So, what is the equation of exchange, and how does it translate into a mathematical representation?
This is the Equation of Exchange Formula: || MV = PY
where
M = money supply
V = velocity of money
P = average price level
Y = real GDP of the economy
In this exchange equation, MV is the product of the money supply of currency units out in circulation and the number of times the currency changes hands in a year. This left side of the equation equals the amount of money used for spending in an economy for a certain period. PY is the product of the average price level and the real value of purchases in the economy. This right side of the equation equals the total money spent on buying goods in a certain period. This is also known as the nominal GDP of the economy.
This equation of exchange led the way in analyzing the relationship between money supply and its effect on the price level of goods. This relationship is known as the Quantity Theory of Money, developed by Irving Fisher. He says that any changes in the money supply will have a proportional change in the price level, which is also directly proportional to inflation.
Equation of Exchange Example
- Example 1
- Using Equation of Exchange to Show Total Amount of Money in Circulation
Country A has the following given information:
| Money Supply | $5,000,000 |
|---|---|
| Unemployment Rate | 12% |
| Price Level | $3,000 |
| Real GDP | $10,000,000 |
| Nominal GDP | $30,000,000 |
- SOLUTION
From the Equation of Exchange MV =PY, V can be isolated by doing algebraic rearranging of the variables:
V = PY/M
where
P = 3,000
Y = 10,000,000
M = 5,000,000
Therefore, V = (3,000)(10,000,000)/5,000,000 = 6,000
The total amount of money in circulation is on either side of the equation.
MV = (5,000,000)(6,000)= $ 30,000,000,000
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Taking the Equation of Exchange and differentiating both sides of the equation gives:
| % change in (MV) = % change in (PY) |
|---|
| % change in M + % change in V = % change in P + % change in Y |
|---|
In the long run, the change in velocity becomes stable and constant. When this happens, the percentage change is zero. Rearranging to highlight the change in the price level in the equation,
| % change in P = % Change in M - % Change in Y |
|---|
This new equation shows that subtracting the change in the real GDP of any economy from the percentage of its money supply will give the percentage change in inflation. This is also known as the Inflation Equation of Exchange. The inflation equation of exchange shows how the money supply is the greatest driving force for inflation. When the percentage increase in money supply is higher than the percentage increase in real GDP, there is an increase in the percentage change of price level that leads to the economy having inflation. However, if the growth in GDP is higher than the increase in the money supply, the effect is a decline in the price level. This is also known as deflation.
Inflation Equation of Exchange Example
- Example 2
A small island country had a ten percent increase in its money supply from the prior year and a five percent increase in real GDP. Calculate the change in the price level.
- SOLUTION
Using the inflation equation of exchange, the price change is simply the result when changes in real GDP are subtracted from the changes in its money supply.
In this example, change in price level is 10% -5% = 5% increase.
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The equation of exchange shows how money supply, the velocity of money, and price level relate to each other. It is written as MV = PY, where M stands for the money supply, V stands for velocity of money, P stands for the average price level in the economy, and Y stands for the real GDP of the economy. This equation of exchange can be converted into another equation known as the inflation equation of exchange by taking the derivatives on both sides of the equation. Following the mathematics of derivatives of products, a new equation is formed: % change in M + % change in V = % change in P + % change in Y. Rearranging this gives the formula for the changes in the price level, which is directly linked to inflation. That is, % change in P = % Change in M - % Change in Y.
In the long run, the velocity of money becomes stable and constant. This is because, in the long run, the changes in how fast money circulates from one person to another through monetary economic transactions decrease and eventually stabilize, and velocity becomes constant. With velocity assumed constant, high inflation will be seen if the percentage change in money supply outpaces the growth in real GDP. Conversely, if the real GDP growth outpaces the increase in money supply, the price levels will decrease, and deflation will happen in the economy.
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Video Transcript
Inflation and Money Supply
Inflation is an important concept in economic analysis that has real world importance. In a nutshell, inflation is an increase in the general price level in an economy. A high rate of inflation can wreak havoc on an economy. If wages don't keep up with prices, for example, people can't buy as much. If people can't buy as much, businesses stop producing as many goods and services. If production slows, people get laid off, businesses shut down and personal and business debts are not paid.
While more than one factor contributes to inflation, such as the general level of aggregate supply and demand in the overall economy, today we're going to focus on money supply as a factor that influences inflation. Money supply is simply the total supply of money currently in the economy. Keep in mind that the money supply includes not only the bills and coins in your pocket, but also all the electronic balances in checking and savings accounts throughout the economy.
We can analyze the effect of money supply on inflation through the use of the equation of exchange. Let's take a look.
Equation of Exchange
The equation of exchange is an equation that shows us how money supply, the velocity of money, and price level relate to each other. The velocity of money refers to how fast money passes from one person to another through economic transactions (for example, buying and selling) over a period of time.
We can state the equation of exchange as:
M * V = P * Y
Let's parse the equation. M stands for the money supply, while V stands for the velocity of money. On the other side of our equation, P stands for the average price level in the economy, while Y is the real GDP of the economy. GDP is short for gross domestic product, which is the value of all the goods and services produced in a country during a specific period of time. Real GDP is GDP that is corrected to take inflation into account by using the prices of a base year. This way you can see how much growth is 'real' as opposed to just inflation making it look like the economy is growing. So the equation tells us that the money supply times the velocity of money equals the price level times real GDP.
In the real world, the calculation of the equation of exchange can be quite complex because economies are very complex. So we're going to simplify things by using a fictional island economy known as Economia to illustrate the principle behind the equation.
Let's say that our island paradise is populated by only 10 people who each have $25, for a total money supply of $250.00. Economia is a simple place for relaxing, not for the hustle and bustle of economic activity. Our island denizens only engage in one economic transaction a month: every islander gives one back massage each month to another islander for $25. Since money trades hands only once a month, the velocity of money is 1. The price level is the cost of the massage, $25, and GDP is the number of massages given during the month, which is one per person or 10 massages. Let's plug in the numbers:
M * V = P * Y
$250 x 1 = $25 x 10 $250 = $250
Inflation & Money Supply
Through some mathematical manipulation, the equation of exchange can be rewritten to show the relationship between the variables in terms of the percentage rate of change of each variable. The equation looks like this:
In plain English, this equation tells us that we can obtain the approximate percentage change in the price level (remember that P is for price level; the triangle is called delta and means change) of the economy by subtracting the change in the potential real GDP (Y) from the percentage change in the money supply (M). You may be wondering what happened to the velocity of money. This model assumes that the velocity of money remains constant, which means we don't have to include it in our new equation. Let's see how the equation works.
We're returning to our tiny island country for this example to keep it simple, but the principles are the same regardless of whether we are dealing with $10 or $10 trillion. Let's say a couple of years have passed on our island, and the economy has started to develop beyond giving massages. Last year the money supply was a whopping $1,000 and is now an astonishing $1,100, amounting to a 10% increase in the supply of money. The GDP of our little island has increased a respectable 3% from $1,000 to $1,030. Let's plug in the numbers:
10% - 3% = 7%
The change in the rate of inflation is 7%. Note that if the money supply increased twenty percent and the rate of GDP growth remained at 3%, our island paradise would have a rate of inflation of 17% (20% - 3%), which is a huge increase in prices.
So what does this tell us about inflation? A key fact is that the rate of GDP growth is usually pretty darn small - typically just a few percent a year. This means that inflation is largely driven by the rate at which the supply of money increases in the economy. Assuming the velocity of money remains constant, if the supply of money outpaces the growth in GDP by a significant amount you'll see high inflation. On the other hand, if the growth in GDP is higher than the increase in the money supply, you'll actually see a decline in the price level, called deflation.
Lesson Summary
The equation of exchange can be used to see the relationship between inflation and the supply of money in an economy. The basic equation of exchange:
M * V = P * Y
can be rewritten as this:
This equation illuminates an important fact about inflation and the supply of money. If the supply of money increases rapidly, the rate of inflation will also increase rapidly to the extent that real GDP does not keep up with it. On the other hand, if real GDP increases faster than the rate of money supply, deflation may occur.
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