Question

Suppose an economy has enough labor, capital, and land to produce 1,000 apples per year. Apples are the only product of the economy and the price is $10 per apple. In 2019, money supply is $5, 000 and velocity of money is constant.

a. State the quantity theory of money.

b. Compute nominal GDP and velocity of money in 2019.

In 2020, the central bank of the economy increases the money supply by 10%.

c. Compute nominal GDP and price level in 2020. What is the inflation rate between 2019 and 2020?

d. According to the Fisher effect,

i. how are nominal and real interest rates related to one another?

ii. what will be the impact of the increase in money supply by 10% on nominal and real interest rates respectively?

Answer 1

(a) Quantity theory of money states that there is direct relationship between the quantity of money supply and price level.

MV = PY   

Where M is money supply

V is velocity of money

P is the price level

Y is the real GDP.

PY is nominal GDP

(b) Nominal GDP = Price * Quantity of apple produce.

Nominal GDP = $10 * 1000

Nominal GDP = $10,000

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MV = PY

=> $5000 * V = $10000.

=> V = ($10,000 / $5000)

=> V = 2

Velocity of money is 2

(c) In 2020, money supply increase by 10%. Velocity remains constant, Apple production remains constant.

MV = PY

in terms of growth:

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

=> 10 + 0 = % change in P + 0

=> % change in P = 10.

The inflation rate between 2019 and 2020 is 10%.

New price level = $10 (1+0.1)

New price level = $11.

Nominal GDP in 2020 = P*Y

Nominal GDP in 2020 = $11 * 1000

Nominal GDP in 2020 = $11000.

(d)

• (i) According to Fisher effect, Real interest rate is nominal interest rate minus inflation rate.

Real interest rate = Nominal interest rate - Inflation rate.

• (ii) Increase in money supply by 10%.

According to money neutrality increasing the money supply decreases the nominal interest rate but doesn't change the real interest rate