MONEY. VELOCITY,AND AGGREGATE DEMAND

First, how did the classical economists link up changes in money with changes in aggregate demand (money g.n.p.)? They asked, (1) how much money do people have, and (2) how fast do they spend it? A simple “equation of exchange” (proposed by Professor Irving Fisher a half-century ago) points up the relationships involved in this approach. The equation is:

MV = PT = GNP

M stands for the amount of money in the hands of the public; V for the average “velocity of circulation,” or the number of times each dollar is spent per time period; P for the price level, or average price per unit sold; and T for the number of units sold during each time period, i.e., for the “real” volume of transactions carried out at average price P. If we think of T as the real goods and services produced in any year, it becomes the real g.n.p. of the economy; and P can be thought of as the “g.n.p. deflator” from Chapter 4.Then V is called “income velocity” because it shows the average number of times each year a dollar is spent on income-creating transactions in the g.n.p. accounts.

For example, in a very simple hypothetical economy, suppose M is $1,000. Suppose further that during some year 2,000 units of physical goods are sold, and that their average price is $2. The T (real g.n.p.) in our equation would then be 2,000, and the P would be $2; PT equals $4,000, the total amount paid for the goods sold. This leaves the V, the average number of times per year each dollar is spent. Here the V is obviously 4, since total expenditures on the goods sold were $4,000 (P times T) so each of the one thousand dollars must have been spent four times during the year on the average to account for the $4,000 of expenditures. The whole equation is then

MV = PT, or

$1,000 x 4 = $2 x 2,000

If you think a minute about this equation, you will see that the two sides are defined so that they will always be equal. MV is simply the total amount spent on goods and services during the time period—the total number of dollars multiplied by the average number of times each dollar is spent in the period. PT is the total amount received for goods and services during the period —the number of units sold multiplied by the average price per unit. The two are identical; what someone spends, someone else receives. If we now add another $1,000 of money in our example, and keep V and T unchanged, clearly P will have to be $4 to make the equation balance at $8,000. In economic terms, prices would be twice as high on the average because expenditures doubled but only the same physical volume of goods was sold.

The equation of exchange is obviously a truism. It just says that every dollar spent by someone is received by someone else. Why, then, is it a significant analytical tool? The answer is, because it sets out four important variables on which attention may usefully be centered in analyzing booms and depressions, inflations and deflations. And it sets forth these variables in a way that points up some of their broad relationships— for example, it is the amount of money people have, multiplied by the average number of times each dollar is spent, that gives the total annual amount of spending. The equation certainly doesn’t provide any answers, but it is a simple framework for looking at the complex real world. It skips over the whole detailed analysis of consumer and business spending decisions in Chapters 6-7. But it suggests that behind the scenes, the quantity of money may be a basic factor controlling the level of spending.

M, V, Total Spending

The equation of exchange focuses attention on M and V as determinants of the level of aggregate demand. Think of the receipts (PT) side as being by and large passive, as the classical economists did. Then the equation says that an increase in the amount of money will lead to a higher volume of expenditures, unless it is offset by a decrease in the velocity at which the money is spent.

World War II provides an historical example. The money stock increased from about $36 billion to $110 billion, largely because we financed the war in considerable part by creating new money. The equation of exchange suggests that with such a big increase in the money supply, g.n.p. should have risen in the same proportion unless income velocity increased or decreased during the war.

What did happen? V declined substantially over the war period, and total spending rose much less than in proportion to the money supply. On the average, people held their dollars longer before spending them. This was partly because many goods were unavailable, partly because there was a lot of patriotic pressure against spending, and partly because interest rates were so low that holding securities was a relatively unattractive alternative to holding money. As a result, money g.n.p. (MV) rose only from $91 billion to $211 billion, as indicated in the lines for 1939 and 1946 in the table below:

1929: M ($ 26 billion) X V (4.0) = g.n.p. ($104 billion)
1939: M ($ 36 billion) X V (2.5) = g.n.p. ($ 91 billion)
1946: M ($110 billion) X V (1.9) = g.n.p. ($211 billion)
1966: M ($170 billion) X V (4.3) = g.n.p. ($740 billion)

The 1929 and 1966 lines of the table provide some historical perspective. Back at the peak of the boom in the 1920’s, V was high. People were spending their money fast, holding. their idle money balances to a minimum. Then came the big drop of the depression and war years, as billions were piled up in temporarily idle balances. After World War II, people began to spend down their accumulated balances, and V rose persistently. Higher interest rates provided an inducement to put idle money into securities and other assets, and as money became “tighter” both businesses and individuals were again forced to “economize” their cash balances, cutting them back to the minimum consistent with their needs.

FIG. 8-2 Income velocity has been relatively stable over
the long run, with a groduol updrift. However, it rises and
falls in booms and depressions, and sometimes falls dra.
matically for special reasons—note the World War II
period. (Calculated by dividing money stock into money
g.n.p. for each year.)

If V were stable, changes in M would be a good predictor of g.n.p. Indeed, by controlling M we could control g.n.p. Professor Fisher argued that by and large his V (which was a little different from ours) was relatively stable over long periods, so that changes in M could be expected to have roughly proportionate effects on PT.5 This expectation simplified the job to predicting M, and M is something (as we shall see in Chapter 11) the government can control reasonably well. He emphasized, however, that over short periods V might fluctuate sharply, largely because people’s expectations about future prices and business conditions might shift in response to temporary conditions. Still, these shifts would be temporary, and the stabler long-term V was fundamental.

Has the evidence borne Fisher out? Yes and no. The table above makes V look highly unstable. But over the long pull, V has been reasonably stable. Figure 8-2 provides the data since 1900. If we eliminate the Great Depression and the World War II period, V has generally stayed in the 3—4 range. But that’s a fairly wide range, and nothing more than a long-term relationship is clear. In general, both M and V have dropped sharply in depressions and have increased in booms. The World War II experience cited above provides an instructive example of how far astray an assumption that V is stable can lead you if you use it as an automatic predictor.

MV = PT needs to be used with care. Certainly the crude quantity theory of money (that prices always change in proportion to the stock of money) to which the equation is sometimes tied is not acceptable; nor does the quantity theory necessarily follow from the equation. But simple at it is, MV = PT provides a useful framework for thinking about money in relation to prices and output, especially over the long run and when big changes in the money supply occur.