Question

The quantity theory of money we discussed in class assumes that the ratio of money to GDP is constant. This can be equivalently expressed by the Fisher equation:

M ×V = P × Q

Where:

• M represents the money supply.

• V represents the velocity of money. which is the frequency at which the average same unit of currency is used to purchase newly domestically-produced goods and services within a given time period. In other words, it is the number of times one unit of money is spent to buy goods and services per unit of time.

P represents the average price level.

Q represents the volume of transactions in the economy (real GDP). This implies that:

V = (P × Q) / M = Nominal GDP / MoneySupply

The quantity theory assumes that this ratio is constant (the velocity of money is constant). The theory then implies that if Real GDP (Q) and velocity of money (V ) are constant then a percentage increase of the money supply will lead (in the long run) to the same increase of the Price level. More generally, if money velocity is constant then the growth rate of the money supply equals the growth rate of the price level (inflation) plus the growth rate of real GDP.

Use this information to answer the following question. Suppose that this year’s money supply is $500 billion, nominal GDP is $10000 billion and real GDP is $5000 billion.

(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% each year. Assuming the central bank can perfectly control the money supply, 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 to keep the price level stable?

(d) What money supply should the central bank set next year if it wants inflation of 10%?

Answer 1

a.
P *Q = Nominal GDP
P*5000 = 10,000
P = $2

V = (P × Q) / M
V = 10000/500 = 20

b.

V = 20, M = 500 and new Q = 1.05*5000= 5250

P = MV/Q = 500*20/5250 = 1.90

It will fall: Nominal GDP = New Q * New P = 5250 * 1.90 = $9975 which is less than earlier level of nominal GDP of $10,000.

c.

V = 20, P=2 and new Q = 1.05*5000= 5250

M = P*Q/V = 2*5250/20 = 525

d.

Inflation of 10% means that the new price, P = 2.20

V = 20, P=2.20 and new Q = 1.05*5000= 5250

M = P*Q/V = 2.20*5250/20 = 577.50