Question

Suppose that this year’s velocity is 10, nominal GDP (PY) is $50 billion, and real GDP (Y) is $10billion

(a)  What is the price level and money supply? Please show all calculations for full credit

(b) Suppose that velocity constant and the economy’s output of goods and services (Y) decreased by 5 percent. What will be the new price and new nominal GDP if the Fed increases the money supply by 5%?

(c) Suppose that velocity constant and the economy’s output of goods and services (Y) decreased by 5 percent. What will be the growth rate of price and growth rate of nominal GDP if  the Fed increases the money supply by 5%?

Answer 1

(a) Quantity 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.

-----------------------------------------------------------------

Nominal GDP = Price level * Real GDP

=> $50 billion = Price level * $10 billion

=> Price level = ($50 billion / $10 billion)

=> Price level = 5

----------------------------------------------------

MV = PY

=> M * 10 = $50 billion

=> M = $50 billion / 10

=> M = $5 billion.

Money supply is $5 billion.

----------------------------------------------------------------------------------------------------------------

(b) MV = PY

in terms of growth:

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

Given information:

% change in Y = -5

% change in M = 5

% change in V = 0 (: because V remains constant)

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

=> 5 + 0 = % change in P + (-5)

=> 5 = % change in P - 5

=> % change in P = 5 + 5

=> % change in P = 10

Thus, the price level will increase by 10%.

Nominal GDP = PY

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

=> % change in nominal GDP = 10 + (-5)

=> % change in nominal GDP = 5

Thus, the nominal GDP will increase by 5%

New price level = 5 ( 1+ 0.1) = 5.5

New nominal GDP = $50 billion (1 + 0.05) = $52.5 billion.

-------------------------------------------------------------------------------------------------------------------

(c) The growth rate of price is 10% and growth rate of nominal GDP is 5%.

See part (b) for calculation.