# Quantity Theory of Money

## Definition of the Quantity Theory of Money:

The quantity theory of money is an economic model that explains the direct relationship between the money supply and price levels.

## Detailed Explanation:

Money, like all commodities is subject to the law of supply and demand. When the money supply is increased, the price of money, (its value), decreases. If the value of a dollar decreases, then it takes more dollars to purchase a given item. In other words, inflation occurs. The quantity theory of money illustrates mathematically how increasing the money supply either increases the average price of goods and services (thereby causing inflation), or stimulates production. In other words, this simple macroeconomic model shows how the supply of money is directly related to the price level and production of goods in an economy. The quantity theory of money is expressed with the following equation:

M x V = P x Y

Where:
M = money in circulation P = price level
V = velocity of money Y = total number of units produced

Everything we purchase is paid for with money, so it makes sense that the amount of money we spend equals the value of all the goods and services produced. Gross domestic product is the market value of all final goods and services produced within a country in a given period of time. An economy’s total output, GDP, can be computed by adding up the price of each unit sold multiplied by the number of units sold. This can be simplified by taking the weighted average of all prices multiplied by the number of units sold, or P x Y in our equation.

To illustrate, let’s assume Chatty is a small country that only produces cell phones. It sells all the phones it produces. (This eliminates any complications from inventory adjustments.) Assume the weighted average price of phones equals \$300 and Chatty produced 1,000 cell phones last year. Chatty’s GDP, or the value of its production (P x Y) would equal \$300,000.

Returning to our formula, we know that the amount of money in circulation (M) multiplied by the number of times each dollar is spent (V) must equal the total amount spent in an economy. The velocity of money is the average frequency a unit of currency is used to purchase a final good or service annually in an economy. For example, if a \$5 bill has been used three times, then the velocity equals three and the total purchases using the \$5 bill must equal \$15. Now assume the money supply equals \$500,000 and is comprised of 100,000 \$5 bills. If each bill is spent three times (V), \$1,500,000 (M x V) was spent in the economy.

If the velocity of money is increased, then the total expenditures increases. In our above example, assume the velocity of money increases from three to four. In this case the amount spent in the economy increases from \$1,500,000 to \$2,000,000 even though the money in circulation remained unchanged. If the velocity of money increases, then more transactions have taken place. The velocity of money has been remarkably stable over short periods, so economists generally view V as being constant when using the quantity theory of money to explain inflation.

Let us return to Chatty to illustrate how an increase in the money supply would impact the economy. Recall that last year’s economy produced 1,000 cell phones with a weighted average price of \$300. If the velocity of money equals 3, the money supply equals \$100,000.

M x V  =  P x Y
(M) x 3  =  \$300 x 1,000
M  =  \$100,000

Now assume the government wants to build some roads, but leaders are fearful of the political implications if they raise taxes, so government officials decide to print \$100,000. The money supply suddenly doubles to \$200,000. Also, assume the economy is operating at full capacity; it would be difficult to allocate additional factors of production to increase output beyond 1,000 cell phones. The new price level is derived using the formula above, and assuming the velocity of money is constant, P doubles to \$600. Doubling the money supply doubles the price level in this simple economy.

M x V  =  P x Y
\$200,000 x 3  =  P x 1,000
P  =  \$600

Now assume the economy is in a recession, and its factors of production are not being used to their capacity. The government prints \$100,000. Perhaps banks increase their appetite for loans because they have added funds, which make it easier for manufacturers to borrow the money needed to increase their output. If production increased to 2,000 cell phones, the new price level would equal \$300.

M x V  =  P x Y
\$200,000 x 3  =  P x 2,000
P  =  \$300

When an economy grows and companies operate near capacity, an increase in the money supply is more inflationary because an increase in production is restrained by limited capacity. In this case, too many dollars chase too few goods. In the long-run, where production is limited by a country's factors of production any increase in the money supply must result in an increase in the price level assuming the velocity has remained constant. However, many economists believe increasing the money supply during a recession can spark short-term economic growth. Banks would have more money to lend. It would be easier for businesses and consumers to borrow the money to grow a business or purchase consumer goods. In these cases, increasing the money supply could stimulate economic growth. This was one of the objectives when the Federal Reserve (the US central bank) significantly increased the money supply following the Great Recession of 2008.

Historical examples illustrating the direct relationship between printing money and inflation include the hyperinflation in Germany following WWI and more recently in Zimbabwe.

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