9. (Appendix 4.A) A consumer lives three periods, called the learning period, the working period, and the retirement period. Her income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period. The consumer’s initial assets are 300. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime.

a. What are consumption and saving in each period, assuming no borrowing constraints? What happens if the consumer faces a borrowing constraint that prevents her from borrowing?

b. Assume that the consumer’s initial wealth is zero instead of 300. Repeat Part (a). Does being borrowing-constrained mean that consumption is lower in all three periods of the consumer’s life than it would be if no borrowing constraints applied?