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the overinvestment in production goods and the overcapitalization of business opportunities.

Any one of a number of things may be sufficient to precipitate a panic under such conditions. The whole business structure may fall to pieces through sheer topheaviness. That is, so much production today is indirect, so large a share of productive effort is devoted to forwarding in indirect ways the production of goods that will be ripe for human use only in the comparatively distant future, that the mere operations of supply and demand among business men themselves may maintain prosperous business conditions for some time. But in the long run the maintenance of the values of producer's goods and privileges depends on the demand, and hence on the income, of ultimate consumers. Wages do not usually rise as rapidly as prices in periods of business expansion. This simple fact may in itself keep the average purchasing power of consumers from expanding rapidly enough to furnish a solid support for the growing structure of capital values.

Crop failures may precipitate a panic by diminishing the purchasing power of those engaged in agriculture, and, possibly, by reducing exports and thus necessitating the taking of gold from the bank reserves to ship to Europe in payment for our imports. When the credit situation is at all strained, the failure of one important bank may be enough to precipitate a panic. The bank's creditors are prevented from meeting their own obligations; the solvency of others is in turn dependent upon them, and thus losses in expected and often already hypothecated income are transmitted from firm to firm and from industry to industry in a constantly widening circle. The reduction of bank reserves by reason of the flow of money into hand-to-hand circulation in order to effect exchanges at the higher level of prices may itself be a contributing cause of a panic.

In fact, whatever may be the immediate cause of a panic, it is bound to grow, in a condition of inflated capital values, with tremendous rapidity. The collapse of credit leads to forced sales of property in order that credit obligations may be met. These reduce prices, lessen the security on which credit is

founded, and render banks less able and less willing to make loans. Moreover, the hoarding of money, which is apt to be a feature of a panic, has a destructive effect on bank reserves. In a serious panic the liquidation of obligations has to work itself out. Then the industrial process starts afresh, with lowered values imputed to capital goods and to business opportunities, and with property rights shifted, in some measure, to creditors. Crises seem to be unpreventable so long as competition and the credit system dominate in industry. Yet there are some recent developments that may make them less frequent, and possibly less serious.

The "integration of industry," whereby a whole series of productive processes, from the production of the raw material to the sale of the finished product, are brought together under one management, decreases the number and complexity of credit relations between producers, and tends to prevent the undue expansion of those parts of the productive process that are farthest removed from the consumer. The strong position of the steel industry in the United States is a case in point. The improvements in the bargaining power of wage earners resulting from their organization have enabled them partly to prevent the widening of the gap between wages and prices in prosperous times, as recent American statistics show. On the other hand, crop failures are and always will be a factor of uncertainty. The best way of softening the rigors of a panic and of restoring normal conditions promptly is through a wise use of the lending power inherent in a system of really elastic bank reserves, just as the best way of preventing panics is through a firm control of discount rates when all other conditions are ripe for a period of business inflation. It is in these ways, perhaps, that the new federal reserve system can best serve the country.

The Standard of Deferred Payments. The relation of changes in the purchasing power of money to long-time debts and credits has some very important aspects. If prices increase, the principal of a loan represents less purchasing power at the time of repayment than at the time the loan was made. If prices

decrease, the reverse is, of course, true. In periods of cheap money agitations the additional burdens imposed upon debtors in a period of decreasing prices are emphasized. An important function of money, then, is found in its use as a standard of deferred payments.

There is a partial, but only partial, compensation for the injustice to debtors and creditors resulting from general changes in prices in the fact that the interest rate usually increases when prices increase and decreases when prices decrease. This is largely because rising prices increase profits, thus inducing business men to pay higher interest rates in order to secure larger supplies of funds for investment; while falling prices decrease profits and lessen the demand for loanable funds. The result of this is that the changing purchasing power of the principal of a loan is to some extent offset or discounted by changes in the rate of interest. The decline in interest rates as prices fall makes it possible for debtors to pay off their old obligations with funds borrowed at a lower rate of interest. Creditors cannot so easily take advantage of the fact that interest rates are increasing when the purchasing power of the principal of their outstanding loans is decreasing. Nevertheless, more emphasis has been given to the question of the standard of deferred payments in periods of declining prices, when debtors are injuriously affected, than in periods of rising prices, when creditors are the losers. The United States is rapidly ceasing to be a "debtor nation," and the farmers, in particular, are becoming less distinctively a "debtor class." We may expect, therefore, that in a future period of declining prices we shall hear less about the injustice of our variable standard of deferred payments.

Index Numbers. - General changes in prices are indicated statistically by the use of index numbers. An index number, in the most general sense, is some magnitude which varies with some other magnitude or complex of magnitudes, and whose variations can therefore be taken as representing or indicating the other variations. In studying the variations of the price of some specific thing we need no index number; but when we

have to deal with the variations of many different prices, we find the use of index numbers necessary.

The simplest way to form an index number of general changes in prices is, first to select a list of things whose prices are to be taken into account, next to ascertain the average price per unit paid for each of these things in each successive month or year of the period being studied, and finally to take the sum of these unit prices in each of a number of successive months or years as the index numbers. Such index numbers show the variations in the total expense of a purchase consisting of one unit each of the commodities included in the list. Thus if bananas of a certain grade sell at a certain time for 15 cents a dozen, oranges at 40 cents, and peaches at 25 cents; and if a month later the prices are 20 cents for bananas, 50 cents for oranges, and 20 cents for peaches, the summed prices used as index numbers are 80 cents and 90 cents respectively. This means merely that the total money cost of a dozen each of these fruits has increased by 12 per cent.

For some purposes we get more significant results by weighting the specific prices in accordance with the relative importance of the different commodities. If, for example, we think that twice as many bananas as peaches are ordinarily used, and three times as many oranges as peaches, we may take as our weighted sum at the earlier date, .25 plus (2 X .15) plus (3 X .40), or $1.75. For the later date the weighted sum is $2.10, indicating a general rise of 20 per cent in the retail prices of this small group of commodities. Accurate weighting is thus of great importance in forming index numbers from a small list of price quotations. If a very large list of prices is used, weighting becomes of less importance, for there is no necessary connection between the importance of a commodity and the degree to which it has risen or fallen in price. Errors due to the lack of weighting or to imperfect weighting thus tend to offset each other. But even with a large and thoroughly representative list of prices, the highest degree of accuracy in index numbers cannot be reached without careful weighting.

Index numbers are, however, more often constructed as averages than as sums. Thus the ordinary arithmetic averages of the prices of these kinds of fruit at the two dates are .80 ÷ 3 and .903, or .27 and .30 respectively. The weighted arithmetic averages are 1.756 and 2.10 ÷ 6, or .29 and .35. The averages, of course, indicate the same proportionate general change in prices as do the sums, but when the price list is large the use of the average makes the series of price changes somewhat more easy to inspect and interpret.

It is a common practice in making index numbers to substitute relative prices for actual prices before summing or averaging them. The price of each commodity at each date is set down as a per cent of its price at some one specific date (or of its average price during a certain period). Thus, in the illustration already given, if we use the earlier date as the "basing period," the price per dozen of each kind of fruit is set down as 100. The relative prices in the later period then are: bananas, 133; oranges, 125; peaches, 80. This gives an unweighted sum of 338, and an unweighted arithmetic average of 113, indicating an average relative change in prices of 13 per cent. Relative prices may also, of course, be combined by means of weighted sums and averages. Index numbers utilizing relative prices should be constructed and interpreted with great caution, because the results will vary according as one period or another is used as the basing period. If, for example, in the illustration already given, prices at the later date are used as the basing prices, average relative prices at the earlier date become 93, indicating an average increase of only a little over 7 per cent instead of the 13 per cent indicated when the earlier prices. were used as bases. When a large price list is used this particular source of error becomes of less (though not of negligible) importance. But there remains the difficulty that for periods. remote from the basing period this method exaggerates a rise in prices and understates a fall. It is accordingly sometimes desirable to use chain index numbers, in which the relative prices

1 This grows out of the fact that a price cannot fall by more than 100 per cent but can rise without definite limit.

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