1. Consider the standard OLG model of money. Individuals are endowed with y units of the endowment good when young and nothing when old.
Assume that people face a lump�sum tax of τ goods when old and a rate of expansion of the fiat money supply of z > 1. The tax and the expansion of the fiat money stock are used to finance government purchases of g goods per young person in every period. There are N people in every generation.
a. Find the individual’s budget constraints when young and when old. Combine them to form the individual’s lifetime budget constraint and graph this constraint.
b. Find the government’s budget constraint.
c. Graph together the feasible set and the stationary monetary equilibrium.
d. Find the stationary monetary equilibrium when z = 1 and add it to the graph in part c.
e. Use a ruler on your graph to compare the real balances of fiat money when z > 1 to the values when z = 1.
Now assume that the utility function of people in the economy described in this economy is log(c1,t) + log(c2,t+1).
f. Find the real demand for money (vtmt) as a function of z and τ .
g. Find the government budget constraint in stationary equilibrium. Solve it for τ as a function of z . (The expression will also involve y and g.)
h. Substitute your expression for τ from the government budget constraint (part g) into the demand for money (part f).
Use this to represent seigniorage as a function of z alone. Graph seigniorage as a function of z. For the graph, use the following parameter values: N = 1000, y = 100, and g = 10
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