determination of each price separately by this method will supply data for a summary of the market situation as a whole. In the one form in which the utility theory avoids a circle,--that presented by Schumpeter, and discussed in an earlier part of this chapter--it is not a causal theory. Marginal utility is not a cause of market prices, but rather, marginal utilities and market prices are alike resultants, effects, of more fundamental factors. No writer[104] who has presented the utility theory in this form has tried to apply it to the value of money, and even if it could be so applied, it would not give a causal explanation of the value of money in terms of marginal utility. In most of the efforts to apply the utility theory to money, the circle becomes so obvious that one marvels that able theorists should for a moment fail to see it. PART II. THE QUANTITY THEORY CHAPTER VI THE QUANTITY THEORY OF PRICES. INTRODUCTION The quantity theory, in its usual formulations, is a theory, not of the value of money, in the absolute sense of value, but of the general price-level, the average price of goods exchanged for money. It is not a psychological theory. It does not deal with psychological quantities, or psychological forces. It is a mechanical theory, concerned simply with quantities, and the relations between them. The essence of the quantity theory comes out in the following brief statement: given a number of units of money; given a number of units of goods to be exchanged; assume these two numbers to be independent[105] of each other; assume all the goods to be exchanged for all the money; then the average price will be a simple function of the quantities of goods and of money respectively, such that an increase in the amount of money will increase the average price per unit of goods proportionately, if goods remain unchanged in amount, or an increase in goods will lower the price per unit proportionately, money being assumed to remain unchanged in amount. The qualification is commonly added that if goods have to be exchanged more than once, the effect is the same on prices as if there were an added number of goods equal to the added number of exchanges, and that if money is used more than once in exchanging a given number of goods, the effect is the same as if there were proportionately more money. Both quantity of goods and quantity of money are commonly defined as actual quantity multiplied by "rapidity of circulation." Rapidity of circulation, however, for both money and goods, is commonly thought of as a constant, so that the original formula remains unaffected by the qualification, so far as a prediction as to the effect of increase or decrease of money or goods on prices is concerned. Involved in the quantity theory, and explicitly stated by many writers, is the doctrine that the substance of which money is made is irrelevant, that it is the number, and not the quality or size of the money-units that counts. "In