325_PracticePS3_Soln

# 325_PracticePS3_Soln - Department of Economics University...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 3 Suggested Solutions Professor Sanjay Chugh Spring 2011 1. The Wealth Effect on Consumption. Consider the two-period consumption-savings model we have been developing in class. a. As in class, maintain the simplifying assumption that 0 0 A . Show graphically how a rise in the period-1 nominal price of consumption can lead to a decrease in optimal consumption in period 1. Solution: Recall from the standard two-period consumption-savings model that the when plotting the lifetime budget constraint (LBC) with 2 c on the vertical axis and 1 c on the horizontal axis, the price 1 P affects the slope but not the vertical intercept (refer to Figure 17 in Chapter 3). It follows that if 1 P rises, then the vertical intercept is unaffected but the budget line becomes steeper. As shown in the figure below, this can lead to lower consumption in period 1. c 2 c 1 Initial LBC ((1+i)Y 1 /P 2 ) + (Y 2 /P 2 ) New LBC Initial c 1 * New c 1 *

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2 Notice that as drawn, the optimal choice of 2 c has also fallen. There is nothing in the structure of the model as we have discussed it that can lead us to definitively conclude that this must be the case – however, it is the most likely case. b. Now suppose that 0 0 A z . Show graphically how a decrease in 0 A can lead to a decrease in optimal consumption in period 1. Solution: We saw that the LBC in the two-period model is 22 2 11 0 (1 ) ) ) c Pc Y Y i A ii ± ±± ± . If we keep 0 0 A z , then solving for 2 c gives us the LBC 2 12 21 1 0 2 2 ) 1 ) Pi i Y i cc Y A PP P P §· § · § · ± ² ± ± ± ¨¸ ¨ ¸ ¨ ¸ ©¹ © ¹ © ¹ . Clearly, 0 A (regardless of whether it is positive or negative) affects only the intercepts of the LBC but not the slope. Thus a decrease in 0 A leads to a parallel shift inwards of the LBC, thus leading to a fall in the optimal choice of 1 c as shown in the figure below. c 2 c 1 Initial LBC New LBC Initial c 1 * New c 1 *
3 c. The two effects you analyzed in parts a and b work through seemingly different channels. Actually, they are usefully thought of as operating through the same broadly-defined channel. Explain this broadly-defined channel. Solution: The perfectly-rational representative-agent considers all his lifetime resources (both labor income as well as initial wealth) when making his optimal consumption-savings decision. Thus, both the change in price in part a and the change in initial wealth in part b (as well as possible changes in the nominal interest rate, the price of consumption in period 2, or labor income in either period!) have their effect by impacting the real value (as opposed to nominal value) of lifetime resources. The real value of lifetime resources is sometimes called “lifetime wealth” – thus, it is lifetime wealth that the individual considers when making his optimal consumption-savings choice.

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## 325_PracticePS3_Soln - Department of Economics University...

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