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Problem Set 9 Solutions

Problem Set 9 Solutions - Economics 3213 Answers to Problem...

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Economics 3213 Answers to Problem Set 9: Aladdin Prof. Xavier Sala-i-Martin 1. Jafar a. If the firm buys real capital, it will receive the same amount as usual: [MPK t +1 + (1 - δ )] P t +1 . b. If the firm buys a bond, it will receive (1 + R ) P t . c. If the firm is optimizing, it will compare the returns to real investment from part (a) and buying bonds from part (b). If one is higher than the other, the firm will do more of the high return activity until the returns are equalized: [MPK t +1 + (1 - δ )] P t +1 = (1 + R ) P t . This is exactly the same relation that we found in class and simplifies to MPK t +1 + (1 - δ ) = (1 + R ) P t / P t +1 . Remember that inflation is defined as π = ( P t +1 - P t )/ P t = P t +1 / P t - 1. Hence, 1 + π = P t +1 / P t or P t / P t +1 = 1/(1 + π ). Remember also that real and nominal interest rates are linked by the Fisher equation: R = r + π + r π or 1 + R = (1 + r )(1 + π ). Substituting these in the above expression, we get: MPK t +1 + (1 - δ ) = (1 + r )(1 + π )/(1 + π ) MPK t +1 + (1 - δ ) = 1 + r MPK t +1 = δ + r This is exactly the same relation that we obtained in class. The amount of capital desired by firms and hence investment demand are not affected by whether firms borrow or use their own funds.
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2. King of the Thieves a. The credit crunch shifts the investment curve to the left. The aggregate demand curve also shifts to the left because it is simply the sum of investment demand and consumption demand: Y d = C d + I d . In the Keynesian model, the short run equilibrium is found at the intersection of the aggregate demand and the LM curve (Diagram 1). Thus real output and real interest rate both go down. Aggregate supply is greater than aggregate demand at the new equilibrium; therefore, prices begin to fall in the medium run. The LM curve shifts downward until it reaches the intersection of the aggregate demand and supply curves. Remember that the LM curve is given by . The interest rate drops further, while output increases a little. In the long run, the overall effect is the reduction of output, interest rate, and prices compared with the initial equilibrium. b. To prevent output from declining, the Fed may want to increase the money supply. Expansionary monetary policy can shift the LM curve downwards, so that real interest rate goes down and output stays at the initial level (LM 3 in Diagram 2). However, demand is greater than supply at the new short run equilibrium, and prices will rise. The LM curve will shift back to LM 2 (Diagram 2). Output will fall, and the interest rate will rise compared to the equilibrium induced by
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expansionary monetary policy. The long run equilibrium will still be
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