Assume that the utility function of people in the economy described in Exercise 3.6 is log (c_1,t) + log (c_2,t+1).

a. Find the real demand for money (q = v_tm_t) as a function of z and τ.

b. Find the government budget constraint in a stationary equilibrium. Solve it for as a function of. (The expression will also involve and.)
c. Substitute your expression for τ from the government budget constraint (part b) into the demand for money (part a). Use this to represent seigniorage as a function of z alone. Graph seigniorage as a function of. For the graph, use the following parameter values: N = 1,000, y = 100, and g = 10.