Front Page Titles (by Subject) CHAPTER IX: THE DISPERSION OF PRICES MAKES NECESSARY AN INDEX OF PURCHASING POWER - The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises
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CHAPTER IX: THE DISPERSION OF PRICES MAKES NECESSARY AN INDEX OF PURCHASING POWER - Irving Fisher, The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises 
The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises, by Irving Fisher, assisted by Harry G. Brown (New York: Macmillan, 1922). New and Revised Edition.
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THE DISPERSION OF PRICES MAKES NECESSARY AN INDEX OF PURCHASING POWER
WE have found that the general level of prices is determined by the other magnitudes in the equation of exchange. But we have not hitherto defined exactly what a "general level" may mean. There was no need of such a definition so long as we assumed, as we have usually done hitherto, that all prices move in perfect unison. But practically prices never do move in perfect unison. Their dispersion would render impossible the statistical study of general price movements were there no practical method of indicating the general movement. A simple figure indicating the general trend of thousands of prices is a great statistical convenience. It also simplifies our equation of exchange by converting the right side, which now consists of thousands of terms, into a single simple term.
Such an indication is called an "index number" of the price level. Its reciprocal indicates, of course, the purchasing power of money.
The present chapter will, then, treat of the dispersion of prices, the next chapter of index numbers which this dispersion renders a practical necessity, and the two following chapters of the practical statistical use of index numbers.
The chief conclusion of our previous study is that an increase of money, other things equal, causes a proportional increase in the level of prices. In other words, the p's in the sum SpQ tend to rise in proportion to the increase in money. It was noted, however, that the adjustment is not necessarily uniform, and that if some p's do not rise as much as in this proportion, others must rise more. In this connection, we observe that some prices cannot adjust themselves at once, and some not at all. This latter is true, for instance, of prices fixed by contract. A price so fixed cannot be affected by any change coming into operation between the date of the contract and that of its fulfillment. Even in the absence of explicit contracts, prices may be kept from adjustment by implied understandings and by the mere inertia of custom. Besides these restrictions on the free movement of prices, there are often legal restrictions; as, for example, when railroads are prohibited from charging over two cents per passenger per mile, or when street railways are limited to five-cent or three-cent fares.
Whatever the causes of nonadjustment, the result is that the prices which do change will have to change in a greater ratio than would be the case were there no prices which do not change. Just as an obstruction put across one half of a stream causes an increase in current in the other half, so any deficiency in the movement of some prices must cause an excess in the movement of others.
In order to picture to ourselves what are the classes of prices which rise or fall, we must survey the entire field of prices. Prices, measured as we are accustomed to measure them, in terms of money, are the ratios of exchange between other goods and money. The term "goods," as previously explained, is a collective term comprising all wealth, property, and services, these being the magnitudes designated in sales. The chief subclasses under these three groups, which occur in actual sales, may be indicated as follows:—
The prices of these various classes of goods cannot all move up and down in perfect unison. Some are far more easily adjustable than others. Only by extremely violent hypotheses could we imagine perfect adjustability in all. The order of adjustability from the least to the most adjustable may be roughly indicated as follows:11 —
Take, for instance, bonds and mortgages. In order that the prices of these may be perfectly adjustable, we should have to suppose, not only that there were no restraint from custom or law, but that the contracts were perfectly readjusted to each new price level. We should have to suppose, for instance, that after the price level had doubled in height, because currency had doubled, there would be a $2000 bond wherever there had been a $1000 bond. This, obviously, is not the case. The holder of a $1000 bond can receive at its maturity only $1000, besides interest payments in the interim. If, meanwhile, the price level doubles, he will receive no more. It is true that a change of price level will, in time, change the volume of new loans. A merchant, to lay in a given stock of goods, will need to borrow a larger sum if prices are high than if they are low. Personal notes and bills of exchange will be drawn for double the amount which would have obtained had the price level not doubled. Similarly, a corporation issuing bonds for new projects may have to issue a larger amount. But obligations outstanding when the price levels change cannot be thus adjusted; their prices can vary only slightly during the interim between issue and maturity. The fact that their face value is expressed in money sets very definite limits to their prices.12 If, because of a doubling in the quantity of money, the value and profits of a railroad measured in money were doubled, the bondholder could not, on that account, realize more money for his bond. The value of the bond is not greatly affected by the valuation and profits of the railroad, so long as these are sufficient to guarantee the bond. The bond is an agreement to pay stated sums at stated times. It represents a limited money value carved out of the road. The only ways in which the money price of a bond or salable debt can vary at all are by variations in the rate of money interest and by changes in the degree of certainty of payment. Only so far as these features are affected by the changes in the volume of money will the value of bonds be affected. We have seen, for instance, that inflation, while it is taking place, raises interest.13 It therefore lowers the price of bonds during the transition period.14 Again if violent changes in the price level increase or decrease the number of bankruptcies, they thereby affect the degree of certainty of payment, and consequently affect the value of bonds. But these ways of affecting prices of such securities expressed in money are of less account than the ordinary effect of inflation or contraction on price levels, and of a different character.
The chief peculiarity of these forms of property lies, then, in the fact that they are expressed in terms of money and therefore are compelled to keep in certain peculiar relations to money. Being based on contracts, the money terms of which during a given period must not be changed, they are not free to be influenced in the same ways as other property. The existence of such contracts constitutes one of the chief arguments for a system of currency such that the uncertainties of its purchasing power are a minimum. An uncertain monetary standard disarranges contracts and discourages their formation.
The longer the contract, the larger the nonadjustability. A fifty-year bond usually means a relative fixity of price for half a century. Only at the end of that time, if prices have risen, can bonds, issued de novo for the means of purchasing goods, be correspondingly more numerous or of correspondingly larger denominations. A 30-days' bill of exchange, on the other hand, while it cannot change much in price, is canceled at the end of a month. The relative fixity of price is, therefore, of shorter duration.
A special class of goods, the prices of which cannot fluctuate greatly with other prices, are those special commodities which consist largely of the money metal. Thus, in a country employing a gold standard, the prices of gold for dentistry, of gold rings and ornaments, gold watches, gold-rimmed spectacles, gilded picture frames, etc., instead of varying in proportion to other prices, always vary in a smaller proportion. The range of variation is the narrower, the more predominantly the price of the article depends upon the gold as one of its raw materials.
From the fact that gold-made articles are thus more or less securely tied in value to the gold standard, it follows also that the prices of substitutes for such articles will tend to vary less than prices in general. These substitutes will include silver watches, ornaments of silver, and various other forms of jewelry, whether containing gold or not. It is a fundamental principle of relative prices that the prices of substitutes will move in sympathy. In the case of perfect substitutes, the prices must always be equal or must bear a fixed ratio to each other.15
The remaining items in our list require little comment. The imperfect adjustability of prices fixed by law and custom and the perfect adjustability of wholesale prices of commodities and prices of stocks are familiar to all.
The fact that wages, salaries, the price of gold in nonmonetary forms, etc., and especially the prices of bonded securities, cannot change in proportion to monetary fluctuations, means, then, that the prices of other things, such as commodities in general and stocks, must change much more than in proportion. This supersensitiveness to the influence of the volume of currency (or its velocity of circulation or the volume of business) applies in a maximum degree to stocks. Were a railroad to double in money value, the result would be, since the money value of the bonds could not increase appreciably, that the money value of the stock would more than double. Stocks are shares in physical wealth the value of which, in money, can fluctuate. Since the money price of bonds is relatively inflexible, that of stocks will fluctuate more than the price of the physical wealth as a whole. The reason is that these securities not only feel the general movement which all adjustable elements feel, but must also conform to a special adjustment to make up for the rigid nonadjustability of the bonds associated with them.
To illustrate, let us suppose the right side of the equation of exchange to consist of the following elements:—
Let us suppose that, with no change in the velocities of currency circulation or in the volume of business, there is an increase of 40 per cent in the quantities of currency. Then, the total value of goods exchanged will have to increase from $125,000,000 to $175,000,000. Let us assume that the last two items are absolutely nonadjustable; then none of the increase of $50,000,000 can occur through any change in these items, which will remain at $5,000,000 and $20,000,000, respectively, or $25,000,000 in all. Consequently, the first two items must rise by the whole of the $50,000,000, that is, from $100,000,000 to $150,000,000 or 50 per cent. To distribute this increase of $50,000,000 over the first two or adjustable items, let us assume that the total $10,000,000 worth of actual wealth, which consists half of stocks and half of bonds, will rise in the same ratio as the $95,000,000 worth of adjustable elements rise. Now the whole (comprising all three items) evidently rises from $105,000,000 to $155,000,000, making an increase of 47.6 per cent. This, therefore, is the common percentage which we are to assume applies equally to the first item and the combination of the second and third. Applied to the former it makes an increase from $95,000,000 to $140,200,000. Applied to the latter it makes an increase from $10,000,000 to $14,800,000. But since half of the property consists of bonds and cannot increase, the whole of the increase, $4,800,000, must belong to the stock alone. This will, therefore, rise from $5,000,000, to $9,800,000, a rise of 96 per cent. The four items then change as follows:—
Besides the dispersion of price changes produced by the fact that some prices respond more readily than others to changes in the factors determining price levels, M,M', V,V', and the Q's, a further dispersion is produced by the fact that the special forces of supply and demand are playing on each individual price, and causing relative variations among them. Although these forces do not, as we have before emphasized, necessarily affect the general price level, they do affect the number and extent of individual divergencies above and below that general level. Each individual price will have a fluctuation of its own.
Among the special factors working through supply and demand, changes in the rate of interest should be particularly mentioned. Whether or not due to monetary changes, a movement of interest will tend to make the prices of different things vary in different directions or to different extents. The prices of all goods, the benefits of which accrue in the remote future, depend on the rate of interest. The standard example is that of bonds and other securities. Another good example is that of real estate. In the case of farm lands yielding a constant rental, a reduction of interest causes an increase of value in the inverse ratio. If interest falls from 5 per cent to 4 per cent, the value will increase in the ratio 4 to 5. If the benefits or services are not constant each year, but are massed together in the remote future, the price may be still sensitive to a change in the rate of interest. In the case of land used for forest growing from which the trees are to be cut in half a century, the value will be extremely sensitive. A fall in interest from 5 per cent to 4 per cent will cause a rise of the value of the land, in the ratio not of 4 to 5, but nearly of 4 to 7.16 On the other hand, mining land or quarries with a limited life will be less sensitive. The same is true of dwellings, machinery, fixtures, and other durable but not indestructible instruments, and so on down the scale until we reach perishable and transient commodities, such as food and clothing, which are only indirectly affected by changes in the rate of interest.
It is evident, therefore, that prices must constantly change relatively to each other, whatever happens to their general level. It would be as idle to expect a uniform movement in prices as to expect a uniform movement for all bees in a swarm. On the other hand, it would be as idle to deny the existence of a general movement of prices because they do not all move alike, as to deny a general movement of a swarm of bees because the individual bees have different movements.
Corresponding to changes in an individual price there will be changes in the quantity of the given commodity which is exchanged at that price. In other words, as each p changes, the Q connected with it will change also; this, because usually any influence affecting the price of a commodity will also affect the consumption of it. Changes in supply or demand or both make changes in the quantity exchanged. Otherwise expressed, the point of intersection of the supply and demand curve may move laterally as well as vertically.
This changing of the Q's introduces a new complication. We have in many of our previous discussions been assuming, as was admissible theoretically, that all the Q's remain unchanged while we investigate the changes in the p's due to changes in the currency or in velocities of circulation. But practically we can never get an opportunity to study such a case. Again, in order to show the effect of a change in "the volume of business" upon the price level, we supposed a case in which all the Q's were uniformly changed. Such a supposition is not only impossible to carry out in practice, but is difficult to conceive even in theory; because, as we have just seen, each Q is associated with a p. In showing the effect of a change in the volume of business upon the level of prices we cannot assume that all the Q's change uniformly in one direction and all the p's uniformly in the other. If the first set change uniformly, the second cannot change uniformly. A doubling in the quantities of all commodities sold, or (what is almost the same thing), a doubling of the quantities consumed, would change their relative desirabilities and therefore their relative prices. To double the quantity of salt might make its marginal desirability zero, while to double the quantity of roses might scarcely lower their marginal desirability at all.17
We see, therefore, that it is well-nigh useless to speak of uniform changes in prices (p's) or of uniform changes in quantities exchanged (Q's). In place of positing such uniform changes, we must now proceed to the problem of developing some convenient method of tracing these two groups of changes. We must formulate two magnitudes, the price level and the volume of trade. This problem is especially difficult because, in measuring changes in the price level, we shall need to use the quantities (Q's) in some way as weights in our process of averaging; and we now find, not only that the prices whose average we seek are extremely variable, but that the weights by which we attempt to construct the average are variable also.
It is desired, then, in the equation of exchange, to convert the right side, SpQ, into a form PT where T measures the volume of trade, and P is an "index number" expressing the price level at which this trade is carried on. These magnitudes—price level (P) and volume of trade (T)—need now to be more precisely formulated. Especially does P become henceforth the focal point in our study.
As explained in the next chapter, there are an indefinite number of ways of conceiving and forming index numbers of prices and volume of trade. We shall here mention only the simplest. T may be conceived as the sum of all the Q's, and P as the average of all the p's. This method is practically useful only provided suitable units of measure are selected. It must be remembered that the various Q's are measured in different units. Coal is sold by the ton, sugar by the pound, wheat by the bushel, etc. If we now add together these tons, pounds, bushels, etc., and call this grand total so many "units" of commodity, we shall have a very arbitrary summation. It will make a difference, for instance, whether we measure coal by tons or hundredweights. The system becomes less arbitrary if we use, as the unit for measuring any goods, not the unit in which it is commonly sold, but the amount which constitutes a "dollar's worth" at some particular year called the base year. Then every price, in the base year, is one dollar, and therefore the average of all prices in that year is also one dollar. For any other year the average price (i.e. the average of the prices of the newly chosen units which in the base year were worth a dollar) will be the index number representing the price level, while the number of such units will be the volume of trade.
The equation of exchange now assumes the form
MV + M'V' = PT
and its right member is the product of the index number (P) of prices multiplied by the volume of trade (T).
In this chapter we have seen that prices do not, and in fact cannot, move in perfect unison. The reasons for dispersion are principally three: (1) Many prices are restrained by previous contract, by legal prohibition, or by force of custom. (2) Some prices are intimately related to the money metal. (3) Each individual price is subject to special variation under the influence of its particular supply and demand. There exists, however, a compensation in price movements in the sense that the failure of one set of prices to respond to any influence on the price level will necessitate a correspondingly greater change in other prices.
The quantities sold likewise vary, and their variations are bound up with those of prices.
In order to express in one figure the general movement of prices, an index number (P) is constructed; and in order to express in one figure the general movement of trade, an index of trade (T) is constructed. The nature of these indices will form the subject of the next chapter.
[11.] Cf. Jevons's admirable "Classification of Incomes according as they suffer from Depreciation," Investigations in Currency and Finance, London (Macmillan), 1884, p. 80, and after. See also The Gold Supply and Prosperity, edited by Byron W. Holt, New York (The Moody Corporation), 1907, especially the Conclusion or Summary by the editor, beginning on page 193.
[12.] See article by Walter S. Logan on the "Duty of Gold," in The Gold Supply and Prosperity, edited by Byron W. Holt, New York (The Moody Corporation), 1907, p. 106. See also Ricardo, "Essay on the High Price of Bullion," Works, 2d ed., London (Murray), 1852, p. 287.
[13.] Supra, Chapter IV, § 1.
[14.] See article by Robert Goodbody, "More Gold means Higher 'Time' Money and Lower Bond Prices," in The Gold Supply and Prosperity, edited by Byron W. Holt, New York (The Moody Corporation) 1907, p. 163 and after.
[15.] See Irving Fisher, "Mathematical Investigations in the Theory of Value and Prices," Transactions of the Connecticut Academy of Arts and Sciences, 1892, p. 66 and after.
[16.] From figures showing yield of forest of white pine in New Hampshire, New Hampshire Forestry Commission Report, 1905-1906, p. 246. See F. R. Fairchild, "Taxation of Timberland," Report of the National Conservation Commission, 60th Congress, 2d Session, Senate Document 676, vol. II, p. 624.
[17.] Cf. Jevons, Theory of Political Economy, London (Macmillan), 1888, pp. 155-156.