Learning Objectives

Present Value Of Money Formula
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Value Of Money Formula Real Output Calculator

Explain the meaning of the equation of exchange, MV = PY, and tell why it must hold true.
Discuss the usefulness of the quantity theory of money in explaining the behavior of nominal GDP and inflation in the long run.
Discuss why the quantity theory of money is less useful in analyzing the short run.

Aug 20, 2019 If we want to see the growth in Tinyland's real GDP, the gross domestic product as measured by inflation-adjusted dollars, we need to adjust 2013's output for the 20% inflation. Velocity of Money = $4,800 / $200 Velocity of Money = 24 As seen above, the total GDP of this economy in this month was $400. The same kind of transactions happens throughout the year making the GDP to $4800 and the velocity of money for the year to 24. The formula below calculates the real value of past dollars in more recent dollars: Past dollars in terms of recent dollars = Dollar amount × Ending-period CPI ÷ Beginning-period CPI. The answer will be a negative percentage.) Here’s the formula: Output growth = (real GDP in Year 2 – real GDP in Year 1) x 100 real GDP in Year 1. For example, if real GDP in Year 1 = $1,000 and in Year 2 = $1,028, then the output growth rate from Year 1 to Year 2 is.

So far we have focused on how monetary policy affects real GDP and the price level in the short run. That is, we have examined how it can be used—however imprecisely—to close recessionary or inflationary gaps and to stabilize the price level. In this section, we will explore the relationship between money and the economy in the context of an equation that relates the money supply directly to nominal GDP. As we shall see, it also identifies circumstances in which changes in the price level are directly related to changes in the money supply.

The Equation of Exchange

We can relate the money supply to the aggregate economy by using the equation of exchange:

Equation 11.1

The equation of exchange shows that the money supply M times its velocity V equals nominal GDP. Velocity is the number of times the money supply is spent to obtain the goods and services that make up GDP during a particular time period.

To see that nominal GDP is the price level multiplied by real GDP, recall from an earlier chapter that the implicit price deflator P equals nominal GDP divided by real GDP:

Equation 11.2

[latex]P = frac{Nominal ; GDP}{Real ; GDP}[/latex]

Multiplying both sides by real GDP, we have

Equation 11.3

[latex]Nominal ; GDP = P times real ; GDP[/latex]

Letting Y equal real GDP, we can rewrite the equation of exchange as

Equation 11.4

We shall use the equation of exchange to see how it represents spending in a hypothetical economy that consists of 50 people, each of whom has a car. Each person has $10 in cash and no other money. The money supply of this economy is thus $500. Now suppose that the sole economic activity in this economy is car washing. Each person in the economy washes one other person’s car once a month, and the price of a car wash is $10. In one month, then, a total of 50 car washes are produced at a price of $10 each. During that month, the money supply is spent once.

Applying the equation of exchange to this economy, we have a money supply M of $500 and a velocity V of 1. Because the only good or service produced is car washing, we can measure real GDP as the number of car washes. Thus Y equals 50 car washes. The price level P is the price of a car wash: $10. The equation of exchange for a period of 1 month is

[latex]$ 500 times 1 = $ 10 times 50[/latex]

Now suppose that in the second month everyone washes someone else’s car again. Over the full two-month period, the money supply has been spent twice—the velocity over a period of two months is 2. The total output in the economy is $1,000—100 car washes have been produced over a two-month period at a price of $10 each. Inserting these values into the equation of exchange, we have

[latex]$ 500 times 2 = $ 10 times 100[/latex]

Suppose this process continues for one more month. For the three-month period, the money supply of $500 has been spent three times, for a velocity of 3. We have

[latex]$ 500 times 3 = $ 10 times 150[/latex]

The essential thing to note about the equation of exchange is that it always holds. That should come as no surprise. The left side, MV, gives the money supply times the number of times that money is spent on goods and services during a period. It thus measures total spending. The right side is nominal GDP. But that is a measure of total spending on goods and services as well. Nominal GDP is the value of all final goods and services produced during a particular period. Those goods and services are either sold or added to inventory. If they are sold, then they must be part of total spending. If they are added to inventory, then some firm must have either purchased them or paid for their production; they thus represent a portion of total spending. In effect, the equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.

To apply the equation of exchange to a real economy, we need measures of each of the variables in it. Three of these variables are readily available. The Department of Commerce reports the price level (that is, the implicit price deflator) and real GDP. The Federal Reserve Board reports M2, a measure of the money supply. For the second quarter of 2008, the values of these variables at an annual rate were

M = $7,635.4 billion

P = 1.22

Y = 11,727.4 billion

To solve for the velocity of money, V, we divide both sides of Equation 11.4 by M:

Play game and earn money quora. Equation 11.5

Using the data for the second quarter of 2008 to compute velocity, we find that V then was equal to 1.87. A velocity of 1.87 means that the money supply was spent 1.87 times in the purchase of goods and services in the second quarter of 2008.

Money, Nominal GDP, and Price-Level Changes

Assume for the moment that velocity is constant, expressed as V¯. Our equation of exchange is now written as

Equation 11.6

A constant value for velocity would have two important implications:

Nominal GDP could change only if there were a change in the money supply. Other kinds of changes, such as a change in government purchases or a change in investment, could have no effect on nominal GDP.
A change in the money supply would always change nominal GDP, and by an equal percentage.

In short, if velocity were constant, a course in macroeconomics would be quite simple. The quantity of money would determine nominal GDP; nothing else would matter.

Indeed, when we look at the behavior of economies over long periods of time, the prediction that the quantity of money determines nominal output holds rather well. Figure 11.6 “Inflation, M2 Growth, and GDP Growth” compares long-term averages in the growth rates of M2 and nominal GNP for 11 countries (Canada, Denmark, France, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the United Kingdom, and the United States) for more than a century. These are the only countries that have consistent data for such a long period. The lines representing inflation, M2 growth, and nominal GDP growth do seem to move together most of the time, suggesting that velocity is constant when viewed over the long run.

Figure 11.6 Inflation, M2 Growth, and GDP Growth

The chart shows the behavior of price-level changes, the growth of M2, and the growth of nominal GDP for 11 countries using the average value of each variable. Viewed in this light, the relationship between money growth and nominal GDP seems quite strong.

Source: Alfred A. Haug and William G. Dewald, “Longer-Term Effects of Monetary Growth on

Value Of Money Formula Real Output