# Quantity Theory of Money: causes of inflation and its implications on monetary policies

#### What are the factors that cause inflation?

A standard approach to analyse inflation is to use the famous “Quantity Theory of Money” shown below. it is originally formulated by Polish mathematician Nicolaus Copernicus in 1517 and later popularized by economists Milton Friedman and Anna Schwartz.

MV = Py

• M = Money Supply
• V = Velocity of money
• P = Price level
• y = real output

The equation provides an overview of the relations among the quantity of money, velocity of money, price level and real output. It indicates that the quantity of money in an economy is significantly influential on its level of economic activities.

Theoretically, V and y in long run are assumed to be held constant (money supply have no long-run effect on the real variable in the long run – called long-run neutrality of money), the increase in money supply will cause a proportional increase in the price level, thus leading to inflation. As inflation occurs, the purchasing power of money declines simultaneously, which imply a decrease in the value of money. It requires more units of currency to buy the same quantity of goods or services.

The growth rate version of the above equation can be employed to show how the inflation rate depends on the growth rate of M, V, and y.

gM + gV = gP + gy

• g = growth rate

The rate of growth of the quantity of money plus the rate of growth of the velocity of money equals the rate of inflation plus the rate of growth of real output.

The well-known monetary economist Milton Friedman claimed that: “Inflation is always and everywhere a monetary phenomenon.” What he meant is that the sustained growth in the inflation rate has always been due to sustained growth in the money supply.

Referring to the “Quantity Theory of Money, the growth rate of price level depends not only on money supply but also the velocity of money and real output. What are the supports of Milton Friedman’s statement that inflation is a monetary phenomenon?

The answer lies in the fact that historically, the rate of growth of velocity and real output changed much more slightly, compared to the growth in the money supply. Even during the time of recession, the annual growth of GDP rarely falls by more than three percentage points, whereas the Velocity of money normally rises by less than one percentage point per year. As a result, when comparing high-inflation and low-inflation countries, the difference mostly rests in the rate of growth in the quantity of money, rather than the difference in the rate of growth in velocity of money and rate of growth in real output.

Notice that what Milton Friedman suggested only holds in the long run. In the short run, the changes in the money supply could affect the level of real economic activities and impose a lesser influence on the inflation rate.

#### The implications from the quantity theory of money

The theory can be applied to the help manage inflation rate of a country by its central bank. By assuming the velocity of money to be constant (zero rates of growth), the equation evolves to be as follow:

gP = gM – gy

the growth rate of the price level (inflation) equals the rate of growth in money supply minus the rate of growth in real output. It is commonly suggested that long-run growth of the real output depends on the accumulation of labour, capital, and technological advancement, which are independent of the nominal variables such as money supply.

As a result, the equation again demonstrates that the changes in money supply will lead to proportional changes in the price level. Below are some implications for the formulation of monetary policies.

• To lift the inflation rate, the growth rate of the money supply should be set higher than the long-run growth rate of real output.
• To reduce the inflation rate, the growth rate of the money supply should be set lower than the long-run growth rate of real output.
• To achieve a zero inflation rate, the growth rate of the money supply should be equal to the long-run growth rate of real output.
• To increase the inflation rate by a little year over year, like around a 2% target set by the Fed, Bank of England and European Central Bank, the growth rate of the money supply should be just slightly higher than the growth rate of real output.

Note that, all of the above only holds assuming the velocity of money is constant, and the long-run growth of real output is independent of the growth of money supply.

#### Real-world processes of increasing the money supply by the FED

Through the open market operation, the Federal Reserve of the USA (FED) firstly buys bonds from the banks with newly created liabilities, whereas the bond seller’s banks in turn receive the money from the FED as reserves. Secondly, the banks use the money to buy additional securities, such as making additional loans or purchasing more assets, by which extra money will be injected and circulated in the market. While the supply of loanable funds increases, the interest rate will drop and thus encourage borrowing for starting business or consumption to stimulate the growth of output.