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# Answer3 - ECO 301 Intermediate Macroeconomics Spring 2010...

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ECO 301 Intermediate Macroeconomics, Spring 2010 Instructor: Yangyi Shan Homework Assignment 3 Answer Key 1. (40 points) Consider two consumers, A and B. A and B both want perfect consumption smoothing (c = c f ) and both have no current wealth. However, the two consumers have different income streams. Person A’s current income, y A , = 100, and future income, y f A , = 121. Person B’s current income, y B , is 120, and future income, y f B , = is 99. The real interest rate is 10% (0.10). a. Calculate the present value of lifetime resources (PVLR) for consumer A and B. (4 points) PVLR A = 100 + 121/(1 + .1) = 210 PVLR B = 120 + 99/(1 + .1) = 210 b. How does the budget constraint of consumer A compare to the budget constraint of consumer B? Explain. Draw consumer A’s budget constraint. (4 points) Since both consumers face the same real interest rate, both budget constraints have the same slopes. Since both consumers have the same PVLR, both budget constraints have the same horizontal intercept. So the two budget constraints are the same. c). Find consumer A’s optimal lifetime consumption plan, (c A , c f A ). How does consumer B’s optimal lifetime consumption plan, (c B , c f B ), compare to consumer A’s lifetime consumption plan? Explain. (6 points) Consumer A’s budget constraint is c f A = -1.1c A + 231 Using the perfect consumption smoothing assumption, we can substitute c A = c f A into the budget constraint and solve for c A : 210 231 c A Slope = –1.1 c f A

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c A = -1.1c A + 231 2.1 c A = 231 c A = 231/2.1 = 110.
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Answer3 - ECO 301 Intermediate Macroeconomics Spring 2010...

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