 7 square miles

Park is 1,200 square miles

Bridal Veil Falls

Economies of scale

Some technologies are such that as the quantity produced increases, ATC decreases for all reasonable quantities produced This is due to increasing returns to scale

This happens when ALL inputs double and production MORE THAN doubles

Often happens with large fixed costs and nearly-linear variable costs

One firm could gain market power When a firm gains

market control with economies of scale, it is called a natural monopoly

There are problems with natural monopolies if left uncontrolled

Price ($)

Q

D

ATC

Network economies example

Picture phones Each company in this

industry is trying to become the leader in video calling programs

This technology has improved since the PicturePhone (at right) was unveiled in 1964

Market failure & government intervention In some of the topics this quarter,

government intervention will be justified by market failure Governments can fail, too

More in Chapter 6

Cost-benefit analysis/CE value We now move on to Chapter 8 for the last

“tools” chapter Cost-benefit analysis

Present value Internal rate of return Benefit-cost ratio Valuing public projects

Certainty equivalent value

Present value

Present value shows how much future payments are worth today Example: $100 paid today is not worth the same

as $100 paid a year from now Lost interest in safe investments

Using future value to derive present value Suppose we put $1,000 into the bank today,

earning 1% per year on it Value today: $1,000 Value 1 year from now: $1,010

$1,000 * (1 + 0.01) Value 2 years from now: $1,020.10

$1,000 * (1 + 0.01)2

$1,010 * (1 + 0.01)

Projecting Future Dollars into the Present If we multiply to get future value, we divide to find present

value of a future payment

R0 = $1000

R1 = $1000*(1+.01) = $1010

R2 = $1010*(1+.01) = $1020.10

R2 = $1000*(1+.01)2 = $1020.10

RT = R0*(1+r)T

R0 = RT/(1+r)T Present Value

discount ratediscount factor

Present Value of a Stream of Money

PV RR

r

R

r

R

rT

T

01 2

21 1 1( ) ( ). . .

( )

Present value, permanent annual payment Special case

Present value of an annual payment of R every year forever (starting today), when the annual interest rate is r :

r

RPV

Cost-benefit analysis

Welfare economic theory framework Find present value of benefits and costs If benefits exceed costs, the project should be

done Information for cost-benefit analysis is often

difficult to obtain

Cost-benefit analysis

Present value criteria When there are two mutually exclusive projects,

the preferred project is the one with the highest net present value (assuming it is positive)

What about “fairness?”

Factoring in inflation

Unless otherwise mentioned, we assume costs and benefits are in real terms Real costs and benefits account for inflation

When costs and benefits are in nominal terms, inflation must be factored in

Note that we get same result, once we cancel inflation terms

PV RR

r

R

r

R

r

TT

T T

0

12

22 2

1

1 1

1

1 1

1

1 1

( )

( )( )

( )

( ) ( ). . .

( )

( ) ( )

Private Sector Project Evaluation Comparing two projects

R&D project Advertising project

Choice depends on interest rate (see bolded #s)

Annual Net Return PV

Year R&D Advertising r = R&D Advertising

0 -$1,000 -$1,000 0 $150 $200

1 600 0 0.01 $128 $165

2 0 0 0.03 $86 $98

3 550 1,200 0.05 $46 $37

0.07 $10 -$21

Internal rate of return

The internal rate of return is the discount rate needed to make the present value of a project equal to zero

0)1(

...)1(1 2

221100

TTT CBCBCB

CB

Internal rate of return versus NPV Note that internal rate of return does not necessarily

imply which project to do Project X has the higher internal rate of return Project Y has the higher present value Do Y

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

Assume 6 percent interest rate in calculating profit

Benefit-cost ratio

Benefit-cost ratio is simply B / C If this ratio is greater than one, then benefits

exceed costs The project is worth considering when the benefit-

cost ratio exceeds one We should only use benefit-cost ratios to

determine if a project is worth considering Use present value criteria to determine which

project gets done

Valuing public benefits and costs There are many ways to value public benefits

and costs Market prices Adjusted market prices and shadow prices

Problems due to monopoly Problems due to taxes Problems due to unemployment

Consumer surplus Economic behavior

Value of time Value of life

Market prices

Market price is a good measure of marginal social cost if the market is perfectly competitive with no government intervention Problem: Many markets have market power

Adjusted market prices

There are instances in which social marginal cost is not clear Underlying social MC is known as shadow price

Examples where social MC is not clear Monopoly: Market power controls price Taxes: Taxes change price Unemployment: Lack of employment makes

valuing a worker’s skills difficult

Consumer surplus

Decisions by a single firm typically have minimal consequences on a market

Prices often change substantially with some government projects Consumer surplus

can also change substantially with the implementation of government projects

Pounds of avocadosper year

Pric

e pe

r po

und

of a

voca

dos

Da

Sad

A0

Sa’

$1.35

$2.89b

c g

A1

e

Increased CS when price drops from $2.89 to $1.35 per pound

Economic behavior

Some things that are valuable are not formally traded Time

“Time is money” for each person Convenience

Driving versus public transit Life

How much is a life worth? Lost earnings and value of leisure time Probability of death versus wages in dangerous industries

Certainty equivalent

If people were risk neutral, utility would be linear

Most people are risk averse Concave utility function Expected utility of a gamble is less than the utility

of the expected value More on uncertainty in Chapter 9

Calculating the Certainty Equivalent Value

75% probability of gaining y

CE Value: An example

Let our two possible incomes be $6,400 (E) and $10,000 (E + y) Each possible income has probability of 0.5 of occurring

U(x) = x½

A gamble versus a sure thing

Let our two possible incomes be $6,400 (E) and $10,000 (E + y) Each possible income has probability of 0.5 of

occurring U(x) = x½ How much money am I willing to take to be

indifferent to the above gamble?

Expected income of the gamble Recall expected value from last Wednesday’s

lecture ½ ($10,000) + ½ ($6,400) = $8,200

Expected utility of the gamble U($10,000) = 100 U($6,400) = 80 Expected utility of the gamble

½ (100) + ½ (80) = 90

Certainty equivalent value

This risk averse person will be indifferent between the following two options $10,000 with probability 0.5 and $6,400 with

probability 0.5 Some amount of money with certainty

How much?

Notice that the first option has an expected utility of 90 How much money (paid with certainty) will lead to

a utility of 90?

Certainty equivalent value

We need to find some y such that U(y) = 90 y½ = 90 y = 8100 The certainty equivalent value is 8100

Recall that the expected income of the gamble is 8200 This risk-averse person is willing to lose $100 in

expected income to remove all risk

Summary

Welfare economics is important in determining what outcomes are efficient

Market failure can occur when there are not competitive and complete markets

Cost-benefit analysis helps to determine which projects are most useful to society

Certainty equivalent value determines how much money a risk-averse person is willing to give up in order to remove risk

End of Unit 1

This concludes our tools lectures Beginning Wednesday: Unit 2

Public goods Externalities Voting Government growth Education

For Wednesday: Read Ch. 4 Public goods

See you Wednesday

What type of utility function do you think gamblers have?