Question

Suppose that this year's money supply is $500 billion, nominal GDP is $10 trillion and real GDP is $5 trillion.

a. What is the price level?

b. What is the velocity of money?

(Please calculate your answers in billions, i.e. leave off the zeros (0) if necessary.)

c. Suppose that velocity is constant and the economy's output of goods and services rises by five percent each year. What will happen to nominal GDP  and the price level  next year if the Fed keeps the money supply constant?

(These are numerical answers.)

d. What money supply should the Fed set next year if it wants to keep the price level stable?

e. What money supply should the Fed set next year if it wants an inflation of 10 percent? What will happen to real GDP in this situation?

(These are numerical answers.)

Answer 1

(a) Nominal GDP = $10 trillion

Real GDP = $5 trillion

Price level = Nominal GDP / Real GDP

Price level = ($10 trillion / $5 trillion)

Price level = 2

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(b) According to quantity theory of money.

M*V = P*Y

Where M is the money supply

V is the velocity of money

P is the price level

Y is the real GDP

Note: 1 trillion = 1000 billion

M= $500 billion

P = 2

Y = $5 trillion = $5000 billion

MV = PY

$500 billion * V = 2 * $5000 billion

V = ($10,000 billion / $500 billion)

V =20

Velocity of money is 20

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(c) MV = PY

In terms of growth

% change in M + % change in V = % change in P + % change in Y

Given information:

% change in V = 0

% change in M = 0

% change in Y = 5

=> 0 + 0 = % change in P + 5

% change in P = -5

Hence, the price level will fall by 5%

Nominal GDP = Price level * Real GDP

% change in nominal GDP = % change in Price level + % change in Real GDP

% change in nominal GDP = -5 +5

% change in nominal GDP = 0

Hence, there will be no change in the nominal GDP.

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(d) Now, % change in V = 0

% change in P = 0

% change in Y = 5

% change in M + % change in V = % change in P + % change in Y

=> % change in M + 0 = 0 + 5

=> % change in M = 5

There should be 5% increase in money supply.

New money supply = $500 billion (1+0.05)

New money supply = $525 billion.

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(e)

Now, % change in V = 0

% change in P = 10

% change in Y = 5

% change in M + % change in V = % change in P + % change in Y

=> % change in M + 0 = 10 + 5

=> % change in M = 15

There should be 5% increase in money supply.

New money supply = $500 billion (1+0.15)

New money supply = $575 billion.

Real GDP will rise by only 5%.