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L1061: ADVANCED MICROECONOMICS

SECTION A

[30 marks]

Attempt ALL questions for a maximum of 5 marks each

State whether the following statements are true or false and explain your answer in each case in no more than 3 lines. (6 questions, 5 points each, 30 points total)

1)  A seller will always get identical revenue whether she runs an English auction or a first price sealed bid auction.

2)  With one dimensional policy space and any type of preference structure, the social choice following a majority voting system will select the outcome most preferred by the median voter.

3)  With the right set of endowments, any Pareto Efficient allocation can be achieved as a competitive general equilibrium.

4)  In repeated games, cooperation becomes harder to achieve as the players become more patient (i.e. the discount factor becomes higher).

5)  When prospective employees are able to signal their ability, employers are no better off,    employees with lower productivity are definitely worse off, and even employees with higher productivity might be worse off.

6)  Under a Rawlsian social welfare function , a society with one million poor people with a utility of 10, has the same social welfare as a society with 999,999 rich people with a utility of 1000 and one poor person with a utility of 10 .

 

SECTION B

Attempt ONE question for a maximum of 40 marks

7)  Consider a competitive exchange economy with two individuals, Adam and Beth, and two        goods, candy bars X and cookies, Y. The economy has 30 units of each good. Initially, Adam   has 30 candy bars, and Beth has 30 cookies. Preferences are presented by the following utility functions:

UA  = XA(1)/3YA(2)/3

UB  = XB(1)/3YB(2)/3

Where UA  represents Adam’s preferences and UB  represents Beth’s. Let pY  = 1 and pX  = p .

a.  Write down the budget constraint for each consumer.

b.  Write down each consumer’s constrained optimisation problem.

c.  Find the demand curves for the two goods for Adam and Beth.

d.  Write down two market clearing conditions. Hence find the Walrasian equilibrium relative price and allocation of this economy.

e.  Draw an Edgeworth box, putting good X on the x-axis and good Y on the y-axis. Identify  the initial endowment, the budget line and the Walrasian equilibrium allocation; sketch     indifference curves for each consumer at the Walrasian equilibrium allocation.

f.   A government official proposes a redistribution of goods between Adam and Beth in order to attain allocation (XA, YA ) = (XB , YB ) = (15, 15). Sketch the utility possibilities set and        identify the competitive general equilibrium allocation and the proposed allocation in your diagram. Which of the two allocations would a Rawlsian social planner prefer? How about a Utilitarian social planner? Explain your answer.

8)  Michael, a farmer, has an initial wealth of 100. He can invest all his wealth in planting a new crop, which has a 50:50 chance of succeeding. If the crop succeeds, his final wealth will be 196, but if it fails,  his final wealth will  be 25.  Michael’s  preferences over  monetary outcomes, y , are summarised by the utility function: U(y) = 20y1/2

a.  Find the certainty equivalent of Michael’s risky opportunity and explain why Michael will prefer not to plant the new crop.

b.  Peter, also a farmer, has the same preferences and initial wealth as Michael. Peter suggests to Michael that they each invest 50 in planting the new crop in Michael’s farm and divide the yield equally. Should Michael accept Peter’s offer? Illustrate and explain Michael’s choice in a diagram.

c.  Suppose instead Peter can use his wealth to plant the new crop in his own farm, and has    the same chances of success and failure as Michael, though crop success or failure in each farm is independent. Now Peter suggests they each plant the new crop on their respective  farms and divide total proceeds equally between them. Should Michael accept Peter’s offer? Explain your answer.

d.  Suppose Michael’s initial wealth were 200. Show he is now willing to plant the new crop in  his farm. Use the Arrow-Pratt coefficient of absolute risk aversion to explain why Michael     displays less risk averse behaviour when he gets wealthier.


SECTION C

Attempt ONE question for a maximum of 30 marks

9)      What limitations are there in making social choices based on individual preference orderings? How might equity considerations be incorporated into a social welfare function? (Word limit is

500 words)

10)   Since employees can always be induced to work hard with sufficient provision of incentives, moral hazard is not a problem.” Use the Principal-Agent model to evaluate the validity of this statement. (Word limit is 500 words)

11)   The first welfare theorem and the Coase theorem convey the same message: self-interested economic agents can bring about efficient outcomes. Discuss . (Word limit is 500 words)