Inflation and the Money Supply  


Inflation is a change in the value of money. It is a function of the growth rate of the money supply. The money supply is the total amount of money in an economy. A country’s economy is affected by business cycles, fluctuations of the money supply, and economic policy.

The Velocity of Money

Assume a very small economy of John and Mary, with a money supply of $10. John has the $10 and spends $5 to buy flowers from Mary and pays Mary $5 to wash his car. Mary in turn spends $10 to buy potatoes from John. Through these transactions, the two have created $20 of their joint “gross domestic product” from a money supply of just $10.

In the John and Mary economy, the money supply is $10. The $10 are exchanged for goods and services (potatoes, flowers and car washing) produced in their economy. The total value of the goods and services produced in one year depends on how often the $10 is exchanged for products. The velocity of money is the average frequency with which a unit of money is spent. If John and Mary carry out these transactions every two months, in a year they would have $120 of “gross domestic product” from their $10 monetary base. (($10 + $5 + $5) x 6 = $120).

In a national economy, Gross Domestic Product (GDP), Y, is a function of how fast the money supply, M, moves through the economy. The velocity of money measures how fast money changes hands.

Y = M V, where V is the velocity of money.

Since V = Y / M, for the John and Mary economy, V = $120 / $10 = 12. In their economy, money changes hands 12 times per year.

The Equation of Exchange

Nominal GDP, Y, can be expressed as Y = P Q, where Y is equal to the Price paid, P, times the total Quantity of goods sold, Q.

Therefore, since Y = M V,

M V = P Q

The M V = P Q relationship is called the Equation of Exchange. It relates the money supply and the velocity of money to price levels and the quantity of goods sold.

Inflation as a Function of the Growth Rate of the Money Supply

Inflation, the rate of change of Price, can be derived from the Equation of Exchange,

M V = P Q,

so P = M V / Q

If V and Q are assumed constant,

dP / P = dM / M, where dP is an increment of Price, and dM is an increment in the money supply,

and (dP / P) / dt = (dM / M) / dt,

where t = time, dt is an increment of time, (dP / P) / dt is the rate of change of Price, and (dM / M) / dt is the rate of change of the money supply

The relationship (dP / P) / dt = (dM / M) / dt indicates inflation is a function of the growth rate of the money supply. The accuracy of this relationship depends on the extent to which V and Q remain constant.

The Money Supply

To maintain a constant value for money, the size of the money supply should grow each year as a function of the growth in the size of the economy, plus an amount reflecting population growth, and an amount accounting for changes in productivity. If the money supply grows by a smaller amount than necessary, deflation will occur. If the money supply grows too much, inflation will happen.

Money is an artifact used in the settlement of debts and as a ready store of value. Quantifying the money supply is more complex than it may seem, because the money supply has several components. The various measures of money supply differ in the forms of money which they aggregate.

M0 is the total of all currency, plus accounts at the central bank that can be exchanged for currency.

M1 is M0 plus the amount in checking or current accounts.

M2 is M1 plus savings accounts, money market accounts, retail money market mutual funds, and certificates of deposit of under $100,000.

M3 is M2 plus certificates of deposit over $100,000, institutional money market mutual fund balances, dollar deposits outside the United States (eurodollars), and repurchase agreements.

U.S. Federal Reserve money supply estimates as of February 11, 2010 (in billions of dollars): M0 860.4, M1 1667.8, M2 8452.1. In March, 2006, the Federal Reserve ceased publishing M3 money supply statistics.

Federal Reserve reports include data from which M3 can be constructed. Estimate as of February, 2010 (in billions of dollars): M3 13629.0 (source

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