Section A (This section counts for 40% of the exam mark) Question 1

a)  Answer each part of the following question. Show the appropriate mathematical steps. You should also explain your answer and the process intuitively (you can use diagrams too).

I.     Suppose there are two consumers in an exchange economy, consumer A and consumer B, who consume only two goods, X and Y, available in the economy. There are 20 units of X available and 20 units of Y.

Assume A’s preferences are described by  =  . 5 0. 5  and B’s preferences are described by  = 2  , where  ,  ,  , and  are the consumption of X and Y by consumers A and B, respectively. Now derive an equation for the contract curve. [Word limit: 50] [10 marks]

II.     Suppose that consumer A has an initial endowment of 5 units of Xand 15 units of Y, and consumer B has the remainder of what’s available. Their preferences are the same as in part (I). Show, using the concept of MRS and the Edgeworth Box, that a trade could benefit both consumers. [Word limit: 50] [5 marks]

III.     Given the same preferences, now assume the consumers can trade as much as they like at the prices of  = 1  and  = 1. Starting out with the same endowments as in part (I), how much will each consumer want to buy/sell of each good? Is the result a competitive equilibrium? [Word limit: 100] [5 marks]

b)  As we discussed in the lecture, Vickrey auction (1961) is considered to be demand revealing as each rational bidder’s dominant strategy is to bid their true value.  However,  experimental  studies  document  overbidding  behaviour  as bidders could increase the probability of winning the auction by overbidding without adding huge costs of losing (as they pay the second highest bid). Some people criticise such results from lab experiments—they are not that sincere in choosing their actions in the lab because they receive the monetary endowment for free. To address such a concern, propose an experimental design that can examine bidders’ sincere biding behaviour, given induced and independent private values and Vickrey auction in the lab. [Word limit: 500] [20 marks]

Section B (This section counts 60% of the exam mark)

Answer TWO questions from this section.

Question 2

a)  [Word limit 500] Consider the following Public good game. There are 4 players in a group and each player has £y as endowment. Player i’s  pay-off function is given by:   =   −   +  ∑=1    , where    is player i’s voluntary contribution to the public good,   is the marginal per capita return from a contribution to the public good  and  0 <  < 1 < 4 .    Following  rational  choice  theory,  if  it  is  common knowledge  that  every  player  is  rational  and  self-interested  and  they  can  do backward induction, the dominant strategy of each player is to give zero to the public good (i.e.   = 0). Suppose, a researcher conducts a finitely repeated public good game with the randomly chosen players in each group over all rounds and the same pay-off function described above.

i.     What results would the researcher expect based on the results from the existing literature (e.g. Fehr and Gächter 2000) ? [5 marks]

ii.     Explain intuitively whether an institution with pre-commitment of contribution through an endogenous group formation can improve the outcome? Briefly state how one can conduct an experiment to test this. [15 marks]

a)  State and explain the Coase mechanism. Critically evaluate the relevance of Coase mechanism [Word limit 500] [10 marks]

Question 3

a)  Consider  a  model  of voluntary  incentive  mechanism  design for  protecting endangered   species   on   private   land.  After   a   regulator   has   identified endangered species on private land, she wants private landowners to retire the land from production. The landowners suffer a monetary loss when they retire land for species protection. They would voluntarily participate in the program of species protection if they received monetary compensation from the regulator to offset their loss. The regulator designs a contract to maximize social welfare from species  protection subject to the  landowner’s  participation constraint. Social welfare is the utility of the individual landowner and social benefits from species protection, minus the monetary compensation scaled by the social value of public funds.

Assume:

    Each landowner has fixed land-endowment, i.e.,  acres, and th landowner

retires   (with   ≤ ) acres of land

    Suppose, there are only two types of landowners—high (who own high quality

land and that means they have higher opportunity costs of land retirement) and

low

    Each landowner’s rent function from land is   ( −  ,   ), where   denotes

land quality,   = high, low. The rent function is increasing and concave; and marginal-rent is increasing in types.

   Also note that (i)  ( ,   ) is the rent when a landowner does not participate in

the program; and (ii) landowners are risk neutral

      denotes monetary transfer from the regulator to the landowner                         ()  denotes social benefit from species  protection when    acres of land

retired. This function is concave in acres

i.         Under conditions of complete information about the land quality, the regulator knows the value of land and offers a contract specifying a monetary compensation for the land’s retirement. Set up the objective function and identify the constraints. Comment on the optimal transfer the farmers would receive in this case. [Word limit 100]  [5 marks]

ii.        Under asymmetric information about the quality of land, the regulator cannot distinguish the types—she does not want to disincentives the high-type by offering less money and does not want to pay higher than the true opportunity costs for the low type (due to the opportunity costs of  public fund). The  regulator  seeks  to  maximize  social welfare  by choosing an optimal contract, designed to extract private information cost-effectively and protect the habitat efficiently. Set up the objective function and identify the constraints. Assuming interior optimal solution, comment  on the  optimal transfers that  each type  of farmers would receive in this case. Explain why this would be a second-best solution. [Word limit 150] [20 marks]

a)  Explain (intuitively and with Edgeworth box diagram) the role of the Second Welfare Theorem reaching a more equitable Pareto equilibrium. [Word limit 200] [10 marks]