4. Velocity and the quantity equation Consider a simple economy that produces on

Question

4. Velocity and the quantity equation

Consider a simple economy that produces only cell phones. The following table contains information on the economy's money supply, velocity of money, price level, and output. For example, in 2010, the money supply was $400, the price of a cell phone was $5.00, and the economy produced 800 cell phones.

Fill in the missing values in the following table, rounding to the nearest cent when necessary.

The money supply grew at a rate of   from 2010 to 2011. Since cell phone output did not change from 2010 to 2011 and the velocity of money   , the change in the money supply was reflected   in changes in the price level. The inflation rate from 2010 to 2011 was   .

Year Quantity of Money Velocity of Money Price Level Quantity of Output Nominal GDP (Dollars) (Dollars) (Cell phones) (Dollars) 2010 400 5.00 800     2011 404 10     800    

Explanation / Answer

Quantity theory states that

M x V = P x Y

M: Money supply, V: Velocity ofmoney, P: price level, Y: Real GDP

[P x Y = Nominal GDP]

(a)

Year 2010:

V = (P x Y) / M = ($5 x 800) / $400 = 10

Nominal GDP = $5 x 800 = $4,000

Year 2011:

P = (M x V) / Y = ($404 x 10) / $800 = 5.05

Nominal GDP = $5.05 x 800 = $4,040

(b)

Money supply grew at [(404 - 400) / 400] x 100 = 1%

Velocity of money did not change.

Inflation rate = Change in P = (5.05 - 5) / 5 x 100 = 1%

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