(The Cagan Model and Output Growth). Suppose that the demand for money is given by Ma Yt Pt 1 + it V = where M is the nominal demand for money, P, is the price level, Y, is real output, and it is the nominal interest rate, in period t. Suppose that people have rational expectations. Suppose further that Y grows at 3 percent, that Yo 1, that the nominal money supply, denoted Mt, grows at 5 percent, that Mo= 100, and that the real interest rate, denoted r, is constant and equal to 4 percent. = Mt 1. Guess the equilibrium growth rate of the real money supply, M, and explain why you think your Pt Pt guess makes sense. Let It = - 1 be the inflation rate in period t. Given your guess, what is Pt+1 the inflation rate in periods 1, 2,.... 2. Given your guess, use the Fisher equation to calculate the nominal interest rate, it, in periods t = 0, 1, 2, ... Check whether your guess is correct, that is, check whether, given your guess, the Mt real demand for money, grows at the same rate as the real money supply, Pt Yt 1+it' 3. Given your guess, what is the price level in period 0, Po?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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(The Cagan Model and Output Growth). Suppose that the demand for money is given by
Pt
1+it
where M is the nominal demand for money, P, is the price level, Y, is real output, and iç is the
nominal interest rate, in period t. Suppose that people have rational expectations. Suppose further
that Y, grows at 3 percent, that Yo
percent, that Mo = 100, and that the real interest rate, denoted r, is constant and equal to 4 percent.
= 1, that the nominal money supply, denoted Mt, grows at 5
Mt
1. Guess the equilibrium growth rate of the real money supply,
and explain why you
Pt
think
your
Pt
guess makes sense. Let t =
Pt+1
1 be the inflation rate in period t. Given your guess, what is
the inflation rate in periods 1, 2,
2. Given your guess, use the Fisher equation to calculate the nominal interest rate, i,, in periods t
= 0, 1, 2, . . . Check whether your guess is correct, that is, check whether, given your guess, the
real demand for money,
1+i
Mt
grows at the same rate as the real money supply,
Pt
3. Given your guess, what is the price level in period 0, P,?
Transcribed Image Text:(The Cagan Model and Output Growth). Suppose that the demand for money is given by Pt 1+it where M is the nominal demand for money, P, is the price level, Y, is real output, and iç is the nominal interest rate, in period t. Suppose that people have rational expectations. Suppose further that Y, grows at 3 percent, that Yo percent, that Mo = 100, and that the real interest rate, denoted r, is constant and equal to 4 percent. = 1, that the nominal money supply, denoted Mt, grows at 5 Mt 1. Guess the equilibrium growth rate of the real money supply, and explain why you Pt think your Pt guess makes sense. Let t = Pt+1 1 be the inflation rate in period t. Given your guess, what is the inflation rate in periods 1, 2, 2. Given your guess, use the Fisher equation to calculate the nominal interest rate, i,, in periods t = 0, 1, 2, . . . Check whether your guess is correct, that is, check whether, given your guess, the real demand for money, 1+i Mt grows at the same rate as the real money supply, Pt 3. Given your guess, what is the price level in period 0, P,?
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