EC201 Microeconomic Principles I
[Answer ALL questions. If during this examination you feel you need to make additional assumptions in order to proceed, then please do so stating your assumptions clearly].
Question 1 微观经济学原理test代考
Angela has income m and faces prices p1 and p2 for consumer goods 1 and 2, respectively. Her preferences are described by utility function u(x1, x2).
(a) Define uncompensated demand. [5 marks]
(b) If a tangency exists between Angela’s budget line and an indifference curve, can we always conclude that Angela’s utility is maximised at that bundle? [5 marks]
(c) If Angela’s utility is maximised at a particular consumption bundle, must this bundle be a tangency between her budget line and an indifference curve? [5 marks]
Question 2 微观经济学原理test代考
Ted’s preferences over goods 1 (fuel) and 2 (food) are described by utility function u(x1, x2) and satisfy non-satiation and convexity. For Ted both fuel and food are normal goods.
(a) Define the compensating variation of a price increase. [5 marks]
(b) A fuel tax t is introduced raising the price of fuel from p1 to p1 + t. The price of food is unchanged. Illustrate the effect of the fuel tax on Ted’s budget constraint and on his uncompensated demand for fuel. [10 marks]
(c) To prevent protests over the rise in the price of fuel, the government gives Ted and others like him the compensating variation of the fuel price increase. Illustrate the effect of this on Ted’s
demand for fuel. Can Ted’s fuel consumption be higher than when the price of fuel was p1? [10 marks]
Question 3 微观经济学原理test代考
Pedro is an expected utility maximiser with a utility function u(W)=2√ W, where W denotes wealth. Pedro’s initial wealth is 36, but he faces a risk of flood damage of 20 with probability ½ (and no damage otherwise).
(a) Calculate Pedro’s expected utility and his expected wealth without insurance. Find his certainty equivalent and use it to explain why Pedro is risk averse. (Note: no diagram is required). [10 marks]
(b) Pedro can buy insurance at a premium p per unit. How much insurance will Pedro buy if premium p = ½ ? Illustrate Pedro’s situation in a state-contingent income space diagram, clearly indicating Pedro’s wealth in the two states before and after purchasing insurance. [10 marks]
(c) Pedro’s situation can be viewed from two perspectives.
Perspective A: Wealth 36 and loses 20 with probability ½ if it floods
Perspective B: Wealth 16 and gains 20 with probability ½ if it does not flood
Briefly explain why some decision-makers may view these two perspectives of the same situation differently. [5 marks]
Question 4 微观经济学原理test代考
The function c(r, w, q) is the cost function associated with production function f(K, L) = K¼L½ , where q is output and inputs are capital K and labour L, with factor prices r and w, respectively.
[Note: you do not need to derive c(r, w, q) to answer this question].(a) What returns to scale does the production function display? [5 marks]
(b) If both r and w increase by 40%, by how much would c(r, w, q) increase? [10 marks]
(c) Explain the distinction between short run and long run total cost. Suppose K is fixed at K* = 1. Find the short run total cost function s(r, w, K*, q) for f(K, L) = K¼L½. [10 marks]
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