澳门大学经济学研究生入学考试样卷

------------------------------------------------Sample----------------------------------------------- Prepared by Department of Economics University of Macau 1 University of Macau Faculty of Social Sciences and Humanities Department of Economics Admission Test on Master Programme Part A – Macroeconomics 1. Please use an IS-LM model to derive the aggregate demand curve graphically. Explain you answer briefly. ------------------------------------------------Sample----------------------------------------------- Prepared by Department of Economics University of Macau 2 Part B – Mathematics and Econometrics 1. For function ),( 21 xxfz = , what is the partial derivative of z with respect to 2x ? (Write down the math formula and give an intuitive interpretation). Suppose that )ln( 21 αα xxz += , calculate 1x z ∂ ∂ . 2. In a simple regression about the sales y and advertise spending x for 87 companies, we get: 25.0 )85.0( 11.133.1 2 =+= Rxy) (Number in the parenthesis is the standard error) From the regression, is there evidence that advertise spending can increase the sale? Why? ------------------------------------------------Sample----------------------------------------------- Prepared by Department of Economics University of Macau 3 Part C – Microeconomics Section A. Multiple-Choices Questions 1. Colette consumes goods x and y. Her indifference curves are described by the formula y = k / (x+7). Higher values of k correspond to better indifference curves. A. Colette likes good y and hates good x. B. Colette prefers bundle (12, 16) to bundle (16, 12). C. Colette prefers bundle (8, 5) to bundle (5, 8). D. Colette likes good x and hates good y. E. More than one of the above statements are true. 2. Georgina consumes only grapefruits and pineapples. Her utility function is U(x, y) = x2y8 , where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina’s income is $105, and the prices of grapefruits and pineapples are $1 and $3, respectively. How many grapefruits will she consume? A. 10.5 B. 7 C. 63 D. 21 E. None of the above. 3. Cindy consumes goods x and y. Her demand for x is given by x(px , m) = 0.05m – 5.15px. Now her income is $419, the price of x is $3, and the price of y is $1. If the price of x rises to $4 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then A. DI = -0.28 and DS = -0.52. B. DI = -0.28 and DS = -4.88. C. DI = -0.52 and DS = -0.52. D. DI = 0 and DS = -2.00. E. None of the above. ------------------------------------------------Sample----------------------------------------------- Prepared by Department of Economics University of Macau 4 Section B. Short Questions Write your answers on the space below. 1. Let ( ) ( )21212 ,,,: xxfxxf aℜ→ℜ+ be a continuous and differentiable production function. Suppose that 0/ 2 ≠∂∂ xf Derive the following formula for the technical rate of substitution (TRS) (or marginal rate of technical substitution (MRTS)): ( ) ( ) 221 121 1 2 /, /, xxxf xxxf dx dx TRS ∂∂ ∂∂ −=≡ Prepared by Department of Economics University of Macau Applicants are required to have a written test on microeconomics, macroeconomics, mathematics and econometrics. The following book titles are provided as references: Microeconomics Applicants are expected to have preliminary knowledge on intermediate microeconomics. More preparation on an advanced undergraduate level will also be helpful. Intermediate Microeconomics: • Varian, Hal R., Intermediate Microeconomics: A Modern Approach, 7th Ed., New York: Norton, 2006 (including the mathematical appendices). Advanced undergraduate Microeconoimcs: • Jehle, Geoffrey A., and Philip J. Reny, Advanced Microeconomic Theory, 2nd Ed., Boston: Addison Wesley, 2001. Macroeconomics • Mankiw, Gregory. Macroeconomics, 6th ed., Worth Publisher, 2006. • Dornbusch, Rudiger. Macroeconomics, 9th ed., McGraw-Hill, 2004. Mathematics • Chiang, Alpha, and Wainwright, Kevin. Fundamental methods of mathematical economics, 4th ed., McGraw-Hill, 2005. Econometrics • Wooldridge, Jeffrey M. Introductory econometrics: a modern approach, 3rd ed., Thomson, 2006.