(Reliquefication). Consider a Cagan-type economy in which the demand for money is of the form= (1 + i,)¯"YPtfor t= 0, 1, 2, ..., where M denotes the demand for nominal money balances, P, the price level,the nominal interest rate, Y real output, and 7> 1 is a parameter. Suppose that the Fisher equationitholds and that the real interest rate is constant and equal to r> 0. Suppose further that economicagents have rational expectations. The money growth rate is u > 0 for t T. Compare tT underthe stabilization program studied here and explain why they are or they are not equal to each other.2. In class, we showed that if n> 1, the central bank can avoid deflation in period Tby increasingthe money supply just in period T at a rate ũ > µ. We called this feature of the stabilizationprogram reliquefication. Find ũ in the present environment as a function of u and 7 and compareit to the one obtained in class. Provide intuition.

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Question

(Reliquefication). Consider a Cagan-type economy in which the demand for money is of the form
= (1 + i,)¯"Y
Pt
for t= 0, 1, 2, ..., where M denotes the demand for nominal money balances, P, the price level,
the nominal interest rate, Y real output, and 7> 1 is a parameter. Suppose that the Fisher equation
it
holds and that the real interest rate is constant and equal to r> 0. Suppose further that economic
agents have rational expectations. The money growth rate is u > 0 for t <T-1, that is, M.
(1+u) M.-1 for t 1, 2, ..., T-1. Before period T, economic agents believe that the money supply
will grow at this rate forever. In period T, unexpectedly, the central bank announces that starting
in Tit will stop printing money, that is, M = MT-1 for t = T, T+1, T+ 2, ... Note the difference
with the case studied in class (lecture 17), in which the central bank stops printing money in T+
1, not in T.
Pt
1. Find the inflation rate n =
Pt-1
1 for the periods t< T, t = T, and t> T. Compare tT under
the stabilization program studied here and explain why they are or they are not equal to each other.
2. In class, we showed that if n> 1, the central bank can avoid deflation in period Tby increasing
the money supply just in period T at a rate ũ > µ. We called this feature of the stabilization
program reliquefication. Find ũ in the present environment as a function of u and 7 and compare
it to the one obtained in class. Provide intuition.

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