Imagine an economy with a constant population, N. There is a nonstorable consumption good. Individuals are endowed with y units of the consumption good when young and nothing when old. Money supply growth Mt = zMt-1 where z > 1 is the gross growth rate of the money supply. People face lump-sum tax of t goods when old. The tax and the expansion of monetary equilibrium are used to finance government purchases of g goods per young person in every period.
a) Find the individual’s budget constraint when young and old. Combine them to form an individual’s lifetime budget constraint. Graph this constraint.
b) Find the government 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) In a figure, compare the evolution over time of real balances of fiat money with z=1 and with z>1.
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