Consider a Cagan-type economy in which the demand for money is of the form Ma =...

Transcribed Image Text:

Consider a Cagan-type economy in which the demand for money is of the form Ma = (1 + it)"Y, Pt for t = 0, 1, 2, ..., where M denotes the demand for nominal money balances, Pt the price level, it the nominal interest rate, Y real output, and n> 1 is a parameter. Suppose that the Fisher equation 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 μ> 0 for t ≤T-1, that is, M₁ = (1+µ)Mt-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 T it will stop printing money, that is, M₁ = 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. 1. Find the inflation rate πt = = Pt/Pt-1 1 for the periods t < T, t = T, and t > T. Compare TT under the stabilization program studied hear 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 T by increasing the money supply just in period T at a rate μ> μ. We called this feature of the stabilization program reliquefication. Find ũ in the present environment as a function of µ and ʼn and compare it to the one obtained in class. Provide intuition. = Consider a Cagan-type economy in which the demand for money is of the form Ma = (1 + it)"Y, Pt for t = 0, 1, 2, ..., where M denotes the demand for nominal money balances, Pt the price level, it the nominal interest rate, Y real output, and n> 1 is a parameter. Suppose that the Fisher equation 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 μ> 0 for t ≤T-1, that is, M₁ = (1+µ)Mt-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 T it will stop printing money, that is, M₁ = 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. 1. Find the inflation rate πt = = Pt/Pt-1 1 for the periods t < T, t = T, and t > T. Compare TT under the stabilization program studied hear 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 T by increasing the money supply just in period T at a rate μ> μ. We called this feature of the stabilization program reliquefication. Find ũ in the present environment as a function of µ and ʼn and compare it to the one obtained in class. Provide intuition. =

Answer rating: 100% (QA)

1 Find the inflation rate t Pt P t 1 1 for the periods t T t T and t T ANS WER The inflation rate for t T is The inflation rate for t T is zero and th... View the full answer