Question

   Using the quantity theory of money, suppose that this year's money supply is $50 billion, nominal GDP is $1 trillion, and real GDP is $500 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 percent each year. What will happen to nominal GDP and the price level next year if the Bank of Canada keeps the money supply constant?

c.    What money supply should the Bank of Canada set next year if it wants to keep the price level stable?

d.   What money supply should the Bank of Canada set next year if it wants inflation of 10 percent? (5marks)

Answer 1

Quantitiy theory of money:

MV = PY

Where M is the money supply

V is the velocity of money

P is the price level.

Y is the real GDP

PY is the nominal GDP.

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(a) Nominal GDP = Price level * Real GDP

=> $1000 billion = Price level * $500 billion.

Note: 1 trillion = 1000 billion

=> Price level = $1000 billion / $500 billion

=> Price level = 2

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MV = PY

=> V = (PY / M)

=> V = (2 * $500 billion) / $50 billion

=> V = 20

Velocity of money is 20.

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(b) MV = PY

In terms of growth:

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

Given information:

% change in M = 0

% change in V =0

% change in P = ?

% change in Y = 5

Note: Velocity and money supply is constant. So, % change in M = % change in V = 0

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

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

=> % change in P = -5

Hence, there is 5% fall in price level.

Nominal GDP = PY

=> % change in Nominal GDP = % change in P + % change in Y

=> % change in Nominal GDP = -5 + 5

=> % change in Nominal GDP = 0

Hence, there is no change in Nominal GDP

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(c)

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

Given information:

% change in M = ?

% 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 will be increase in money supply by 5%

Money supply in next year = $50 billion (1 + 0.05)

Money supply in next year = $52.5 billion

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(d)

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

Given information:

% change in M = ?

% 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 will be increase in money supply by 15%

Money supply in next year = $50 billion (1 + 0.15)

Money supply in next year = $57.5 billion