midterm_10_3430M_sol

midterm_10_3430M_sol - Monetary Economics I: Financial...

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Monetary Economics I: Financial Markets and Institutions ECON 3430 M Midterm Test Solutions – February 25, 2010 Professor Ahmet Akyol Start: 1:00pm. Finish: 2:15pm. Show all your work. Good Luck! Questions 1. –60 points– Consider an economy with a constant population of N = 100. Individuals are endowed with 20 units of the perishable good when young and 10 units of the perishable good when old. Thus, y 1 = 20 and y 2 = 10. Suppose that the initial old are endowed with a total of M = 250 units of fiat money. The amount of fiat money in the economy is constant (i.e. M t = M t +1 = M .) (a) Write down the equation that represents the individual’s budget constraints in her first and second period of her life. Combine these constraints into a lifetime budget constraint. The first-period budget constraint is c 1 ,t + v t m t = y 1 The second period budget constraint is c 2 ,t +1 = y 2 + v t +1 m t Combining the two, we get life-time budget constraint c 1 ,t + v t v t +1 [ c 2 ,t +1 - y 2 ] = y 1 or c 1 ,t + v t v t +1 c 2 ,t +1 = y 1 + v t v t +1 y 2 c 1 ,t + v t v t +1 c 2 ,t +1 = 20 + v t v t +1 10 1
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(b) Write down the condition that represents the clearing of the money market in an arbitrary period, t . Using this condition, find the real rate of return of fiat money in stationary equilibrium. The clearing of money market in
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midterm_10_3430M_sol - Monetary Economics I: Financial...

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