Question

Assume that in Country X, the velocity of money is constant. Read GDP grows at 2% per year and the money stock grows at 10% per year. Let’s assume further that the nominal interest rate is equal to 12%.

a. What is the growth rate of nominal GDP?

b. What is the inflation rate?

c. What is the real interest rate?

What equations do you use to solve the following questions, please provide formulas of how it was set up showing work, and the answer.

Answer 1

According to quantity theory of money following equation of exchange holds.

MV = PY

Where M is the money supply

V is velocity of money. It is assume to be fixed.

P is price level

Y is real GDP.

PY is nominal GDP.

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In terms of growth

MV = PY

=> %growth in M + %growth in V = %growth in P + %growth in Y --------- (1)

and,

Nominal GDP = PY

=> % growth in nominal GDP = %growth in P + %growth in Y ---------(2)

Substitute (1) in (2)

=> % growth in nominal GDP =%growth in M + %growth in V

Given information:

% growth in M = 10

% growth in V = 0 (because it is fixed)

=> % growth in nominal GDP = 10 + 0

=> % growth in nominal GDP = 10.

Growth rate of nominal GDP is 10%

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(b)

MV = PY

=> %growth in M + %growth in V = %growth in P + %growth in Y

Given information:

% growth in M = 10

% growth in V = 0 (because it is fixed)

% growth in Y = 2

=> 10 + 0 = % growth in P + 2

=> % growth in P = 10 -2

=> % growth in P = 8

Hence, inflation rate is 8%

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(c) Real interest rate = nominal interest rate - inflation rate

=> Real Interest rate = 12% - 8%

=> Real interest rate = 4%