題組內容

1. Suppose you divide your life into two periods: working age and retirement age. When you work, you earn labor income y; when retired, you earn no labor income, but must live off your savings and the interest it earns. While working, you save the amount s, earning interest at a constant rate r, so you have (1 + r)s to live on when retired. Because you don't need to consume as much when retired, you want to set consumption when working ($c^w$) twice as high as consumption when retired ($c^r$).

(2) Suppose a social security system will pay you 25% of your working income when you are retired. Now, with \( y = \)1,000,000, as in part (a), how much will you save and how much will you consume each period? (5 分)