Consider a model in which an individual lives only two periods. The individual has diminishing marginal utility of consumption and receives an income of $20,000 in period 1 and an income of $5,000 in period 2. The private interest rate is 10 percent per period, and the person can borrow or lend money at this rate. Assume also that the person intends to consume all of his income over his lifetime (that is, he won’t leave any money for his heirs).
a. If there is no public pension program, what is the individual’s optimal consumption in each period?
b. Now assume there is a public pension program that takes $3,000 from the individual in the first period and pays him this amount with interest in the second period. What is the impact of this system on the person’s saving?