Problem
Money and inflation in the Ramsey model (based on Sidrauski, 1967; Brock, 1975; and Fischer, 1979) Assume that the government issues fiat money. The stock of money, M, is denoted in dollars and grows at the rate µ, which may vary over time. New money arrives as lump-sum transfers to households. Households may now hold assets in the form of claims on capital, money, and internal loans. Household utility is still given by equation (2.1), except that u(c) is replaced by u(c, m), where m ≡ M/P L is real cash balances per person and P is the price level (dollars per unit of goods). The partial derivatives of the utility function are uc > 0 and um > 0. The inflation rate is denoted by π ≡ P? /P. Population grows at the rate n. The production side of the economy is the same as in the standard Ramsey model, with no technological progress.
a. What is the representative household's budget constraint?
b. What are the first-order conditions associated with the choices of c and m?
c. Suppose that µ is constant in the long run and that m is constant in the steady state. How does a change in the long-run value of µ affect the steady-state values of c, k, and y? How does this change affect the steady-state values of π and m? How does it affect the attained utility, u(c, m), in the steady state? What long-run value of µ would be optimally chosen in this model?
d. Assume now that u(c, m) is a separable function of c and m. In this case, how does the path of µ affect the transition path of c, k, and y?
U = 0∫∞ u[e(t)] · ent · e-pt dt 2.1
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.