Suppose the monetary authority prints fiat money at the rate but now does not distribute the newly printed money as a lump-sum subsidy. Instead, the government distributes the newly printed money by giving each old person α 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 find α as a function of z.
b. Find the individual’s budget constraints when young and old. Combine them to form the individual’s lifetime budget constraint.
c. What is the inflation rate p_{t + 1}/p_t ? What is the real rate of return on fiat money? Hint: The real rate of return on a unit of fiat money is not simply v_{t + 1}/v_t in this case.
d. Compare the individual’s lifetime budget constraint with the feasible set. Demonstrate that the monetary equilibrium satisfies the golden rule regardless of the rate of inflation. Explain why inflation does not induce people to reduce their real balances of fiat money in this case.