# Money Demand and Money Velocity

The equation of exchange states that the money supply (M) times the velocity of money (V) equals prices (P) times the real growth (Y) in the Gross Domestic Product (GDP):

M × V = P × Y = Nominal GDP

For small changes in M and V, the following equation is also true:

∆M + ∆V = ∆P + ∆Y

or

Inflation = ∆P = ∆M + ∆V – ∆Y

So inflation occurs when the increase in the money supply plus the increase in the velocity of money exceeds the increase in real GDP. The quantity theory of money is derived from the above equation by considering money velocity and real growth as constants, which simplifies the equation:

∆P = ∆M

or

Inflation = Money Growth

The equation simply states that money growth causes inflation. The supply of money is also the only factor that politicians can control, at least directly. Real GDP and the velocity of money cannot be controlled legally or politically.

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Over the long-term, the link between money growth and inflation is strong in low-to medium-inflation environments. However, in many cases, money velocity is not constant over the short term. Although the velocity of money cannot be measured directly nor is it predictable over the short term, it is determined by the demand for money.

So to control inflation by targeting the money growth rate, a central bank must know what influences the demand for money and how changes in monetary policy rules will influence the demand.

The demand for money results from people's desire to hold money. When the money is held — not spent or invested — then it does not contribute to the velocity of money. Money velocity increases only when the people spend or invest it. Therefore, any factors that cause people to hold money will decrease the velocity of money, while factors that increase spending or investment will increase the velocity of money. Therefore, the demand for money is inversely related to the velocity of money. To understand how the velocity of money changes, one must understand what causes changes in the demand for money.

## Transactions Demand for Money

The transactions demand for money is the demand for money to be used as a medium of exchange, or as a means of payment. The portfolio demand for money results from people's desire to invest money, to serve as a store of value.

The primary factors affecting the transactions demand for money are the

• inflation rate,
• nominal income,
• nominal interest rates, and
• technology.

Inflation increases demand for money because higher prices requires more money for a given amount of goods and services. Higher inflation also increases the holding costs of money. For instance, if the inflation rate is 10%, then the cost of holding money is -10%. So when inflation is high, people will either spend it or invest it before the money loses value. Hence, higher inflation rates increases the velocity of money, which increases inflation even more. With low inflation, money growth will usually exceed inflation because the economy is also growing and, thus, requires a greater supply of money to keep prices constant. This results from the equation of exchange — where a higher real GDP growth reduces the inflationary effect of money growth.

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Because money is used as a means of payment, a higher nominal income will tend to increase the amount of money that people desire to hold, since wealthier people buy more expensive products and services and have a higher level of expenditures.

Higher interest rates reduces the demand for money by increasing the opportunity cost of holding money, which is the interest that could be earned if the money was invested. So if the interest rate is 5%, then the cost of holding money is the 5% that could have been earned in interest.

Technology that provides liquidity, such as credit cards or demand deposits that earn interest, such as interest-paying checking accounts, reduces the demand for money, since these payment substitutes provide a means of payment without the need to hold the money itself.

Technology can also reduce the demand for money by reducing the cost or time to convert assets into a means of payment. For instance, if a bank provides an electronic method of transferring funds from your savings account into your checking account, then you will tend to hold less money in your checking account so that you can earn more interest.

There is also a precautionary demand for money, which is money held for emergency expenses. Since people with higher incomes generally have higher expenses, they tend to hold more money for emergencies. The precautionary demand for money will also be greater when there is greater uncertainty about the future. For instance, if you do not feel secure in your job, you will tend to hold more money because of the increased risk of losing your job.

## Portfolio Demand for Money

The portfolio demand for money increases with wealth and portfolio risk and decreases with increased portfolio returns or lower opportunity costs. In other words, the portfolio demand for money is influenced by the same factors that influence the demand for bonds. Generally, greater portfolio returns and reduced risk decreases the demand for money, since there is an opportunity cost of not investing, and vice versa. For instance, when banks pay 1% interest or less on savings accounts, then people will tend to hold more money in their checking accounts, because it is more liquid and the opportunity cost of earning interest in a savings account is low. If interest rates are expected to rise in the future, then people will hold more money, because rising interest rates causes the value of bonds and other interest-paying financial instruments to fall in value.

## Central Banks Target Interest Rates Rather Than Money Growth to Control Short-Term Inflation

Since the factors that influence the demand for money are difficult to measure directly, central banks use statistics to predict how changes in monetary policy will affect the demand for money. Nonetheless, because the demand for money and, therefore, the velocity of money, fluctuates considerably over the short term, the link between money supply and inflation is weak. Hence, by targeting money growth, interest rates fluctuate with the velocity of money. Because a stable interest rate helps to stabilize the economy, but money growth causes interest rates to fluctuate, central banks target interest rates rather than money growth as a means to control short-term inflation.

## Money Demand and Money Velocity

• If the velocity of money is considered stable and the change in real GDP is considered constant, then inflation is caused by an increase in the money supply.
• Although the velocity of money is stable over the long-term, it can be highly variable over the short term.
• The velocity of money depends on the demand for money, which is the amount of money that people desire to hold for future purchases or investments.
• To control the inflation rate, central banks must know how their monetary policies affect the demand for money, and so they must know what affects the demand for money.
• Factors that increase the demand for money increase the velocity of money, which may increase inflation, while factors that decrease the demand for money decrease the velocity.
• The transactions demand for money is the money that people want to hold to pay for future purchases. The primary factors affecting the transaction demand for money are the inflation rate, nominal income, nominal interest rates, and technology.
• Inflation decreases the demand for money because money held loses value at the rate of inflation. So, if the inflation rate is 5%, then held money will lose 5% of its value annually. However, inflation also increases the demand for money because purchases cost more.
• Higher incomes will also increase the demand for money, since wealthier people tend to buy more expensive things.
• Higher interest rates reduce the demand for money by increasing the opportunity cost of holding the money, thus forfeiting any interest that could be earned by investing it.
• Technology that provides payment substitutes, such as credit cards or interest-paying checking accounts, reduces the demand for money.
• Uncertain future expenses, such as for healthcare or other emergencies, or an uncertain future economy, such as reduced employment opportunities,  increases the demand for money.
• The portfolio demand for money is the money that people want to hold for potential investments.
• The portfolio demand for money increases with wealth and with investment risk. Higher risk causes people to hold more money rather than invest it.
• Higher investment returns and reduced risk reduces the portfolio demand for money, since the opportunity cost of holding money is higher.
• Because the velocity of money is uncertain over the short term, the short-term effect of money supply on inflation is also uncertain. Therefore, central banks target interest rates rather than money growth to control short-term inflation.