Consider a consumer who lives for three periods: youth, middle age and old age.When young, the consumer earns $20.000 in labor income. Earnings during the middle age are uncertain: there is a 50% chance that the consumer will earn$40.000 and a 50% chance that the consumer earns $100.000. When old, the consumer spends savings accumulated from the previous periods. Assume that inflation, expected inflation, and the real interest rate are equal to zero. Ignore taxes for this problem.
- What is the expected value of lifetime earnings in the middle period of life?
- Given this number, what is the present discounted value of the expected lifetime labor earnings?
- If the consumer wishes to maintain constant expected consumption over her lifetime, how much will she consumer in each period?
- How will she save in each period?