14.01SC Principles of Microeconomics Scholar, Final Exam Solution Set

14.01 Fall 2010: Final Exam Solution Set 1. True/False/Uncertain Questions (48 points) In this section, write whether each statement is True, False or Uncertain. You should fully explain your answer, including diagrams where appropriate. Points will be given based on your explanation. (a) (4 points) A uniform pricing monopolist has an upward sloping MC curve. Claim: a price ceiling set below the monopoly price will increase welfare relative to the monopoly outcome (assume the monopolist does not shut down). Uncertain. For a certain range of prices, a binding price ceiling will increase welfare because it forces the monopolist to be a price taker and output increases (q moves toward the perfectly competitive outcome). However, if the price ceiling is low enough then the monopolist could produce even less output than the unregulated monopolist and therefore welfare is lower. (b) (4 points) A large box of paper towels which will last you 2 years is on deep discount at Wal-Mart, saving you $1 per roll. Claim: a rational consumer who has perfectly inelastic demand for paper towels should always purchase this large box instead of paying a higher price for individual paper towel rolls. False. For this purchase, you pay a large upfront cost to save dollars in the future. If interest rates are sufficiently high, it is better for you to not buy this boz, since you can earn interest on the money you would have used to buy the big box of paper towels. (c) (4 points) In an oligopolistic market with identical firms, the market price is higher when there are two firms in the market than when there are 100 firms in the market. Uncertain/False This may be true in a market with Cournot competition, but under Bertrand competition any market with more than one firm will have price equal to marginal cost. Even in the Cournot case, if the demand curve is perfectly elastic price will not depend on the number of firms. (d) (4 points) The government of a developing country is worried about the adverse effect that the high interest rate in the economy has on investment. Claim: Since a low interest rate makes more projects have positive NPV, investment in this economy will increase if the government imposes an interest rate cap. False. An interest rate cap below the equilibrium interest rate will lower the supply of funds and increase the demand, leading to excess demand for funds in the capital market. The level of investment in the economy will fall, since the supply of funds is lower. (e) (8 points) There are three individuals in society: Bob, Milton and Paul. There are three possible social states which result in different utility levels for the three individ- uals: 1 Are the following True/False/Uncertain? Explain. (i) No government would choose social state C. True. Social state B always dominates state C since, everybody is better off under B compared to C. (ii) There is a government election in this society and there are two candidates: a Rawlsian and an Utilitarian government candidates. Claim: In a democratic election (majority win election) a Utilitarian candidate will be elected since more individuals in this society prefer the Utilitarian candidate. False. A Rawlsian government would choose social state B, whereas an Utilitarian government would choose state A. Since Bob and Paul are better off under B than under A they would vote for a Rawlsian government. (f) (8 points) Jon spends his entire budget on espresso and gasoline. You have the fol lowing data on his choices: Table 1: Jon's budget Price Price shot espresso Gallons purchased 9 Total income gallon gasoline L 22 February March 2 5/2 3/4 10 31 April 3 Shots purchased 4 8 1/2 8 14 31 Assume Jon's preferences are monotone, the same over the three months, and that he has no way to save or borrow across periods. Are Jon's choices consistent with utility maximization? The key to these problems is to see if two bundles are affordable in a period and if bundle A is chosen over bundle B, then A is preferred to B. Neither the March nor April bundles are affordable in February. The April bundle is affordable in March but it is not chosen, so March is preferred to April. Checking to see if March is affordable in April, we find that it is not, so this is consistent with utility mazimization. (g) (4 points) Marco's monthly income is $1000. He spends 40% of his income on food and the rest on buying designer clothes. The City Council thinks it is unfair that people spend more than 35% of their income for food. In order to lower the proportion of income going to food, the City Council gives Marco $200. Claim: given that Marco's income elasticity of food is 2, the City Council accomplishes its goal. Originally Marco spends $400($1000-40%) on food. After Marco receives $200 from the City Council, his income increases by 20%. Since his income elasticity of food is 2, his spending on food will increase by 40%(20%+2), which is equal to $560(8400* (1+40%)). Then the proportion of Marco's income going to fond is 47% (560/1200), which is higher than 40%. Thus, the City Council will not accomplish its goal. (h) (4 points) Venus Williams likes both tennis rackets and tennis shoes. She has many of both. Her marginal rate of substitution (MRS) of rackets for shoes is 3, meaning 2 that given the opportunity, she is willing to trade 3 tennis rackets for 1 pair of shoes, or vice versa. Unused rackets and shoes may be returned to the local sporting goods store for a refund. The current price for a racket is $200 and the price for a pair of shoes is $100. Claim: Venus can make herself better off by trading in some tennis rackets in return for some shoes at the market rate. True. Since Venus has many tennis rackets (Y) and tennis shoes (X) she hasn't worn, she can return or exchange them. Since her MRSy forx 3, she would be willing to give up 3 rackets for one pair of shoes. However, since the price ratio is Px/Py$100/$200 1/2, she's only required to give up 1/2 racket for each eztra pair of shoes (if you don't like the way that sounds, an equivalent statement is that she's required to give up 1 racket for every 2 extra pairs of shoes). Venus would make herself happier by trading in some tennis rackets in return for some shoes at the market rate. (1) (4 points) Suppose that there are two types of drivers: speeders and slowpokes. Speed- ers are more likely to have accidents, and have expected costs of $5,000 a year in car repair bills. Slowpokes on the other hand have expected costs of only $100 a year. Sup- pose further that speeders are risk-loving and that slowpokes are risk-averse. Claim: a (risk-neutral) private car insurance company will insure only slowpokes even if there are no asymmetric information or moral hazard problems in this market. True speeders will never want to buy fair insurance, so the insurance market will lose money on average by insuring speeders and make money by insuring slowpokes. Insurers can offer a policy aimed at slowpokes and speeders will never try to buy the policy. (j) (4 points) Please outline the pros and cons of the U.S. adopting a tax system with a heavier reliance on a consumption tax. A consumption tax encourages savings, which may be positive for growth, especially given that savings rates in the U.S. are currently extremely low. On the other hand, a consumption tax is generally regressive since the poor consume a higher fraction of their income than the rich, and will thus pay a higher proportion of their income in taz than the rich (unlike the income tax, which is progressive). 2. Uncertainty (20 points) An economy has two agents, Bill and Bob. Bill has $110, and Bob has $200. Utility of agents in this economy is characterized by the following function of income: U= (1) = log(y-60) if y<1 160 if y≥ 160 The minimum level of income possible in this economy is 60. Each agent is about to choose a new business venture, and has a choice between project A and project B. Neither project requires any investment up front. Project A yields revenues of 20 with probability and revenues of -10 with probability. Project B yields revenues of 4 with probability one-half and revenues of 5 with probability one-half. Throughout this problem, assume that fractional income is possible. (a) (5 points) Which project would each agent choose? Provide intuition for your answer. 3