Question 1 (20 points)

Question 1 (20 points). Consider the two-period endowment model. Assume the consumers' preference over current and future consumption is given by U (c,c) = c1c'. Further assume there is no government (no taxes or government expenditures). (a) Formulate the consumer problem and solve for the optimal decisions: c, d' and s. Show your work. (6) 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. ?. (c) 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?