THE EQUATION OF EXCHANGE
It has been a considerable time since the equation of exchange has been asserted to express the relationship between money and the level of prices. The time has come to dispel any doubt about the truth of this relationship.
The equation of exchange simply states that the total value of all money transactions in an economy is equal to the quantity of money (M) used to conduct those transactions times the velocity (V) of money. The value of all the transactions is defined as the average price (P) of the transactions times the quantity (Q) of the goods and services exchanged. That is:
Velocity of money is not quite the same as the velocity of things expressed as miles per hour or feet per second. Money velocity is the average rate at which a specific piece of money, like a coin or dollar bill, is used to make successive exchanges.PQ = MV.
Each time a dollar is spent someone receives that dollar. The recipient then either spends it again, saves it, or uses it to reduce his debts. The average rate of these exchanges is the velocity of money. It is expressed as dollars spent per dollar of supply per unit of time. To obtain its value it is necessary to measure the total amount of money transactions that occur during a period of time and divide that amount by the total amount of money in existence during the same period of time. But, this is not how economists derive their value of money velocity. To show how they determine the value it is necessary to look again at their version of the equation of exchange.
As the equation is presently used by economists, PQ is defined as the Gross National Product. Then one of the various measures of money supply - labeled M1, M2, M3, Mx, etc. - is substituted for M. This gives the equation:
Then, by algebraic manipulation:GNP = Mx*V.
That is, the economists' version of the velocity of money is not a direct measure of the rate of money usage. It is derived by dividing the measured value of GNP by the measured value of money supply. In polite circles this is called a tautology. Using this method to obtain the velocity of money destroys the ability to use the equation of exchange to demonstrate the relationship of money supply to prices. The equation is reduced to a definition of money velocity. However, with a few changes the equation can be returned to its useful form that demonstrates the relationship of money and prices.V = GNP/Mx.
First consider the PQ term. This is a statement that the total value of exchanges is equal to the average price times the quantity of goods and services exchanged. But there are many exchanges that are not counted in the Gross National Product. These are such transactions as the sale of used cars, used houses, stocks, bonds, and all other items not classified as new production. Only items classified as new production are included in GNP.
Another large group of transactions not included in the measure of GNP are all the intermediate transactions that go into making consumer products. These are such transactions as Ford buying tires from Goodyear, selling them as part of a car to an automobile dealer for eventual sale to a consumer. Neither the sale by Goodyear to Ford nor by Ford to the dealer is counted in GNP. Only final sales to consumers and changes in inventories are counted.
Still more transactions not counted in GNP are payments to discharge debts or add to savings. This group of transactions includes such things as payment of principle and interest on a home mortgage, payments on a car loan, tax payments, additions to savings accounts and all other transactions that do not directly result in a good or service measured as part of Gross National Product. However, taxes and all other government revenues and borrowings, when spent by the government or the recipients of government transfer payments, do buy goods and services that are counted in GNP.
The essential point here is that there are many transactions not counted in the Gross National Product. To correct for this error we can say:
This can be expressed more briefly as:PQ = GNP = MV - Transactions not included in GNP
The ~ in the term T~GNP means not. That is, T for transactions and ~GNP for not GNP. Like the distinction between floundies and non-floundies in Chapter I, these two classifications, GNP and T~GNP, exhaust all the possibilities for transactions.PQ = GNP = MV - T~GNP
However, they do not complete the changes necessary to restore the equation of exchange to its useful form. The MV term must also be considered. That is, in addition to exchanges for money there are exchanges without money. These are exchanges of goods for goods or services, services for goods or services, promises for goods or services, and, lastly, goods or services for discharge of debt.
Many of these exchanges are done by barter. In our previous example Ford bought tires from Goodyear. This transaction could have been accomplished as a barter exchange. Goodyear could have negotiated to exchange tires it produces for cars produced by Ford. Although such transactions are not the primary means of exchange in a modern economy, there are occasions when barter is more efficient than money transactions.
The particular exchange described above would result in the cars being counted in GNP (in this case Goodyear is the consumer) but the tires would not count until the cars outfitted with those tires are sold to consumers.
The second type of barter, services for goods or services, is also advantageous to the participants. Consider the case of employees at a restaurant. They may receive meals as partial payment for their labor. These transactions provide a lower cost to the restaurant owner because the pay is also a sale. The employees gain because, even though the meals may be counted as income for tax purposes, the amount counted as taxable income is less than would have been counted if the employees were paid the price of the meals in cash and then purchased the meals for the same cash. And, if the meals can be shown to be for the convenience of the employer, the meals are not counted at all as taxable income for the employees.
A similar transaction occurs when an employer provides uniforms for employees rather than paying higher wages and having the employees buy their own work clothing. But, the most prevalent form of this transaction type is the substitution of insurance or pension benefits for salary or wages. That is, instead of paying workers $30 per hour in cash the employer may pay $15 per hour in cash and $15 per hour in insurance and pension benefits. The cost to the employer is the same. But only the cash payment is counted as taxable income. The employees benefit by receiving the equivalent of a much higher before tax income.
Assume a worker is in the 40 percent tax bracket. He is then receiving the equivalent of $40 per hour. He receives $15 per hour in cash, $10 per hour he would pay on the additional $25 per hour if it were in cash - 40% of $25 = $10 - and finally the $15 per hour he receives in benefits. The reality that workers at much lower wages must make up this unpaid tax by paying higher tax rates than would otherwise be necessary is totally irrelevant to the workers.
With our highly discriminatory tax laws it is not hard to see why unions prefer a substantial portion of their members pay be in the form of non-taxable benefits. Higher tax rates and higher prices of products resulting from this arrangement mean little to the workers. At least the arrangement means little to workers with jobs. The reality that it causes unemployment is apparently not recognized by the unemployed. But employment and taxes are other tales to be held for later analysis. For now let it be sufficient to say there are significant transactions of services for goods or services.
The specific accounting of this form of barter is a bit complex to analyze here. Suffice it to say: These transactions are either part of GNP or part of T~GNP. There are no other choices.
The third type of exchange without money, goods or services for promises, is probably the most prevalent form of exchange. It consists of sales that take place with payment by check, credit card, or term loans.
Payment by check is a promise by the buyer that he has funds on deposit and these funds will be transferred to the credit of the seller. Such short term promises, one to ten days for a check to clear, are probably the most frequent form of payment for relatively small transactions. For larger transactions such as the purchase of a car or house the more common form of payment is a promissory note to pay over time. Although payments over time are made by either check or cash, the actual transaction is the exchange of the good for a promise. Likewise credit card use is a promises to pay. In this case the promise is guaranteed by a third party, the credit card company.
It is perhaps worth noting at this point that contemporary economists almost all agree that demand deposits are a form of money. This is because the transfer of money from one account to another is an unseen transaction. The banking procedure of transferring money by bookkeeping entries is simply a more convenient and efficient method than physically transferring cash. But, this practice does not alter the fact that the original transaction is one of a promise for a good or service.
The last form of exchange without money, goods for discharge of debts, is generally avoided when possible. This form consists of property repossesions for non-payment of a promissory note and discharge of debts by bankruptcy liquidation. Fortunately, this type of exchange is not very often a significant factor in the economy. But at times like the Great Depression of the 1930's they have occasionally become significant. Even in the nineteen- eighties, with substantial foreclosures on homes and farms, exchanges of goods for discharge of debts may be significant to the economy. They are certainly significant to the participants.
A particularly perverse example of this type of exchange was reported on the 4th of March 1984 edition of 60 MINUTES. A steel plant in Midland, Pennsylvania, owned by Colt Industries was apparently profitable and provided approximately 6000 jobs for the residents of Midland. It was shut down. The plant could have been kept operating if Colt Industries were willing to sell the plant to another company identified as willing and able to continue operations. However, because of our ludicrous tax laws, Colt decided to close the plant and take a tax write-off. This example is not intended to digress into demonstrating the perverse nature of our tax laws. If that is your interest, you should attempt to read the incomprehensible language of the law.
Or observe the damage to the Bill of Rights done by IRS agents running roughshod over citizens that dare to object to these self-styled guardians of the American Democracy. This abuse of government power has been well reported by others, including Congressman George Hansen. In his book To Harass our People, The IRS and Government Abuse of Power (Positive Publications, Box 23560, Washington, D.C. 20024), Congressman Hansen has documented many of the IRS abuses of power. No, the example is not for that purpose. It is only to demonstrate that there are exchanges of goods for discharge of debts that are "voluntary." But, without citing the perversity of our tax laws it would be difficult to find another example.
Like transactions not in GNP, we can abbreviate this type of exchange to exchanges without money, or E~M. Adding this term to the equation of exchange we have:
With a little algebra, this becomes:PQ = GNP = MV - T~GNP + E~M.
This is the form of the equation of exchange that will demonstrate the relationship between money and prices.P = (MV - T~GNP + E~M)/Q.