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prelims_Macro Prelim ANSWERS June 2008

prelims_Macro Prelim ANSWERS June 2008 - University of...

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University of California, Davis Date: June 30, 2008 Department of Economics Time: 3 hours Macroeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Directions: Answer all questions. SHORT QUESTIONS 1. Consider two closed economies that have the same real interest rate. If con- sumption growth is higher and less volatile in Economy A relative to Economy B, what implications does this have for preferences in the two economies? ANSWER: A starting point for this question is the Keynes-Ramsey condition describing the optimal consumption path in the Cass-Koopmans model (no uncertainty; assume no population growth) r = ° + ±² c where ° is agent°s subjective discount factor ( ³ ° 1 1+ ° ) , ± is the elasticity of agents° marginal utility, and ² c is the average growth rate of consumption. Assume that ° is the same in both economies. Given that interest rates are the same in both economies, it must be the case that ± is smaller in Economy A: given the higher growth in Economy A, this should imply that interest rates are higher since present consumption is scarce relative to future consumption. But the smaller elasticity of MU in Economy A will counteract this e/ect - i.e. future growth does not lower MU as much in Economy A. If uncertainty is added to this economy (Brock-Mirman model), then the optimal consumption path will be characterized (obtained by either assuming a log normal distribution for consumption growth (see Ljungvist and Sargent handout) or by taking a second order Taylor series expansion of the Euler equation associated with bonds (see Romer, p. 369): r = ° + ±² c ± ± ( ± + 1) 2 ´ c where ´ c is the standard deviation of consumption growth. Lower volatility will, ceteris paribus, cause interest rates to be higher (the certainty equivalence of future consumption increases). Again, a lower value of ± (risk aversion) is needed to keep interest rates the same in both economies. 2. One of the stylized facts of growth is a growing wage rate and a (relatively) constant labor supply. What restrictions does this place on agents°preferences? 1
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ANSWER: Agents°optimization implies: U l ( c; 1 ± h ) U c ( c; 1 ± h ) = w In a balanced growth path, consumption and the real wage grow at the rate of technological progress. If preferences are separable, then a constant labor ( h ) implies the numerator will be constant and that U ( c ) = ln c: If preferences are not separable, then the elasticity of the MU of leisure with respect to consumption must balance the elasticity of the MU of consumption with respect to consumption. 3. In the Solow model, what happens when there is a permanent increase in the savings rate? Describe both the transition and steady-state e/ects. What economic forces are at work? ANSWER: There is a permanent increase in the level in growth of output per worker and a transitory increase in its growth rate. But because of diminishing marginal products, there is no permanent increase in growth.
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