Velocity

Velocity is defined as the average number of times a unit of the money supply (for example M-1) is used for economic transactions during a certain period. If a nation’s money supply is $100 and its citizens spend $600 on goods and services, then the average number of times the $100 was used during that year is 6.

Velocity Determinants

Velocity is determined by the following factors:

  1. The stability of the money.
    If a nation’s money supply is stable, consumers will spend money according to their needs, and businesses will invest money based on their future expected earnings. There is not much reason to believe that consumers and businesses will spend their money more quickly than the year before. However, if the nation’s money supply is not stable (too much money in circulation), and the value of money decreases (inflation), then people will be more likely to spend it more quickly. If, for example, prices double every week, people will spend their paychecks almost immediately. If they hold on to their money until the end of the week, prices will be twice as high. This quicker turnover of the money supply equates to an increase in velocity and makes it feel like there is even more money in circulation than there already is. This combination of too much money in circulation and increased velocity often leads to what is called hyperinflation.
  2. Transportation and technology advances.
    As it becomes easier to transfer and transport money, the money is more quickly available for re-spending. This increases velocity.
  3. People’s ability to save.
    When people save, as opposed to hoard, their money, funds become available to businesses and consumers via financial markets. This increases velocity and leads to greater economic activity. During an economic depression, many people lose faith in the banking system and resort to hoarding. This lowers the money supply and lowers velocity.

The Formula for Velocity

Velocity of final goods and services is defined as the number of times we use our money supply in order to purchase these goods and services during a period of time.

Therefore:

Velocity = Nominal GDP / Money Supply.
Or, abbreviated:
V = GDP / M

In Unit 3 we learned that GDP = P x Q (where P = the nation’s average price level and Q = the quantity of final products produced), so:

V = P x Q / M
After cross-multiplying, we get:
P x Q = M x V

The Quantity Theory of Money

The above equation is the “Equation of Exchange.” The right side (M x V) represents the volume of money exchanged to pay for the left side (P x Q), the volume of goods and services.

The equation implies that there is a direct relationship between changes in the money supply (M) and changes in a country’s price level (P).

Experience in industrialized countries shows that velocity (V) is relatively constant from year to year. Real Gross Domestic Product (Q) increases by an average of 2 or 3% each year. Therefore, if the money supply (M) increases by more than 2 or 3% each year, then the price level (P) increases.

The following numerical examples illustrate the effect on the price level (P), given certain changes in the other variables.

Example 1
Let’s assume that in year 1:
P = 5
Q = 20
M = 25
V = 4

Let’s assume that in year 2:
Q = 21 (approximately 4.88% increase, using the arc formula)
M = 27 (approximately 7.69% increase using the arc formula)
V remains the same at 4.
Problem: What is the price level in year 2, and how much has the price level changed since year 1?

Solution: Using the equation of exchange for year 2:
P x 21 = 27 x 4
Solving for P:
P = (27 x 4) / 21
P = 108 / 21= 5.14
This means that P increased by approximately 2.76%, using the arc formula [(5.14 – 5) / 5.07)] from year 1 to year 2.

In the above example, the Fed increased the money supply from 25 to 27. Consequently, the price level rose from 5 to 5.14. If the Federal Reserve’s goal is to maintain price stability (no change in the price level), and Q and V change in year 2 as indicated above, then the Fed should have increased the money supply to 26.25 (approximately 4.88% increase) instead of 27. At a price level of 26.25, the price level remains at 5:

Year 1: 5 x 20 = 25 x 4
Year 2: 5 x 21 = 26.25 x 4

Example 2
Let’s assume that in year 1:
P = 8
Q = 30
M = 40
V = 6

Let’s assume that in year 2:
Q = 30 (no change)
M = 40 (no change)
V = 5.5
Problem: What is the change in the price level?

Solution: Using the equation of exchange for year 2:
P x 30 = 40 x 5.5
Solving for P:
P = (40 x 5.5) / 30
P = 220 / 30 = 7.33
This means that P decreased by approximately 8.7%.
Example 2 illustrates that, ceteris paribus, if the Federal Reserve keeps the money supply constant, and velocity decreases, then prices fall.

Video Explanation
For a video explanation of velocity and the equation of exchange, please visit: