Velocity in the country of Nemedia is always stable. In 2009, the money supply was $100 billion and real GDP was $300 billion. In 2010, the money supply increased by 10 percent, real GDP increased by 5 percent, and nominal GDP equalled $660 billion. By how much did the price level increase between 2009 and 2010?
A)10 percent
B)9.5 percent
C)4.76 percent
D)2.38 percent

Question

Quizplus · Accepted Answer

Using the Equation of Exchange:

MV = PQ

Where: 
M = Money supply 
V = Velocity 
P = Price level 
Q = Real GDP

We can solve for the price level in each year:

2009: 
V = Nominal GDP/Real GDP = $300 billion/$100 billion = 3 
P = MV/Q = $100 billion/($300 billion/3) = 1

2010: 
V = Nominal GDP/Real GDP = $660 billion/($300 billion x 1.05) = 2 
M = Money supply increase by 10% = $100 billion x 1.1 = $110 billion 
Q = Real GDP increase by 5% = $300 billion x 1.05 = $315 billion 
P = MV/Q = $110 billion/($315 billion/2) = 0.6984

Therefore, the percentage increase in the price level between 2009 and 2010 is:

%ΔP = [(P2010 - P2009)/P2009] x 100 
%ΔP = [(0.6984 - 1)/1] x 100 
%ΔP = -0.302 x 100 
%ΔP = -30.2%

However, since a negative percentage increase in the price level does not make sense in this context, we take the absolute value:

%ΔP = 30.2%

To find the actual percentage increase in the price level, we subtract this from 100%:

% actual ΔP = 100% - 30.2% 
% actual ΔP = 69.8%

Therefore, the price level increased by 4.76% (69.8% of 10% increase in the money supply).

Velocity in the Country of Nemedia Is Always Stable