Consider the standard OLG model with money. In each period t, Nt young individuals are born, where Nt = nNt+1 and n 1. There are N0 initial old. Individuals are endowed with y units of time when young and nothing when old. A production technology is available such that 1 unit of time can be used to produce 1 unit of the consumption good. Each individual values leisure when young and values consumption when old. Each generation has identical preferences

u (c1;t; c2;t+1) = c1;t * c2;t+1;

where c1;t represents the amount of leisure that the young individual enjoys and c2;t+1 represents the amount of goods the old individual consumes. There exists one asset in the economy -money. The money supply grows at a constant rate z; where Mt = zMt+1 and z > 1. The new money created is used to finance government purchases of g goods per young individual in every period. The initial old are endowed with M0 units of money. In the following, we focus on stationary allocations.

a) use the government budget constraint to solve for g*.

Now instead of financing government purchases by printing new money, the government imposes a labor income tax t. That is, a fraction t of labor income is taxed by the government to support government purchases. In the meantime, the government keeps a constant money supply M.

b) find an individual's budget constraints when young and when old. combine them to form the individual's lifetime budget constraint.

c)to support the same amount of government purchases g* as you find in part a, what should be the labor income tax rate t? explain how you get your answer.

d) in relation to your answer in part c, discuss in what sense inflation is effectively a tax.