Spring 2009 Final Exam Solutions

Spring 2009 Final Exam Solutions - Department of Economics...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Final Exam Suggested Solutions Professor Sanjay Chugh Spring 2009 NAME: TA’S NAME: The Exam has a total of four (4) problems and pages numbered one (1) through twelve (12). Each problem’s total number of points is shown below. Your solutions should consist of some appropriate combination of mathematical analysis, graphical analysis, logical analysis, and economic intuition, but in no case do solutions need to be exceptionally long. Your solutions should get straight to the point – solutions with irrelevant discussions and derivations will be penalized. You are to answer all questions in the spaces provided. You may use two pages (double-sided) of notes. You may not use a calculator. Problem 1 / 25 Problem 2 / 25 Problem 3 / 30 Problem 4 / 20 TOTAL / 100
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1 Problem 1. Monetary Neutrality or Nonneutrality? (25 points) . Suppose firms need to use only labor in order to produce output, and output in period t is given by t t t y An ! , where t A is a technology shock and t n is the number of hours of labor. Firms choose their labor in a profit maximizing way every period. Suppose the representative consumer’s period-t utility function is given by ln( ) ln ln t t t t t M B c l P "" , where, as always, 1 tt ln ! # denotes leisure , t B denotes a preference shock, and / M P is real money. Note that rather than supposing there are “168 units of time” available, here we are supposing that there is only “one unit of time” available (hence, both n and l will be fractions between zero and one). Finally, assume the labor supply curve is always upward-sloping (i.e., it never bends backwards), and that the labor tax rate is always zero. a. (7 points) In the diagram below, show the effect on the consumer’s optimal choice of consumption and leisure in period t due to a simultaneous rise in t A and rise in t B . Clearly label your diagram, and explain precisely any and all effects pertinent here. consumption Solution: With the representative firm maximizing profit, we know that the real wage equals the marginal product of labor. In this case (with the linear production technology), the marginal product of labor is simply t A , which means the slope of the budget line in the above diagram (which is the real wage) is t A . The rise in t A means the budget line becomes steeper, pivoting around the fixed point on the leisure axis. Next, consider the MRS between consumption and leisure. We know the MRS between consumption and leisure (i.e., the slope of the indifference curve) is / lc uu . With the given utility function, 1/ l ul ! and /( ) 1/ c u B Bc c ! ! . Note that the B term drops out of the marginal utility of consumption here (you had to use the chain rule to fully differentiate). Thus, the MRS is unaffected by the preference shifter in this case, meaning the indifference map is unaffected.
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2 Problem 1 continued b. (7 points) Suppose instead of the preference and TFP shocks in part a, there were a positive money shock (and no other shocks) at the end of period t (as we described in class – i.e., the
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Spring 2009 Final Exam Solutions - Department of Economics...

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