The graph below shows the lifetime earnings profile of a person who lives for four periods and earns incomes of $30, $60, and $90 in the first three periods of the life cycle. There are no earnings during retirement. Assume that the interest rate is 0.

a. Determine the level of consumption, compatible with the budget constraint, for someone who wants an even consumption profile throughout the life cycle. Indicate in which periods the person saves and dissaves and in what amounts.

b. Assume now that, contrary to part ( a ), there is no possibility of borrowing. The credit markets are closed to the individual. Under this assumption, what is the flow of consumption the individual will pick over the life cycle? In providing an answer, continue to assume that, if possible, an even flow of consumption is preferred. ( Note: You are assuming here that there are liquidity constraints.)

c. Assume next that the person described in part ( b ) receives an increase in wealth, or nonlabor income. The increase in wealth is equal to $13. How will that wealth be allocated over the life cycle with and without access to the credit market? How would your answer differ if the increase in wealth were $23?