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This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON 279 0066 ZB

BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences, the Diplomas in Economics and Social Sciences and Access Route for External Students Microeconomics Monday, 16 May 2011 : 2.30pm to 5.30pm Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to divide their time accordingly. A calculator may be used when answering questions on this paper and it must comply in all respects with the specification given with your Admission Notice. The make and type of machine must be clearly stated on the front cover of the answer book.

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SECTION A

Answer eight questions from this section (5 marks each).

1. Consider an economy with two goods, Bread (B) and Milk (M). Jo likes bothgoods and her marginal rate of substitution between the two goods is dimin-ishing. The price of M is 3 and the price of B is 1. At the current consumptionbasket, her marginal rate of substitution of Milk for Bread (MRSM,B) is 2. Is Jocurrently at her optimum consumption? If your answer is yes, show why. Ifyour answer is no, clarify how her consumption basket should change to reachher optimum.

2. Suppose that the government subsidizes housing expenditures of low-incomeconsumers by providing a dollar-for-dollar subsidy to a consumer’s housing ex-penditure - i.e. if a consumer spends x of his own on housing, the governmentgives him x, making total housing expenditure 2x. Ariel qualifies for this sub-sidy and spends a total of 500 per month on housing: he spends 250 of his ownand receives a government subsidy of 250. Recently, a new policy has been pro-posed that would provide each low income consumer with a lump sum transferof 250 which can be used for housing or other goods. Using a graph, demon-strate whether Ariel would prefer the current program, the proposed program,or would be indifferent between the two.

3. There are two firms in an industry. The output of firm 1 is denoted by q1 andthat of firm 2 is denoted by q2. Let

Q = q1 + q2

The total cost of production for firm 1 is 30q1 and that for firm 2 is 20q2. Thedemand curve is given by

Q = 100 − P

(a) Find the Cournot-Nash equilibrium quantity produced by each firm andthe market price.

(b) If the two firms interact repeatedly, is the outcome likely to be different?Explain informally but carefully.

4. A perfectly competitive market implies a perfectly elastic demand curve, whichthen implies that such a market produces no consumer surplus. Is this true orfalse? Explain carefully.

5. In the long-run equilibrium under monopolistic competition, firms earn a zeroprofit. This is similar to the profit of firms in the long-run equilibrium underperfect competition. It follows that there is no loss of efficiency in the long-run equilibrium under monopolistic competition. Is this true or false? Explaincarefully.

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6. For each of the following statements, state whether the statement is true or false,and explain your answer.

(a) If average product is increasing, marginal product must be less than aver-age product.

(b) If total product is increasing, marginal product must be increasing.

7. It is very expensive to rent a flat in Metropolis. The government of Metropoliswants to use some of its tax receipts to deliver lower rents for its poorer citizens,and decides to subsidize rents for citizens below a certain level of income. Thepoorer citizens mostly live in rented housing in the Eastern part of Metropolis.We also know that the supply of rental housing is very inelastic in the Easternpart due to restrictions on construction. Evaluate this choice of policy. Is thereany other policy that the government of Metropolis could adopt which woulddeliver lower rents for its poorer citizens?

8. Data from a competitive market shows periods in which price is high, salestend to be high, and periods in which price is low, sales tend to be low. Thisimplies that demand is relatively stable, and the pattern of fluctuations in priceand quantity is mostly due to fluctuations in the marginal cost of production ofsellers. Is this true or false? Explain carefully.

9. Consider the production function

Q = LK

where K is the quantity of capital and L is the quantity of labour. Let w denotethe wage rate and r denote the price of capital, where

r = 4w

Derive the demand functions for labour and capital as functions of output (Q).

10. Two firms (1 and 2) must decide simultaneously whether to produce a low out-put (L), a medium output (M) or a high output (H). The payoffs from the dif-ferent output combinations are given by the payoffs in the following game. Ineach box, the first number is the payoff of player 1, and the second number isthe payoff of player 2.

2L M H

L 4,4 2,4 1,51 M 4,2 3,3 0,2

H 5,1 2,0 0,0

Find the Nash equilibria of the game.

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SECTION B

Answer three questions from this section (20 marks each).

11. (a) Oscar’s utility depends upon his wealth W. His utility function is

u(W) =√

W

Oscar’s current wealth is 100, but he faces the risk of losing 60 with proba-bility 1

3 .

An insurance company makes him the following offer: for every dollar thatOscar pays as premium, the insurance company will pay him 3 if the lossoccurs.

i. How much insurance will Oscar buy? [5 marks]ii. Oscar’s friend John has the same current wealth as Oscar and faces

exactly the same risk. However, his utility function is

v(W) = ln W

If the insurance company makes the same offer to John, how muchinsurance will he buy? [5 marks]

(b) Consider an exchange economy with two goods (X and Y) and two con-sumers (A and B). There are 10 units available of each of the two goods.Consumer A is endowed with 5 units of good X and 5 units of Y. Con-sumer B is also endowed with 5 units of good X and 5 units of Y. Thepreferences of the two consumers are as follows. Consumer A has utilityfunction

UA(X, Y) =√

X

and consumer B has utility function

UB(X, Y) = Y

i. Draw an Edgeworth box and draw the contract curve in this economy.[5 marks]

ii. In the Edgeworth box, show the area of mutually beneficial trades be-tween the two consumers. [5 marks]

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12. Consider a market for used cars. There are 10 low quality cars and 10 highquality cars. There are 20 potential sellers with a car each, and 20 buyers. Aseller values a high quality car at 8000 and a low quality car at 4000. A buyervalues a high quality car at 10,000 and a low quality car at 5000. All agents arerisk-neutral.

(a) Suppose quality is unknown to both buyers and sellers. However, bothbuyers and sellers expect a car to be of high quality with probability 1/2.How many cars of each quality would be sold? Write down the interval(s)of possible equilibrium prices. [5 marks]

(b) Suppose quality is observable to sellers but not to buyers. Buyers onlyknow that out of the 20 sellers, 10 offer high quality cars and 10 offer lowquality cars. How many cars of each quality would be sold? Write downthe interval(s) of possible prices. [10 marks]

(c) Is the market outcome in part (b) efficient? If you answer yes, explain why.If you answer no, suggest (informally) a way to reduce the inefficiency.

[5 marks]

13. A competitive market is made up of 100 identical firms. The short-run total costfunction of each firm is given by

C = 5q +q2

4+ 100

where q denotes the output of the representative firm.

(a) Determine the short-run market supply curve. [10 marks]

(b) Calculate the price at which market supply is 2000. [5 marks]

(c) Do you expect the long run equilibrium price in the market to be higher,lower or the same as the price you calculated in part (b)? Explain.[5 marks]

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14. Consider a competitive industry with several identical firms. The market de-mand is given by

QD = 10 − P

where P is the market price. The suppliers have a constant marginal cost ofproduction of 5, and no fixed costs.

(a) Find the equilibrium market price and quantity. [5 marks]

(b) The government grants a subsidy of 1 per unit to the suppliers. Calculatethe new equilibrium price and quantity in the market. [5 marks]

(c) Show that the government expenditure used to pay for the subsidy pro-gram exceeds the sum of the changes in producer and consumer surplus.

[10 marks]

15. Alice and her brother Bill support their elderly parents. There is a single good(call it money). All consumptions are measured in units of money. Alice caresabout the number of units she consumes directly (denoted by yA) and the num-ber of units her parents consume (denoted by x). Her utility function is

uA(x, yA) = x13 yA

Similarly, Bill’s utility function is

uB(x, yB) = x13 yB

where yB is his direct consumption. The parents’ consumption x is simply thesum of the support contributions from Alice (xA) and Bill (xB), i.e.

x = xA + xB

Alice and Bill have an income of 42 each.

(a) Suppose Alice is unable to contribute anything toward the parents’ sup-port, so that Bill must provide for both his own consumption yB, and hisparents’ consumption x. Determine Bill’s optimal choice of x and yB.

[5 marks]

(b) Now suppose Alice is also going to contribute toward the parents’ support.Given any level of contribution from Bill, Alice chooses her optimal con-tribution. Similarly, for any level of contribution by Alice, Bill chooses hisoptimal contribution. What are their equilibrium contributions to supporttheir parents? [10 marks]

(c) Does the equilibrium contributions in part (b) add up to the Pareto optimallevel of support? Explain informally (you do not need to derive the Paretooptimal level of support). [5 marks]

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16. (a) Explain the problem of externalities and discuss how this problem affectsthe conditions for economic efficiency. [8 marks]

(b) In each of the following situations, identify the externality and explainwhether or not the Coase theorem would provide a basis for dealing withthe externality. You must define all relevant economic concepts clearly.

i. The Ganges river in India receives industrial effluents from hundredsof tanneries that operate along its banks. Further, millions of litresof raw sewage are spilled into the river from hundreds of towns andvillages. [6 marks]

ii. Your neighbour has an electrical device that is costly to run, but killsinsects very effectively. The longer he keeps the device on, the fewerinsects appear in your garden. [6 marks]

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