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 ($c^r$).
(1) Suppose you earn $1,000,000 over your working life, and the real interest rate is 50%. How much will you save and how much will you consume in each part of your life? (5 分)