Chapter 13: Problems 
8. Inflation is a longterm phenomenon caused by a too rapid growth in the money supply." Is this statement true or false? Use the quantity theory of money in defense of your answer. (In this example, the capital letter A stands for the delta triangle symbol.)
In order to determine the veracity of the above statement, it is helpful to first discuss the quantity theory of money. The quantity theory of money emphasizes that the money supply is the main determinant of nominal gross domestic product. To understand this theory, the equation of exchange must first be examined. This equation shows the relationship between the money supply, M, the income velocity of money, V (where V is defined as the number of times the money supply is used to purchase final goods and services during the year), the GDP deflator, P, and real gross domestic product, GDP. The equation is written as:

MxV = PxGDP. 
The left hand side of the equation represents the amount spent on final goods and services while the right hand side represents the amount received for these final goods and services. By definition, these two sides must be equal.

The quantity theory of money assumes that the income velocity of money, V, is constant. If V is constant then any increase in nominal gross domestic product, P x GDP, occurs because of an increase in the money supply, M.

The effect of a change in the money supply on inflation can now be determined. First, rewrite the equation in terms of growth rates. When this is done the equation becomes:

AM/M + AV/V = AP/P + AGDP/GDP.

AM/M is the growth rate of the money supply, ~W/V is the growth rate of velocity, AP/P is the growth rate of the GDP deflator (inflation rate), and AGDP/GDP is the growth rate of real gross domestic product. If velocity is constant, its growth rate is zero. Thus it will drop out and the equation becomes:

AM/M = ~P/P + ~xGDP/GDP.

Now solve the equation for the growth rate in the GDP deflator (inflation rate). This is done by rearranging terms to derive:

Ap/p =/xM/M AGDP/GDP.

This equation shows that the rate of inflation is equal to the growth rate of the money supply less the growth rate of real output. The growth rate of the money supply is determined by the Federal Reserve. The growth rate of real output is determined by resources and technology. Historically the longterm growth rate in real output has been approximately 3 percent per year. If the Federal Reserves allows the money supply to grow at an annual rate of approximately 3 percent, no inflation will occur. However, ff the Federal Reserves allows the growth rate of the money supply to exceed the growth rate of real output, inflation will occur. Thus, according to the quantity theory of money inflation is caused by the Federal Reserve allowing the money supply to grow too rapidly.
