Question 1 (50 points). Consider the two-period endowment model. Assume the consumers' preference over current and futur

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Question 1 50 Points Consider The Two Period Endowment Model Assume The Consumers Preference Over Current And Futur 1 (194.86 KiB) Viewed 45 times

Question 1 (50 points). Consider the two-period endowment model. Assume the consumers' preference over current and future consumption is given by U (c, c) = cc. The consumer is endowed with y units of goods in the current period and y' units of goods in the future period. Further assume there is no government (no taxes or government expenditures). The interest rate is r. (a) Write down the consumer's problem. What variables are taken as given? What variables are the consumer's choices? (6) Write the Lagrangian and derive the first-order conditions of the consumer's problem. Inter- pret the first-order conditions. (c) Solve for the optimal decisions: c, d' and s as functions of y, y' ,r. Show your work. (d) Looking at the case of a net borrower, what do we have to assume about the substitution and income effects to generate the result that a decrease in r brings about an increase in current-period consumption? Explain your answer. (e) Use graphs and write a concluding sentence to answer the following questions: i. Suppose y decreases and y' increases in such a way that leave the present value of lifetime income (wealth) unchanged. What are the impact on c and s? ii. Now suppose y increases and y' decreases in such a way that leave the present value of lifetime income (wealth) unchanged. What are the impact on c and s?