Final Exam Problems - Intermediate Microeconomic Theory | ECON 306, Exams of Microeconomics

Download Final Exam Problems - Intermediate Microeconomic Theory | ECON 306 and more Exams Microeconomics in PDF only on Docsity! Department of Economics m4MP^r ^* r Rachel Kranton University of Maryland ^Bl^^ ECON 306, Spring 1994 FINAL EXAM BE SURE AND EXPLAIN YOUR ANSWERS Section I. TRUE, FALSE (5 minutes each) 1. Both perfect competitors and monopolists maximize profits. Total revenue of monopolist and total revenue of a perfectly competitive firm is price times quantity. Therefore, if the price of an input changes (marginal costs change), the effect on both firms profits'would be the same. 2. Because a monopolist can set both price and quantity to maximize profits, it will charge a higher price and produce more output than an identical firm that acts as a price taker (takes price as given). 3. If the seller of a good knows more about its quality than a buyer, there might not exist a market for that good. ..* 4. Consider a world of only two goods: bananas and oranges. Suppose the price of bananas increases. A consumer would then consume more oranges. 5. An individual who is risk averse will never invest in a risky business venture. 6. Consider a lottery ticket L. For a risk neutral individual, the expected value of the ticket is greater than the certainty equivalent of the ticket SECTION H. SHORT PROBLM (IS minutes) 7. Consider a monopolist producing a good X. The monopolist has increasing marginal costs and a standard decreasing demand curve. a) On a graph, compare the price and quantity a monopolist would set with the price and quantity that would maximize economic welfare. b) Suppose the government regulates the monopoly by imposing a price ceiling. For what range of prices would the government be able to increase economic welfare? For what range of prices would the government decrease economic welfare? SECTION III. LONG PROBLEMS (25 minutes each) 8. Coke and Pepsi, as you know, are very similar products. Suppose each firm can set a High price or a Low price. If both firms set the Low price, they each earn 50 in profits. If both set the High price, they each earn 75. If one firm sets the Low price and the other the High price, the firm that sets the Low price earns 100 and the firm that sets the High price earns 25. Suppose that firms interact for only one period. a) Suppose that firms must set their prices simultaneously. Represent this game in a matrix and solve for the Nash equilibria (or Nash equilibrium). b) Suppose now that Pepsi sets it price first. Represent this new game on a tree and solve for the Nash equilibria (or Nash equilibrium). Are these (is this) Nash equilibria (Nash equilibrium) also perfect? Suppose now that the firms interact T periods and discount future profits by a discount rate r. Assume firms set prices simultaneously in each period. c) Suppose firms have a finite time horizon (T is finite), find the perfect equilibrium that maximizes firms' profits. (Be sure to find any necessary conditions on r). d) Suppose firms have an infinite time horizon (T is infinite), find the perfect equlibrium that maximizes firms' prof ts. (Be sure to find any necessary conditions on r). 9. Esther is risk averse. Her utility of income is given by u(I) = I , where I is income. When Esther is lucky in a given year she is employed and earns 1. When Esther is unlucky, she is unemployed and earns 0. The probability that Esther is lucky in a given year is Vz, and the probability that Esther is unlucky is Vz. a) What is Esther's expected income in a given year? What is Esther's expected utility? What is her certainty equivalent? Suppose now that an Insurance Co. offers Esther the following plan to eliminate the variability in her income. If she has a job, Esther must pay the insurance company Vz + Z. If she does not have a job, Esther receives Vi - Z from the insurance company. b) Under the plan, what is Esther's income if she has a job? What is Esther's income is she does not have a job? What is her expected income? How much does she expect to pay the insurance company? c) Call what she expects to pay the insurance company the "premium." What is the highest premium Esther is willing to pay to the insurance company?