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Problem Set 4 solutions

# Problem Set 4 solutions - PROBLEM SET 4 SOLUTIONS(1...

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PROBLEM SET 4 SOLUTIONS (1) Consider a closed economy with the following data: N K Y = K = 100 N K MPN 1 2 1 = Labor supply is inelastic so that: N = 10000 The money market clearing condition is given by 0 ) ( 200 2 . 0 1 = + = e e r Y P M π π High powered money: H = 4000 Currency/deposit ratio: cu = 0.5 Reserve/deposit ratio: res = 0.5 a) Derive the FE line in this economy and compute the real wage Solution: Since labor supply is inelastic, we can plug N = 10000 and K = 100 into the equation for Y to get Y = 10000. This is the full employment output. The real wage is equal to MPN. Plugging in we get W/P = 1/2 b) Suppose that the IS curve is given by r = 10 - 0.0005Y. Derive the LM curve as a function of Y and H/P . [Express it in the form r = f(Y,H/P) ] Hint: Use the formula H res cu cu M + + = 1 1 Solution: Set (1/1,000)M1/P = 0.0002Y - 0.2r and solve for r. By definition: H H res cu cu M 5 . 1 1 1 = + + = Hence the LM curve is given by the equation r = 0.001Y - 0.005M1/P or r = 0.001Y - 0.0075H/P

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