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DEPARTMENT OF ECONOMICS SAN JOSE STATE UNIVERSITY MASTER’S COMPREHENSIVE EXAMINATION DECEMBER 2, 2016 6:00 P.M. TO 9:30 P.M. PROCTOR: HUMMEL & LIU INSTRUCTIONS: 1. Answer ONLY the specified number of questions from the options provided in each section. Do not answer more than the required number of questions. Each section takes one hour. 2. Your answers must be on the paper provided. No more than one answer per page. Do not answer two questions on the same sheet of paper. 3. If you use more than one sheet of paper for a question, write “Page 1 of 2” and “Page 2 of 2.” 4. Write ONLY on one side of each sheet. Use only pen. Answers in pencil will be disqualified. 5. Write ------ END ----- at the end of each answer. 6. Write your exam identification number in the upper right-hand corner of each sheet of paper. 7. Write the question number in the upper right-hand corner of each sheet of paper. Section 1: Microeconomic Theory—Answer Any Two Questions. 1A. Answer the following questions for a consumer with utility function U(x,y) = x1/3 y2/3 and a budget constraint I = pxx + pyy, where “I” is the total amount of income the consumer has available to spend, px is the price of x and py is the price of y. a. What is the marginal utility of x? of y? b. Define the economic meaning of the term “marginal utility.” c. What is the marginal rate of substitution for the given utility function? d. Define the economic meaning of the term “marginal rate of substitution.” e. Using the Lagrange method, find the demand curves for x and y. Use lambda λ as the Lagrange multiplier. f. Define the economic meaning of the Lagrange multiplier as used in this problem. (over) -1- DEPARTMENT OF ECONOMICS SAN JOSE STATE UNIVERSITY MASTER’S COMPREHENSIVE EXAMINATION DECEMBER 2, 2016 6:00 P.M. TO 9:30 P.M. PROCTOR: HUMMEL & LIU 1B. Consider a firm that sells a product in two isolated markets. Suppose that such a firm also has some monopoly power to influence the different prices it faces in the two markets by adjusting the quantity it sells in each. Economists generally use the term “discriminating monopolist” to describe a firm having this power. Suppose that the discriminating monopolist faces two independent demand functions: P1 = a1 –b1 Q1 P2 = a2 – b2Q2 for market areas 1 and 2, respectively. Suppose, too, that the cost function is C = c(Q1+Q2) and all constants are positive. a. How much should be sold in two markets to maximize total profit? What are the corresponding prices? b. What is the monopolist’s pricing strategy if it becomes illegal to discriminate? c. Discuss the consequences of imposing a tax of 5 dollars per unit on the product sold in market 1. d. Discuss the effects of a tax imposed in market 2 of t dollars per unit of Q2. 1C. Once upon a time, in an ancient land perhaps not too far from US, an economy consisted of three industries- fishing, forestry, and boat building. To produce 1 ton of fish requires the service of fishing boats. To produce 1 ton of timber requires tons of fish, as extra food for the energetic foresters. To produce 1 fishing boat requires tons of timber. These are the only inputs needed for each of these three industries. Suppose there is no external demand for fishing boats. a. Find what gross output each of the three industries must produce in order to meet the external demands of d1 tons of fish to feed the general population, plus d2 tons of timber to build houses. b. Based on the solutions from part (a), what are the sign restrictions should be imposed on , and . -2-