Suppose that this year’s money supply is $500 billion, nominal GDP is $50 trilli

Question

Suppose that this year’s money supply is $500 billion, nominal GDP is $50 trillion and real GDP is $5 trillion.

A) What is the price level? What is the velocity of money?

B) Suppose that velocity is constant and the economy’s output of goods and services rises by 5 percent each year. What will happen to nominal GDP and the price level next year if the central bank keeps the money supply constant?

C) What money supply should the central bank set next year if it wants to keep the price level stable given that the economy’s output of goods and services rises by 10 percent each year?

D) What money supply should the central bank set next year if it wants inflation of 5 percent given the economy’s output of goods and services rises by 5 percent each year?

Explanation / Answer

According to quantity theory,

Money supply x Velocity of money = Price level x Real GDP

M x V = P x Y

[P x Y = Nominal GDP]

(A) 50 trillion = 50 x 1,000 billion = 50,000 billion

$500 billion x V = $50,000 billion

V = 50,000 / 500 = 100

Also, P x Y = 50,000

P x 5,000 = 50,000

P = 50,000 / 5,000 = 10

(B)

Change in M + Change in V = Change in P + Change in Y

If M & V both are constant, Change in M = Change in V = 0

Change in P = - Change in Y

As Y increases by 5%, this means P decreases by 5%.

Since Change in P = - Change in Y, Change in nominal GDP (= PY) is zero.

(C)

Assuming V is unchanged,

Change in M = 0 + 10% [Stable price level means change in P is zero]

= 10%

(D)

Change in M = Change in P (Inflation) + Change in Y

= 5% + 5% = 10%

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