Economic Principles II : Microeconomics Revision Lecture 2 Multiple choice questions 1. Suppose a consumer is seen to buy a bundle (5, 10) of x1 and x2 (respectively) at prices (2, 2) (i.e., p1 and p2, respectively). The consumer is also seen to buy bundle (3, 12) at prices (2, 1.5). The following statement can be made about the consumer. a. She violates the Weak Axiom of Revealed Preference (WARP) while choosing the bundle (3, 12), because the bundle (5, 10) is revealed preferred to the bundle (3, 12). b. She violates WARP while choosing the bundle (3, 12), regardless of the bundle (5, 10) is affordable or not. c. She violates WARP while choosing the bundle (5, 10), because the bundle (3, 12) is affordable. d. She does not violate WARP while making any of the choices listed above. 2. A consumer’s marginal utility from food is given by u F = aF a−1C b and marginal utility from clothing is given by uC = bF a C b−1 , where F and C refer to the quantities of food and clothing respectively. Let the prices of food and clothing be denoted by pF and pC respectively. Which of the following statements hold for the consumer’s choice? a. If pF = pC, the consumer will buy 2 units of clothing for every unit of food. b. The marginal rate of substitution of food for clothing will be constant along any given indifference curve. c. If pF = 2 pC, the consumer would like to buy (2b/a) units of clothing for every unit of food. d. The consumer’s expenditures on food and clothing will be equally divided because of the Cobb-Douglas preference. 3. Consider the following table. p1(£) 4 2 2 4 4 p2 (£) 4 4 4 4 2 M (£) 100 100 68 80 80 Optimal bundle (x1, x2) 15 10 25 12.5 20 7 12 8 10 20 Suppose bundle (15, 10) and bundle (20, 7) are on the same indifference curve. Then the following can be said. a. Due to substitution effect of a reduction in p1 the consumer buys 5 more units of x1 and 3 units less of x2. b. The price effect of p1 causes an increase in the consumption of 10 units of x1. c. The compensating variation in income is a reduction of £32. d. The income effect adds only 5 units of x1. e. All of the above f. None of the above Explanation: The key to this question is identifying that bundle (15, 10) and (20, 7) can be compared to measure the substitution effect of a fall in p1. Further, bundle (25, 12.5) can be considered to capture the total price effect. Statements (a)-(d) then appear true. See the graph above Problems 1. Suppose Mr Smith’s preference structure is given by u = ax1 + bx2. His neighbour Mr Jones’s is given by u = Min [ax1, bx2]. Both have the same income M and the two goods cost p1 and p2 per unit respectively. a. Derive the Marshallian demand functions of Mr Smith and Mr Jones. Show your answer graphically. b. Write the Market demand functions of the two goods assuming that they are the only consumers in the market. c. Calculate the own price elasticity of demand for x1 from the individual demand curves, and comment on the finding. ANSWER: a. Smith’s demand: x1 = 0 x1 = M p1 a p2 b a p1 p 2 b p1 if if and x2 = 0 x2 = M p2 a p2 b a p1 p 2 b p1 if if Jones’s demand: x1 = Mb p1b + p 2 a x2 = Ma p1b + p 2 a b. Market demand X1 = Mb p1b + p 2 a X1 = M Mb + p1 p1b + p 2 a p1 if a p2 b p1 if a p2 b and X2 = Ma p1b + p 2 a X2 = Ma M + p1b + p 2 a p 2 p1 if if a p2 b p1 a p2 b c. Own price elasticity of demand: Smith: e11= 0, if p1> (=)(a/b)p2, otherwise equal to -1. bp1 . It is inelastic demand. Jones: e11 = − bp1 + ap 2 2. Mr Aviva’s asset is valued £1600. There is a 20% chance that the asset’s value may drop to £625. His utility function is given as u = y where y denotes the value of the asset. a. Calculate the premium that Mr Aviva may be willing to pay to avoid the risk. Compare this with the maximum insurance premium he might be willing to pay to protect himself against the risk. Show your answer on a graph. b. If he buys insurance from a competitive market, what would be his insurance premium and how much cover he would buy? Contrast this answer with the ‘maximum insurance premium he is willing to pay’ found in part (a) and comment on it. Answer: a. See the graph Risk premium= Expected income - Certainty equivalent=36 The consumer is willing to pay maximum of 231 to ensure a certain income of 1369 or the utility of 37. b. For the optimal insurance part, one needs to maximize the expected utility for the desired cover, say D, which require paying a premium of D. The insurance market decides on . However, a competitive insurance market ensures =0.2 (the probability of loss) via the zero profit condition. Then the consumer’s expected utility maximization problem is as follows: Max Eu = 0.2 625 + D − 0.2 D + 0.8 1600 − 0.2 D . The first order condition with respect to D yields: 0.2 0.8 0.8 0.2 − =0 2 625 + 0.8 D 2 1600 − 0.2 D D = 1600 − 625 = 975 That is, the consumer will seek full cover and have complete insurance. However his insurance premium amount is 195 (=0.2 x 975). His actual payment of premium is far less than his maximum willingness to pay (i.e. 231). This is because the insurance market is competitive, which leaves him some ‘consumer surplus’.