Consider a consumer that lives only two periods and leaves no money behind. This consumer likes consumption (composite good) in both periods. The utility function is:

U=c0 *c1 ,MU0=c1 ,MU1 =c0

In period 0, the consumer's income is M0 = 20,000 and in period 1, the consumer's income is M1 = 5,000. The interest rate at which the consumer can borrow and lend money is 10%.

a) What is the consumer's optimal consumption bundle borrowing or saving decision without a public pension?

b) Now suppose that the government offers a public pension (financed by a pay-as-you-go system) that charges $3,000 in payroll taxes in period 0 and promises a pension of $3,300 in period 1. What is the impact on the consumer's borrowing or saving decision?

c) Now suppose that the government asked for a payroll tax of $8,000 in period 0 and promised a pension of $8,800 in period 1. What is the impact on this consumer's borrowing and saving decision now?