Consider the following scenario: allocation X is socially preferred to allocation Y only if everyone prefers X to Y. This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.

SECTION A - Attempt ALL questions

1. Answer all parts of this question.

a) Consider the following scenario: allocation X is socially preferred to allocation Y only if everyone prefers X to Y. This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.

i) Firstly, explain what do we mean by a social choice rule (Maximum 75 words).

ii) Secondly, discuss the shortcomings of the rule stated in the scenario above, as a rule for making social decisions (Maximum 130 words).

b) Explain Arrow`s impossibility theorem (Maximum 130 words).

c) According to Arrow`s Impossibility Theorem we cannot use a welfare function to arrive at a social preference that is complete, reflexive and transitive. Do you agree with this statement? Discuss your answer (Maximum 165 words).

d) Now suppose a group of friends want to decide on a game to play. They agree to play the game that is preferred by the majority, using pairwise majority rule. Therefore, they will choose the game that defeats any other game in a pairwise vote. The preferences over the games are as follows:

Can these friends decide on one of these games while satisfying the transitivity condition? Discuss. You can use a graph in your discussion (Maximum 165 words. A graph would count as 20 words).

e) Would your answer in part (d) change if the preferences were as follows? Explain. You can use a graph in your discussion (Maximum 165 words. A graph would count as 20 words).

f) Discuss which of the four optimal properties of social choice as stated by Arrow is now restricted under the pairwise majority voting scenario in part (e) above (Maximum 100 words).

2. Answer all parts of this question.

a) Firm A faces the industry demand function p(q) = 8 - 0.2q. The constant marginal cost of producing an extra unit of output is 1.

i) Write down the firm`s maximisation problem.

ii) Find the first order condition for the firm`s problem and hence find the profit maximising output of this firm.

iii) What will be the industry price when the firm produces at its profit maximising capacity?

b) Now consider two firms A and B operating in the same industry and selling a homogenous product. The industry`s demand is the same as in part (a) above and A`s marginal cost is the same as in part (a) above. Firm B`s marginal cost is 2 per extra unit of output. The two firms compete over the market share. Recall that in a Cournot competition, each firm chooses its own output to maximise its profit given the output that it expects the other firm to produce.

i) What is a best response function ? Write down the best response functions for firms A and B.

ii) Solve the two equations in part b(i) to find the Cournot equilibrium output of the two firms and hence find the Cournot equilibrium price.