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Problem Set 8 Solutions

Problem Set 8 Solutions - Economics 3213 Answers to Problem...

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Economics 3213 Answers to Problem Set 8: 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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