Lent Term 2018 Exam PDF

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January

2017/8 syllabus only – not for resit candidates

This paper contains questions: marks). Answer questions.

LSE LT 2018/EC202

short questions (10 marks each) and

long question (60

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This paper contains five questions: four short questions (10 marks each) and one long question (60 marks). Answer all questions. 1. Suppose a monopoly faces the inverse demand function p(q) = q −a and has the cost function C(q) = b + cq 2 and where a, b, c are all positive constants. (a) What is the elasticity of the demand function? [2 marks] (b) What are marginal revenue and marginal cost? [3 marks] (c) Discuss the profit-maximising monopolist’s policy (i) if a < 1 (ii) if a > 1. [5 marks] 2. Consider a consumer’s choice over consumption bundles, where each consumption bundle x is an n-vector with components consisting of real numbers xi ≥ 0. Briefly explain: (a) what assumptions are usually required for a weak preference relation to be representable by a continuous utility function; [5 marks] (b) what the meaning is of a quasiconcave utility function. [5 marks] Pn 3. A person has preferences i=1 αi log(xi ) Pn represented by the utility function where αi > 0 and i=1 αi = 1. (a) Find the consumer’s cost (expenditure) function [5 marks] (b) If the price of good 1 falls while all other prices stay the same, which is greater, the compensating variation or the equivalent variation? [5 marks] 4. Mark each of the following true or false; in each case briefly explain your answer: (a) If an exchange economy is replicated indefinitely the core of the economy shrinks to a single allocation. [2.5 marks] (b) By Walras’ law, the sum over all goods of price times excess demand must equal zero, but only in the neighbourhood of equilibrium. [2.5 marks] (c) A general equilibrium will exist only if the weak axiom of revealed preference is satisfied by all excess demand functions. [2.5 marks] (d) In a general equilibrium it is not necessarily the case that excess demand equals zero in every market. [2.5 marks]

LSE LT 2018/EC202

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5. In the market for a single homogenous good there are N price-taking firms. Each firm has the cost function 16 + q 3i , where qi his the output i of firm i. p The market demand for the good is given by N A − p/3 where p is the market price and A is a positive parameter. (a) Find average cost and marginal cost for firm i. [4 marks] (b) What is the smallest positive amount that the firm would supply to the market? [6 marks] (c) Suppose that N = 1 (but the firm still acts as a price-taker). If A = 6, show that the equilibrium price is 27 and the firm supplies 3 units of output. [15 marks] (d) Continue to assume N = 1. What is the equilibrium price and the quantity supplied in the cases A = 2, A = 3, A = 4? [15 marks] (e) Now suppose that N is a very large number, but that other aspects of the problem remain the same. Explain how, if at all, the market price and quantity supplied by each firm would change for the cases A = 2, A = 3, A = 4, A = 6. [20 marks]

LSE LT 2018/EC202

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