Question

Using the quantity Theory of Money formula, suppose that in 2020: Money supply = $50 Billion; Nominal GDP = $1.0 Trillion; and Real GDP = $500 Billion.

a). Calculate the Price Level (P) and Velocity of Circulation (V) . Show your calculations for a full mark.

b) Suppose the velocity of circulation is constant (the one you calculated in (a), and the economy’s output of goods and services increases by 5% annually. Calculate Nominal GDP (or what will happen to nominal GDP  and the Price Level (P) in 2021 if the Bank of Canada keeps the money supply in 2020 constant or the same?

c). Calculate or What level of money supply should the Bank of Canada set next year (2021) if it wants to keep the price level stable (hint: based on a 5% increase in real GDP).

Please show all steps per question.

Answer 1

(a) Nominal GDP = Price level * Real GDP
$1 trillion = Price level * ($500 billion)

$1000 Billion = Price level * ($500 billion)

Price level = ($1000 billion / $500 billion)

Price level = 2

Note: $1 trillion = $1000 billion.

According to the 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.

M*V = P*Y

$50 billion * V = 2 * $500 billion

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

V = 20

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(b) M*V = P*Y

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 Y =5

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

0 +0 = % change in P + 5

% change in P = -5

There will be 5% fall in the price level.

Nominal GDP = P * Y

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

% change in Nominal GDP = -5 + 5

% change in Nominal GDP = 0

There is 0% change in the Nominal GDP.

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(c) Given information:

% change in V= 0

% change in P =0

% change in Y = 5

In terms of growth

% 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 5% increase in money supply.

New level of money supply = $50 billion (1 + 0.05)

New level of money supply = $52.5 billion