Question 1:

(a) Consider a group of people, A, B, C, ..., and consider the relation, "shorter than". Is this relation transitive?

(b) Explain the statement that averages are not preferred to extremes when an individual's preferences are highly non-convex.

(c) A consumer has a utility function which is linear in the two goods, x1 and x2, that she consumes. Suppose the coefficient on x1 is 3 and that on x2 is 1. Her income is m, and the prices of x1 and x2 are p1 and p2, respectively. Let m = 5, p1 = 2, p2 = 1. Then (i) what is the marginal rate of substitution between x1 and x2, and (ii) what are the optimal amounts of x1 and x2 demanded by the consumer?

(d) Explain, by providing an example, whether it is possible to have decreasing returns to a productive input together with increasing returns to scale.

(e) If a quantity tax is levied on the supplier of a commodity, then how will the deadweight loss of taxation change when market demand becomes less own-price elastic?

Question 2

(a) Why does a monopolist typically produce a different amount compared to what could be produced under a competitive market structure, and in what sense is it inefficient? (12 marks)

(b) Compare and contrast the non-cooperative and cooperative outcomes when duopolists are involved in quantity competition. (13 marks)

(c) Provide an example of a one-shot game where no Nash equilibrium in pure strategies exists.