Consider an economy like the one used in class for the study of ‘Unpleasant Monetarist Arithmetic.' Assume that government debt in period -1 is zero, b-1 = 0. Assume that the country runs a positive primary deficits, def > 0, in all periods. Money demand is given by Mt/Pt = 1 Y , where v ¯ > 0 denotes money velocity and Y denotes output. Let the real v ¯ interest rate be given by r > 0. Borrowing by the government is subject to a no-Ponzi game constraint.
(a) Suppose the money supply grows at the rate μ between periods t-1 and t, find seignorage income in period t. Show that seignorage income is monotonically increasing in μ and bounded above. Find this upper bound in terms of the structural parameters of the model, v ¯ and Y .
(b) Suppose the money supply is constant for T - 1 periods, that is, Mt = M-1 for all periods t < T. And thereafter the money supply grows at the constant rate μ, that is, MT -1+j = (1 + μ)j M-1 for any j ≥ 0. The money growth rate μ is chosen to ensure that the stock of debt, bt, remains constant at the level it reached in period T - 1, that is, bt = bT -1 for all t ≥ T . Using the results from problem (a) find the maximum number of periods that inflation can be delayed. Your answer should be an analytical expression for T in terms of the structural parameters r, v ¯, and def/Y .
(c) Set r = 0.04, v ¯ = 1, and def/Y = 1/11. Find the numerical value for the maximum number of years inflation can be delayed.
(d) Now suppose that the central bank wishes to have price stability in the long run. To achieve this goal the central bank collects (a constant amount of) seignorage revenue only in periods 0 to 10. Is this policy feasible? If so, find μ, the per period growth rate of the money supply for periods 0 through 10. Continue to assume that b-1 = 0, v ¯ = 1, def/Y = 1/11 and r = 0.04. Interpret your results.