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resents the total value of the goods bought expressed as the product found by multiplying the price level by the volume of trade. The price level (P) is the index number of general prices for the year under consideration, e. g. 1910, relatively to 1909 taken as the base year; and the volume of trade (T) is the value of the trade in the year under consideration, e. g. 1910, reckoned at the prices, not of that year, but of the base year, 1909.2
Thus the equation of exchange merely expresses in form convenient for analysis the fact that the currency paid for goods is the equivalent of the value of the goods bought.
In Chapter VIII of my book I have endeavored to show that in the equation of exchange, P is in general the passive element or puppet of the other five factors which stand to it in the relation of cause to effect.3
From the equation of exchange we may evidently express the price level (P) in terms of the five factors which determine it, as follows:
In The Purchasing Power of Money statistical calculations were made for all five of the price-determining magnitudes; and from these calculated magnitudes the resultant value of P was derived. This value of P, as thus indirectly derived, was then compared with its actual value as directly calculated by index numbers. The discrepancies between the results of the direct and indirect methods of obtaining P imply statistical errors in the various calculations but these discrepancies proved to be remarkably small. In order to eliminate these small discrepancies thus found, slight revisions were next made in each of the six magnitudes in the equation of exchange. In other words, each of the six magnitudes, as inde
'T may be conveniently regarded as the total number of units of goods exchanged when the units are expressed not in terms of tons, pounds, etc., in which they are usually expressed commercially, but in terms of specially constructed units, the unit for each commodity being the amount of that commodity which was worth one dollar in the base year (1909). Likewise P may conveniently be regarded as the average price per unit at which these goods are sold, these prices being stated, not in terms of tons, pounds, etc., but in terms of specially constructed units-namely, the "dollar's worth" for each good in the base year (1909).
The cases in which (as during transition periods) this proposition is not strictly true are fully discussed in the book, but need not concern us here.
pendently calculated, was frankly altered in order to make all six exactly fit into the equation of exchange as the true figures necessarily must. The alterations thus necessary were extremely small, seldom exceeding 1 per cent; in more than six sevenths of the cases not exceeding 2 per cent; and reaching at the very utmost only 5 per cent. The final figures are as follows:
*I shall not attempt here to explain in detail how these various magnitudes were calculated, as all details are given in The Purchasing Power of Money. For present purposes the following brief descriptions will suffice: M, the money in circulation, is taken from the estimates of the Director of the Mint and the Comptroller of the Currency, corrections being made for the errors now believed to have been committed in the earlier estimates for gold in circulation. By money in circulation is meant money standing ready for commercial purchases. It therefore excludes money in the United States Treasury and in banks. M' is based on the reports of the Comptroller of the Currency for individual deposits, after adding the estimated unreported deposits and after deduction of all deposits in savings banks and exchanges for clearing houses, and estimated deposits not subject to check,-this last on the basis of calculations by the Monetary Commission for 1909, repeated at my request for 1896, 1899 and 1906. The velocity (V) of circulation of money was worked out by the method explained by me in the Journal of the Royal Statistical Society for December, 1909. (“A Practical Method of Estimating the Velocity of Circulation of Money"). The velocity (V') of circulation of bank deposits was worked out by an analogous method. T, the volume of trade, was based on the statistics of internal commerce as published by the Bureau of Statistics in the Department of Commerce and Labor and includes also statistics of quantities of commodities exported and imported, sales of stocks, railroad tons carried, and postoffice letters carried. P, the price level, was based principally on the figures of the Bureau of Labor for the wholesale prices of two hundred and fifty-eight commodities, but partly also on prices of stocks and wages per hour. FINALLY ADJUSTED VALUES OF ELEMENTS OF EQUATION OF EXCHANGE.
The year 1909, taken as the base year, was the end of the period first under examination, 1896-1909, and affords a beginning for a new series for subsequent years.
There are various methods of representing visually the changes in each of the six magnitudes just given, but most of these methods fail to show the relations mutually existing between these magnitudes. The method of representation here employed is that given in The Purchasing Power of Money. It is based on the analogy between the equation of exchange and the mechanical balance or steelyard; for, in a sense, the expenditures of money and checks exactly balance the value of the goods bought.
The left and the right side of the balance symbolize respectively the left and the right side of the equation of exchange. The smaller weight at the left, symbolized by a purse, represents the money (M) in circulation in the United States. The larger weight at the left, symbolized by a bank book, represents the deposits (M') subject to check. The distance to the left of the fulcrum at which the first weight (purse) is hung represents the efficiency of this money or its velocity (V) of circulation, and in like manner the distance to the left at which the bank book is hung represents the velocity (V') of circulation of bank deposits subject to check. The volume of trade (T) is represented by a tray hanging on the right side and containing a miscellaneous assortment of goods symbolizing the total mass of goods exchanged in a year. The general average of prices (P) at which these goods are sold is represented by the distance to the right of the fulcrum at which the tray hangs. The equality between the two sets of magnitudes is symbolized by the equality or balance between the strains on the two sides of the fulcrum. Each weight exerts on its side a strain measured by the product found by multiplying that weight by its leverage or distance from the fulcrum. Thus, on the left, the purse exerts a strain measured by the product found by multiplying its weight (M) by its leverage (V); and the bank book exerts a strain measured by the product found by multiplying its weight (M') by its leverage (V'); so that the total strain on the left is measured by MV + M'V'. This total strain is exactly balanced by the equal and opposite strain of the tray on the right—a strain measured by the product found by multiplying its weight (T) by its leverage (P).
Thus the equilibrium of the balance symbolizes clearly the equa
MV + M'V' = PT.
An increase in the weights or leverages on one side requires, in order to preserve equilibrium, a proportional increase in the weights or leverages on the other side. If, now, the velocities of circulation (left leverages) remain the same, and if the volume of trade (tray at the right) remains the same, then any increase in the nation's purse or bank account (left weights) will require a lengthening of the leverage at the right, representing prices.
In the figure this symbolism is repeated for each of the fifteen years for which the magnitudes involved have been calculated, and it is easy to trace with the eye the changes in the various magnitudes both singly and in their mutual relations.
We may in general summarize what has happened by stating that there has been a general expansion, that is, an increase of the hanging weights and a movement of them away from the center. The only exception to this general expansive movement worth mentioning was in the year 1908 following the crisis of 1907.
We observe that the nation's purse (M) grew steadily, approximately doubling in the fourteen years between 1896 and 1910, and that its velocity of circulation (V) changed but slightly; that the nation's bank-book (M') grew more rapidly, approximately tripling in the fourteen years; and that the velocity of the deposit circulation (V) or activity of bank accounts also increased rapidly and especially during the last few years; that the volume of trade (T), symbolized by the tray, doubled while general prices increased by three quarters.
The most noteworthy year represented is the crisis year, 1907, in which deposits reached a maximum,—their velocity of circulation having reached a maximum in the previous year. The last two years, 1909 and 1910, are also noteworthy because in those years the velocity of circulation of bank deposits has been unprecedentedly high. This high velocity means that the average man in the United States is now keeping an extremely small bank balance relatively to the large expenditures he is making; that is, he is leaning toward a spendthrift policy. This fact is especially interesting in view of the observation of Pierre des Essars that the activity of bank accounts in the continental banks of Europe increases rapidly prior to a crisis, usually reaching a maximum in the crisis year.
If we seek to explain the relative effect on prices of the changes in the five factors, we note that the changes in only four of them (the left factors M,M',V,V') have tended to produce a rise. The