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Fall 06 Midterm II Solutions

Fall 06 Midterm II Solutions - Midterm II Suggested...

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1 Midterm II: Suggested Solutions Econ 110 Fall 2006 100 points PART I: 50 POINTS 1. (6 points) Is it true that higher real interest rates are always associated with lower equilibrium levels of investment? Explain why it is so, if true, or give a counterexample, if false. The statement is false. The higher real interest rate can be the result of a permanent positive technological shock in the economy. In such case, although output supply and consumption demand shift by the same amount, the additional shift in the investment demand curve will push the real interest rate up. Even though this event implies a movement along the new investment demand curve, reducing its level, the direct effect associated to the shift of the curve itself is likely to dominate, thus yielding a superior investment level in equilibrium. 2. (36 points) Suppose there is a temporary negative productivity shock in a closed economy in the Classical Model. Assume fixed labor supply . a) (6 points) Explain what happens to equilibrium consumption, output, interest rate and price level. Output supply will shift to the left, due to the negative productivity shock. Consumption demand will also decrease, but just by a small amount, due to the temporary nature of the shock and the fact that consumption smoothing is taking place. Graphically: Because people are trying to borrow, the real interest rate will be pushed up. This fact, together with the decrease in equilibrium output, will also decrease money d I d C d Y s Y * 0 r * 1 r * 0 Y * 1 Y Y r
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2 demand. Equilibrium in the monetary market will then be achieved for a higher price level. b) (8 points) Compare your answer with what would happen in a model without capital and investment. In particular, how does the presence of investment affect consumption in this example of a temporary shock? Would investment affect consumption in the same way if this were a permanent shock? With investment we observe a smaller change in the equilibrium real interest rate and in equilibrium consumption: Without investment we observe a greater increase in the real interest rate: d d C Y = s Y * 0 r * 1 r * 0 Y * 1 Y Y r d I d C d Y s Y * 0 r * 1 r * 0 Y * 1 Y Y r M s M ( ) P Y R P M d / , , γ Φ × = P 0 P 1 P
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3 Without I d , we would get greater r* ° greater in C* ° same as saying here Δ C = Δ Y whereas when we have I d (which is very sensitive with respect to r) ° Δ C < Δ Y , i.e. investment acts as a buffer for C. Intuition: if this is a temporary shock, then people want to smooth consumption (in this case, people want to borrow money). If there is no I d , then Aggregate Net Saving 0 and we need a large r* to force aggregate net savings back down to zero. However, with I d , Agg. Net Saving Agg. Net I. So when people want to savings they can I*.
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