Consider the following economy: Individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money stock is constant. The population grows at rate n. In each period, the government taxes each young person τ goods. The total proceeds of the tax are then distributed equally among the old who are alive in that period.
a. Write down the first- and second-period budget constraints facing a typical individual at time t. Combine the constraints into a lifetime budget constraint.
b. Find the rate of return on fiat money in a stationary monetary equilibrium.
c. Does the monetary equilibrium maximize the utility of future generations?
d. Does this government policy have any effect on an individual’s welfare?
e. Does your answer to part d change if the tax is larger than the real balances people would choose to hold in the absence of the tax?