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?