The connection between increases in the money supply and increases in prices has been discussed by writers dating back at least as far as the Greek philosopher Aristotle in the fourth century B.C. During the sixteenth century, the Spanish conquest of Mexico and Peru resulted in huge quantities of gold and silver being exported to Europe, where they were minted into coins, greatly increasing the European money supply. Many writers noted that this increase in the money supply was followed by an increase in the price level and a corresponding loss of purchasing power, which is the ability of consumers to use money to acquire goods and services.
Irving Fisher and the Equation of Exchange
In the early twentieth century, Irving Fisher, an economist at Yale University, developed the quantity theory of money in an attempt to make more explicit the relationship between the money supply and inflation. Fisher began his analysis by using theequation of exchange:
Irving Fisher and the Equation of Exchange
In the early twentieth century, Irving Fisher, an economist at Yale University, developed the quantity theory of money in an attempt to make more explicit the relationship between the money supply and inflation. Fisher began his analysis by using theequation of exchange:
MV = PY.
The equation states that the quantity of money,M,multiplied by the velocity of money, V, equals the price level, P, multiplied by the level of real GDP, Y. Recall that the price level measures the average level of the prices of goods and services in the economy. There are several measures of the price level. The measure that is most relevant here is the GDP deflator, which includes the prices of all goods and services included in GDP. If we multiply real GDP by the GDP deflator, we get nominal GDP, so the right side of the equation of exchange equals nominal GDP. Fisher defined the velocity of money— or, simply, velocity—to be equal to the number of times each dollar in the money supply is spent on a good or a service that is included in GDP, or:
The equation states that the quantity of money,M,multiplied by the velocity of money, V, equals the price level, P, multiplied by the level of real GDP, Y. Recall that the price level measures the average level of the prices of goods and services in the economy. There are several measures of the price level. The measure that is most relevant here is the GDP deflator, which includes the prices of all goods and services included in GDP. If we multiply real GDP by the GDP deflator, we get nominal GDP, so the right side of the equation of exchange equals nominal GDP. Fisher defined the velocity of money— or, simply, velocity—to be equal to the number of times each dollar in the money supply is spent on a good or a service that is included in GDP, or:
For example, in 2009, nominal GDP was $14,256 billion and M1 was $1,693 billion, so velocity in 2009 (using the M1 measure of the money supply) was $14,256 billion/$1,693 billion = 8.4. This result tells us that during 2009, on average each dollar of M1 was spent 8.4 times on goods or services included in GDP. Because Fisher defined velocity to be equal to PY/M, we know that the equation of exchange must always hold true. The left side must be equal to the right side. A theory is a statement about the world that might possibly be false. Therefore, the equation of exchange is not a theory. Fisher turned the equation of exchange into the quantity theory of money, by asserting that velocity is constant. Fisher argued that the average number of times a dollar is spent depends on how often people get paid, how often they go shopping, how often businesses send out bills, and other factors that change only very slowly. Because this assertion may be true or false, the quantity theory of money is, in fact, a theory.
The Quantity Theory Explanation of Inflation
To investigate the effects of changes in the money supply on inflation, we need to rewrite the equation of exchange from levels to percentage changes.We can do this by using a handy mathematical rule that states that an equation where variables are multiplied together is equal to an equation where the percentage changes of those variables are added together. So, we can rewrite the quantity equation as:
% Change in M + % Change in V = % Change in P + % Change in Y.
The Quantity Theory Explanation of Inflation
To investigate the effects of changes in the money supply on inflation, we need to rewrite the equation of exchange from levels to percentage changes.We can do this by using a handy mathematical rule that states that an equation where variables are multiplied together is equal to an equation where the percentage changes of those variables are added together. So, we can rewrite the quantity equation as:
% Change in M + % Change in V = % Change in P + % Change in Y.
If Irving Fisher was correct that velocity is constant say, it always equals 8 then the percentage change in velocity will be zero. Remember that the percentage change in the price level equals the inflation rate. Taking these two facts into account, we can rewrite the quantity equation one last time:
Inflation rate = % Change in M - % Change in Y
Inflation rate = % Change in M - % Change in Y
This relationship gives us a useful way of thinking about the relationship between money and prices: Provided that velocity is constant, when the quantity of money increases faster than real GDP, there will be inflation. The greater the percentage change in the quantity of money, the greater the inflation rate. In the United States, the long-run rate of growth of real GDP is about 3% per year. So, the quantity theory indicates that if the Federal Reserve allows the money supply to increase at a rate faster than this, the result will be inflation.
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