# Macro PS7 Solutions.pdf - Department of Applied Economics...

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PS 7 Solutions | © Sanjay K. Chugh 1 Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Practice Problem Set 7 Suggested Solutions Professor Sanjay Chugh 1.Deriving a Money Demand Function. Denote by (,)tc ithe realmoney demand function. Here you will generate particular functional forms for  using the MIU model we have studied. In an MIU model, recall that the consumption-money optimality condition can be expressed as 1ttmtctuiui, where tmudenotes marginal utility with respect to real money balances (what was named 2uin our look at the MIU model) and tcudenotes marginal utility with respect to consumption (what was named 1uin our look at the MIU model). In each of the following, you are given a utility function and its associated marginal utility functions. For each case, construct the consumption-money optimality condition and use it to generate the function  . In each case, your money demand function should end up being an increasing function of tcand a decreasing function of ti(Note: Be careful to make the distinction between real money holdings and nominal money holdings. The marginal utility function tmuis marginal utility with respect to real money holdings.) t. Solution: For each utility function, we have now written the marginal utility functions tcuand tmu. Also note that you are, in each question, being asked to solve for tMPas a function of tcand ti, which is the consumer’s real money demand.a. ,lnlntttttMMuccPP, with tctucand 1tmttuMP. Solution: Constructing the consumption-money optimality condition with the given functions, we have 1/(/)1/1ttmttttictttuMPPciucMi. Solving for /tMP, we have
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PS 7 Solutions | © Sanjay K. Chugh 2 (1)tttttMciPi. Thus, the function  function is (1),tttttcic ii, which is increasing in consumption and decreasing in the nominal interest rate, as expected. b. ,22ttttttMMu ccPP, with 1tctucand 1/tmttuMP. Solution: Proceeding as above, the consumption-money optimality condition is 1//11/tttttmictttMPPcuiuicM. Solving for /tMP
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