olganswersSP08 - Macro II: Answers to OG Practice Questions...

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Macro II: Answers to OG Practice Questions February 20, 2008 Question 1 Consider an overlapping generations model in which agents live two periods. In period 1, they are endowed with e > 0 units of the single good. They have no endowment of leisure and no access to a production technology. They have a zero endowment in period 2. Agents obtain utility from consuming in both periods of life and thus save to consume in old age. The monetary authority increases (decreases) the money supply with stochastic proportional transfers. Assume the money transfers are iid. There is no other uncertainty in the model. i. Show there exists a SREE in which money is neutral. The representative agent of generation t agent solves max s E x 0 ,p 0 ( u ( e s )+ v ( spx 0 p 0 )) . (1) The f rst order condition is u 0 ( e s )= E x 0 ,p 0 ( px 0 p 0 v 0 ( spx 0 p 0 )) . (2) The condition for market clearing is ps = Mx (3) where M is the inherited money supply and x is the current shock. It is straightforward to see that a SREE exists with p ( M,x )= QMx and s ( M,x )= s .W i th this conjecture, px 0 p 0 =1 .Inth i sSREE , Q = 1 s and s solves u 0 ( e s
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olganswersSP08 - Macro II: Answers to OG Practice Questions...

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