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DEPARTMENT OF ECONOMICS SAN JOSE STATE UNIVERSITY MASTER’S COMPREHENSIVE EXAMINATION DECEMBER 4, 2015 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. Consider an economy divided into an agricultural sector (A), an industrial sector (I), and a service sector (S). To produce one unit in sector A requires 1/2 unit from I. To produce one unit in sector I requires 1/4 unit from S. To produce on unit in sector S requires 1/2 unit from A. Suppose external demands in each of the three sectors are 100 units. a. Set up the Leontief model equations for this economy. b. Rewrite the system of simultaneous equations from part (a) in a matrix form AX = b. c. Use Cramer’s Rule to find the number of units that have to be produced in each sector in order to meet the external demands. 1B. One of the most important insights in microeconomic price theory is: “There are two effects of a price change.” For example, when sandwiches are $7 Arthur purchases 3, when the price increases to $8 Arthur purchases 2. When the price increased, there were two effects that combined to cause the Arthur to buy 1 less sandwich. a. For consumers: Identify and define the two effects of a price change and describe how those two effects interact to determine how the consumer’s level of consumption changes. You may use a mathematical, graphical or verbal approach to answer this question. b. For producers: Identify and define the two effects of a price change and describe how those two effects interact to determine how the firm’s use of an input changes. You may use a mathematical, graphical or verbal approach to answer this question. (over) -1- DEPARTMENT OF ECONOMICS SAN JOSE STATE UNIVERSITY MASTER’S COMPREHENSIVE EXAMINATION DECEMBER 4, 2015 6:00 P.M. TO 9:30 P.M. PROCTOR: HUMMEL & LIU 1C. Each of two firms A and B produces its own brand of a commodity in amounts denoted by Q1 and Q2, which are sold at prices P1 and P2 per unit, respectively. Each firm determines its own price and produces exactly as much as is demanded. The demands for the two brands are given by: Q1 = 25 - 5P1 + 2P2 Q2 = 20 + 4P1 - 2P2 Firm A has total costs 5 + Q1, whereas firm B has total costs 3 + 2Q2. (Assume that the functions to be maximized have maxima, and at positive prices.) a. An anti-trust authority prohibits collusions, so each producer maximizes its own profits, taking the other’s price as given. If P2 is fixed, how will A choose P1? (Find P1 as a function of P2) If P1 is fixed, how will B choose P2? (Find P2 as a function of P1) b. Sketch the price equations for firms A and B in part (a) on a xy-plane. Label the x-axis as P1 and the y-axis as P2 c. Under the assumption in part (a), what constant equilibrium prices are possible? (Hint: Find the point of intersection.) 1D. Matt spends all of his income on two goods: beer (B) and tacos (T). He considers beer and tacos to be compliments with one another. Matt’s preferences can be represented by the utility function: min (2B, T). The price of a bottle of beer is $6 and the price of each taco is $2 at Chacho’s Restaurant. Matt is able to spend a total of $60 per week on these two goods. a. How much utility does Matt gets from consuming tacos? How much utility does Matt get from consuming beer? b. What is the mathematical expression for Matt’s budget constraint. c. If Matt is consuming a bundle of 2 beers and 2 slices of tacos, would that bundle maximize Matt’s utility? Carefully explain why or why not. d. Draw a two-dimensional graph with beer on the horizontal axis, and tacos on the vertical axis. (Suggestion: Use a whole page so your graph is big, clear and readable. You will add more to it in part (f) later.) —Draw and label the 2 beers, 2 tacos bundle from part (c). —Draw Matt’s indifference curve through the (2, 2) bundle and label it with the level of utility it represents. —Draw and label Matt’s budget constraint on the graph. e. Given Matt’s preferences and his constraint, mathematically determine the optimal bundle of beer and tacos for Matt? f. On the graph from part (d): —Draw and label that bundle on your existing graph. —Draw the indifference curve that goes through that bundle. —Label the indifference curve with the level of utility it represents. -2-