Suppose the monetary authority prints fiat money at the rate zbut now does not distribute the newly printed money as a lumpsum subsidy. Instead, the government distributes the newly printed money by giving each old person new dollars for each dollar acquired when young. Assume that there is a constant population of people endowed only when young.

a. Use the government budget constraint to findas a function of z.

b. Find the individual's budget constraints when young and old. Combining both find the lifetime budget constraint.

c. Find the real rate of return on money and the rate of inflation .

d. Compare the individual's lifetime budget constraint with the feasible set to demonstrate that the monetary equilibrium satisfies the golden rule regardless of the rate of inflation.

e. Explain why inflation does not induce people to reduce their real balances of fiat money in this case.