Question

Janet's life can be split into 3 periods.

At t=1, her after-tax income is Y1= 100,000

At t=2, Y2 = 140,000

At t=3, Y3= 0

Assume the market interest rate and the utility discount rate are equal to zero, which implies that savings earn no interest in the city that she lives in and she is relatively patient. In addition, Janet is not very risk averse so she has utility U(Ct) = ln(Ct). Given her utility, the marginal value of an additional unit of consumption in any period of her life is U'(Ct) = 1/(Ct), where Ct is consumption during period t.

1. What are the best amounts of saving in the first and second period?

2. Assume that there are three generations of people exactly like Janet alive in every year. In other words, you have a young, a middle-aged, and an old person alive in every period within her city. What is the total household wealth per capita in her city?

3. Suppose instead that there is a government public pension that reduces income while working by 5%, so that households receive (1-0.05)Yt while working. The government turns around and pays that money to retirees, so all retirees get pension payment equal to five percent of their previous earnings (but actually paid by other people). Assume people re-choose optimally their savings, whether themselves or with the help of advisers. What is the total household wealth per capita now? Where did the wealth go?

4. In many countries, the population is aging so the ratio of elderly retired households to young working households is increasing. What does this do to the national savings rate? Why might this be a concern for government budgets?

Answer 1