Friedmania is a country in which the quantity theory of money operates. The country has a constant population, capital stock, and technology so real GDP does not change

Question

In 2014, real GDP was $500 million, the price level, measured by the GDP deflator, was 150 and the velocity of circulation of money was 10. (Because the price level is measured by the GDP deflator, it must be divided by 100 before it is used in the equation of exchange.) In 2015, the quantity of money increased by 20 percent. a) What was the quantity of money in 2014? b) What was the velocity of circulation in 2015? c) What was the price level in 2015?

Answer 1

a) The equation of exchange states that the quantity of money, M, multiplied by the velocity of circulation, V, equals real GDP, Y, multiplied by the price level, P. In terms of a formula, the equation of exchange is that M × V = P × Y. Using this formula, M = PY/V, [(150/100 ) × $500 billion]/10 gives the quantity of money as $75 billion.
b) The quantity theory of money asserts that the velocity of circulation is not influenced by the quantity of money. So the velocity of circulation remains constant at 10.
c) From the equation of exchange, the price level is P = MV/Y. Because the quantity of money increased by 20 percent, the quantity of money in 2015 is $75 billion × 1.2 = $90 billion. So
P = [($90 billion × 10 )/$500 million] × 100 = 180. Another way to calculate the price level in 2015 is to notice that according to the quantity theory, a change in the quantity of money has no effect on velocity and real GDP. So if the quantity of money increases by 20 percent, to balance the equation of exchange, the price level must also increase by 20 percent. So from this approach, the price level in Friedmania is 150 × 1.2, which is also equal to 180.