1. Derivation of LM curve In a particular economy the real money demand function is = 3000 + 0.1 10000 Assume that = 6000, P=2.0, and = 0.02. a) What is the real interest rate, r, that clears the asset market when Y=8000? When Y=9000? Graph the LM curve. b) Repeat part a) for M=6600. How does the LM curve in this case compare with the LM curve in part a)? c) Use M=6000 again and repeat part a) for = 0.03. Compare the LM curve in this case with the one in part a). Problem 2. IS-LM and price adjustment The labor demand in an economy is = 1000 100 The labor supply curve is = 55 + 10(1 ) where t is the tax rate on wage income, which is 0.5. Desired consumption and investment are = 300 + 0.8( ) 200 = 258.5 250 Taxes and government purchases are = 20 + 0.5 = 50 Money demand is / = 0.5 250( + ) The expected rate of inflation, , is 0.02, and the nominal money supply = 9150. a) What are the general equilibrium levels of the real wage, employment, and output, if production function is given by = 10 0.0052? b) For any level of output, Y, find an equation that gives the real interest rate, r, that clears the goods market; this equation describes the IS curve. (Hint: Write the goods market equilibrium condition and solve for rin terms of Y and other variables.) What are the general equilibrium (long-run) values of the real interest rate, consumption, and investment? c) For any level of output, Y, find an equation that gives the real interest rate that clears the asset market; this equation describes the LM curve. [Hint: As in part (b), write the appropriate equilibrium condition and solve for r in terms of Y and other variables.] What is the general equilibrium (long- run) value of the price level? d) Provide the IS-LM-FE graph using the equations you found in parts a) - c). e) Suppose that government purchases increase to G=72.5. Now what are the general equilibrium (long-run) values of the real wage, employment, output, the real interest rate, consumption, investment, and price level? Show the effects of increase in G in the IS-LM-FE diagram. Problem 3. Shocks in IS-LM-FE Framework, Short- and Long-run Equilibria Use the IS-LM-FE model to determine the effects of each of the following on the general equilibrium values of the real wage, employment, output, real interest rate, consumption, investment, and price level. Indicate with A, B, and C the equilibrium before the shock, short-run equilibrium, and long-run equilibrium respectively. Assume that A is at full employment. a) A reduction in the effective tax rate on capital that increases desired investment. b) The expected rate of inflation rises. c) An influx of working-age immigrants. d) Increased usage of automatic teller machines that reduces the demand for money. Problem 4. Money Markets and IS-LM Suppose an increase in robberies in the streets makes people hold less money. a) How does this event affect the money market in the short-run if the Fed keeps the money supply constant? Graph the effects of this shock in the money market and IS-LM diagrams. b) How does this event affect the money market in the short-run if the Fed keeps the interest rate constant? Graph the effects of this shock in the money market and IS-LM diagrams