The effects of a permanent decrease in the rate of nominal money growth Suppose

Question

The effects of a permanent decrease in the rate of nominal
money growth
Suppose that the economy can be described by the following
three equations:

Ut - Ut -1 = -0.41 (gyt - 3%) Okun’s law
t - t - 1 = -(Ut - 5%) Phillips curve
gyt = gmt - t Aggregate demand

a. Reduce the three equations to two by substituting gyt from
the aggregate demand equation into Okun’s law. (Okun’s
law was presented in Chapter 2.)
Assume initially that Ut = Ut-1 = 5%, gmt = 13%, and
t = 10%.

b. Explain why these values are consistent with the statement
“Inflation is always and everywhere a monetary
phenomenon.”
Now suppose that money growth is permanently reduced
from 13% to 3%, starting in year t.

c. Compute (using a calculator or a spreadsheet program) unemployment
and inflation in years t, t + 1,..., t + 10.

d. Does inflation decline smoothly from 10% to 3%? Why or
why not?

Explanation / Answer

Ut - Ut -1 = -0.41 (gyt - 3%) Okun’s law
t - t - 1 = -(Ut - 5%) Phillips curve
gyt = gmt - t Aggregate demand

Now after substitution

Ut - Ut -1 = -0.41 (gmt - t - 3%)

t - t - 1 = -(Ut - 5%)

Derive (t, ut) in terms of (t1, ut1) and gmt, we get

t = (t - 1 +3.77%+ 0.41gmt - Ut -1 )/1.41

Ut = (0.41t - 1 +3.22% - 0.41gmt + Ut -1 )/1.41

b) From the values given in the question we can see that unemplyment id constant so from the equation se derived for t we can see that inflation now depends only upon the previous level of unemployment and money growth. Which supprts the line that "inflation is always and everywhere a monetary phenomenon.

c) We find inflation and unemplyment by simply substituting values in above derived equations

d) We can see that due to less growth of money the decline of inflation was not smooth, it even went to the state of deflation. The reason was fall in money growth rate, for proving this i will redo the calculation of c) with gmt - 13% and we find that economy is in steady state

S Ut in percent t in percent gmt in percent t 5 10 3 t+1 7.87 7.09 3 t+2 9.05 3.00 3 t+3 8.70 -0.75 3 t+4 7.37 -3.16 3 t+5 5.72 -3.92 3 t+6 4.33 -3.29 3 t+7 3.52 -1.85 3 t+8 3.37 -0.27 3 t+9 3.72 0.96 3 t+10 4.33 1.59 3

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