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Exercise 1. Consider a money demand function L(it

, Yt), where Yt denotes output and it denotes

the nominal interest rate. Suppose that it = 3% and Yt = 100 for t = 0, 1, 2, . . .. Suppose further

that the money supply, Mt grows at 1% for t = 0, 1, 2, . . ..

1. What is the inflation rate in periods t = 1, 2, 3, . . .? Explain.

2. Assuming that agents have perfect foresight, what is the real interest rate for t = 1, 2, . . .?

Exercise 2. Consider an economy in which the nominal interest rate exceeds the real interest rate

by 2 percentage points. Find the expected inflation rate.

Exercise 3. Consider an economy in which the demand for money is of the form Y /(1 + it) for

t = 0, 1, 2, . . ., where Y denotes a constant level of output and it denotes the nominal interest rate

in period t. The real interest rate, denoted r, is constant and equal to 4%. In period 0, the nominal

interest rate is 15%, and the money supply is 100. People have rational expectations. In period 1,

the central bank surprises people and sets the money supply to 104 and announces that starting in

period 2 the money supply will grow at 2 percent forever, that is, Mt/Mt-1 = 1.02 for t = 2, 3, . . ..

Find the inflation rate in period 1. Compare it to E0p1.

Exercise 4. Consider the same economy as in the previous exercise, except that people do not have

rational expectations. Assume instead that E1p2 = E0p1, where Etpt+1 denotes the expected value

in period t of inflation in period t + 1. Find the inflation rate in period 1.

Exercise 5 (Reliquefication). Consider a Cagan-type economy in which the demand for money is

of the form

Md

t

Pt

= (1 + it)

-?Y,

for t = 0, 1, 2, . . ., where Md

t denotes the demand for money, Pt the price level, it the nominal

interest rate, Y real output, and ? > 1 is a parameter, known as the semi-elasticity of money

demand. 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, that is, Mt = (1 + µ)Mt-1 for t = 1, 2, . . ., T. 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 the money supply will be held constant

over time, that is, Mt = Mt-1 for t = T + 1, T + 2, . . . In class (lecture 18), we showed that with

1

? > 1, the economy experiences deflation in period T. We also argued that in period T the central

bank can unexpectedly announce a one-time higher money growth rate in period T, denoted ˜µ > µ,

that is, MT = (1 + ˜µ)MT -1. The purpose of this one-time increase in the money grwoth rate is to

avoid deflation, that is, to ensure that PT = PT -1. Find ˜µ as a function of µ and ?.

Attachments:

hwk5-2019.pdf15.-Lecture-S….pdf16.-Lecture-S….pdf17.-Lecture-S….pdf18.-Lecture-S….pdf