The Theory of Exchange 181

2.

The Limits of Economic Exchange

If each economizing individual had but a single good of each kind at his disposal, and if each of these goods were indivisible with respect to its goods-character, there would be no difficulty in investigating the limits to which exchange operations would proceed in each given case to result in the greatest economic gain for each participant. Suppose that A has a glass goblet and B a piece of jewelry made of the same material, and that neither of the two individuals has command of more than the one unit of each article. According to what was said in the preceding section, only two situations are conceivable: either the basis for an economic exchange between the two individuals exists with respect to the two goods, or it does not. If it does not, the question of an exchange cannot arise at all from an economic standpoint. And if it does exist, there can be no doubt that an actual exchange of the two goods will naturally preclude any further exchange of goods of exactly the same kinds between A and B.

But whenever quantities of goods are at the command of different persons which can be subdivided into portions of any desired size, or which are composed of several discrete pieces, each of which is indivisible by nature or use, the situation is different.

Suppose that A, an American frontiersman, owns several horses but no cow, while B, his neighbor, has a number of cows but no horses. Provided that A has requirements for milk and milk products and B for draft animals, it is easy to see that a basis for exchange operations is present. But no one will maintain that the exchange of one of A’s horses, for example, for one of B’s cows would necessarily exhaust the existing basis for economic exchange operations between A and B with respect to these goods. It is equally certain, however, that a basis need not necessarily exist for exchange of the total quantities they possess. A who owns (for example) six horses may be able to satisfy his needs better if he exchanges one, or two, or perhaps even three, of his horses for B’s cows. But from this it does not necessarily follow that he would derive an economic gain from the exchange transaction if he were to barter all his horses for

182 Principles of Economics

all of B’s cows. Although the initial economic situation pro. vides a basis for economic exchange operations between A and B, the consequence of carrying the exchange too far might be that the needs of the two contracting parties would be less well provided for than before the exchange.

The relationship we are now considering, in which not merely single goods but quantities of goods are at the disposal of men, can be regularly observed in human economy. An endless number of cases can be observed in which two economizing individuals have command of quantities of different goods, and in which the foundations for economic exchange operations are present, but where the gains to be derived from trade would be exploited only incompletely if the two economizing individuals were to exchange too little, and would be again diminished, reduced to nothing, or even converted to losses, if they should drive their exchange operations too far and exchange too much.

But if we can observe cases where “too little” of an exchange does not yield the full gains to be derived from the exploitation of an existing relationship and where “too much” leads to the same result, indeed often even to a deterioration in the economic positions of the two traders, there must be a limit at which the full economic gains to be obtained from the exploitation of the given relationship are reached, and beyond which any exchange of further portions begins to become uneconomic. The determination of this limit is the object of the subsequent investigation.

I shall present a simple case for this purpose in which we can most carefully observe the relationship we wish to consider, undisturbed by secondary influences.

Suppose that in a virgin forest, far away from other economizing individuals, there live two frontiersmen who maintain friendly intercourse with each other. It is assumed that the compass and intensity of their needs are exactly the same. Each of them requires several horses to work his land. One horse is absolutely necessary if he is to be able to produce the food required for the maintenance of his and his family’s lives. A second horse is required to produce the somewhat greater amount of food needed for an adequate diet for himself and his family.

The Theory of Exchange 183

Each of the farmers could use a third horse to transport the timber and firewood he finds necessary from the forest to his log cabin, to draw loads of sand, stones, etc., and to work a field on which he will raise some luxury foods for his and his family’s enjoyment. A fourth would be used solely for pleasure, and a fifth horse would have only the importance resulting from its availability as a substitute in case one of the other horses should become incapacitated. But neither of the frontiersmen could use a sixth horse. It is assumed also that each of them would need five cows to meet his full requirements for milk and milk products, that there is the same gradation in the importance of their needs for these products, and that a sixth cow could not be used by either of them.

For greater clarity, let us cast the situation just described in numerical form (pp. 125 ff.). We can represent the graduated importance of the satisfactions that are provided for by the possessions of the two frontiersmen with a set of numbers that decrease in arithmetic series, with the series 50, 40, 30, 20, 10, 0, for example.3

Assuming that A, the first frontiersman, has 6 horses and only one cow, while B, the other frontiersman, has one horse and 6 cows, the successive degrees of importance of the satisfactions provided for by the possessions of the two persons can be represented in the following table:

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
40			40
30			30
20			20
10			10
0			0
0

From what was said in the first section of this chapter, it is easily seen that the basis for economic exchange operations is

3 I need hardly point out that the figures in the text are not intended to express numerically the absolute but merely the relative magnitudes of importance of the satisfactions in question. Thus when I designate the importance of two satisfactions with 40 and 20 for example, I am merely saying that the first of the two satisfactions has twice the importance of the second to the economizing individual concerned.

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here present. The importance a horse has to A is equal to o, and the importance a second cow would have to him is equal to 40. On the other hand, a cow has a value of o to B, while a second horse would have a value of 40 (p. 131). Thus A and B could both provide considerably better for the satisfaction of their needs if A were to give B a horse and if B were to give A a cow in exchange. There is no doubt that they would actually undertake this exchange if they are economizing individuals.

The importance of the satisfactions that are provided for by the possessions of the two persons after this first exchange will be as follows:

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
40	40	40	40
30			30
20			20
10			10
10

It is easily seen that each of the two traders obtained an economic gain from this first exchange equivalent to the gain that would accrue to him if his wealth had been increased by a good whose value to him is equal to 40.4 But it is just as certain that the basis for economic exchange operations has by no means been exhausted by this first exchange. For a horse still has much less value to A than an additional cow would have (10 as compared with 30), whereas a cow has a value of only 10 to B while an additional horse would have a value of 30 (three times the value of a cow). It is therefore in the economic interest of both economizing individuals to undertake a second exchange operation.

The situation after the second exchange can be represented as follows:

4These considerations completely disprove the contention of a number of economic writers (Lotz and Rau, for example, among the more recent German writers) who have denied the productivity of trade. The effect of an economic exchange of goods upon the economic position of each of the two traders is always the same as if a new object of wealth had entered his possession. Trade is therefore no less productive than industrial or agricultural activity.

The Theory of Exchange 185

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
40	40	40	40
30	30	30	30
20			20
20

It can be seen that each of the two persons derived an economic gain that is no less than if their wealth had been increased by a good valued at 20.

Let us see whether there is a basis for further economic exchange operations even in this situation. A horse has an importance of 20 to A; an additional cow would also have an importance of 20 to him; and B is in a similar position. From what has been said, it is evident that an exchange of one of A’s horses for one of B’s cows under such conditions would not be worth while since there would be no economic gain at all.

But suppose that A and B should nevertheless enter into a third exchange. If performance of the exchange did not require any appreciable economic sacrifices (costs of transport, loss of time, etc.) it is evident that the economic positions of the two men would be neither injured nor improved.5 After this third exchange their positions would be as follows:

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
40	40	40	40
30	30	30	30
	20	20

Let us now ask what would be the economic result of still further exchanges of one of A’s horses for one of B’s cows. The situation after a fourth exchange would be:

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
40	40	40	40
	30	30
	20	20
	10	10

5I classify indifferent exchanges such as this as definitely non-economic since in them the provident activity of men is set in motion aimlessly quite apart from all the economic sacrifices they may entail.

186 Principles of Economics

As can be seen, the economic positions of A and B are both less favorable after the fourth exchange than they were before. By acquiring a fifth cow, A has indeed assured the satisfaction of a need that has an importance of 10 to him. But to obtain it he has given up a horse that had the importance to him of satisfactions that were assumed equal to 30. His economic position after this exchange is exactly the same as it would be if his wealth had been reduced without compensation by a good with a value equal to 20. The same result can be observed with B. The economic disadvantage of the fourth exchange operation is mutual. Instead of gaining from it, A and B would both suffer an economic loss.

If the two persons, A and B, should continue to exchange horses for cows, the situation after the fifth exchange would appear as follows:

	A		B
Horses	Cows	Horses	Cows
50	50	50	50
	40	40
	30	30
	20	20
	10	10
	10	10

And after the sixth exchange it would be:

	A		B
Horses	Cows	Horses	Cows
	50	50
	40	40
	30	30
	20	20
	10	10
	10	10
	10	10

It is easily seen that after the fifth exchange of one of A’s horses for one of B’s cows the two traders would have returned to the same situation, with respect to completeness of provision for the satisfaction of their needs, that they were in at the outset of exchange operations. After the sixth exchange they would have worsened their economic positions considerably more.

The Theory of Exchange 187

They could do nothing better than to revoke these uneconomic exchanges.

What has been shown here in a single instance can be observed wherever quantities of different goods are in the possession of different persons and a basis for economic exchange operations is present. If we were to select other examples, we would find differences in secondary circumstances but not in the nature of the relationship explained.

Above all we would find, in each instance and at any given point in time, a limit up to which two persons can exchange their goods to their mutual economic advantage. But we would find that they cannot overstep this limit without placing themselves in a less favorable economic position. In short, we would everywhere observe a limit at which the totaleconomic gains to be derived from an exchange relationship are exhausted, and beyond which these gains would be diminished by further exchange operations, making the exchange of any further portions uneconomic. This limit is reached when one of the two bargainers has no further quantity of goods which is of less value to him than a quantity of another good at the disposal of the second bargainer who, at the same time, evaluates the two quantities of goods inversely.

Thus we see that in the reality of practical life men do not trade indefinitely and without limit. We see instead that particular persons, at any given time, with respect to any given kinds of goods, and in any given economic situation, reach a certain limit at which they cease to make further exchanges.6

A social economy is made up of individual economies, and what has been said above is therefore just as valid for the trade of entire peoples as it is for single economizing individuals. Two nations, one chiefly engaged in agriculture and the other primarily in industry, will be in a position to satisfy their needs much more completely if each exchanges a portion of its produce for the produce of the other (the first nation a portion of its agricultural produce and the second a portion of its manufactures). But they will not undertake the exchange indefinitely and without limit. At any given point in time they will reach a limit beyond which any further exchange of agricul-

6The next paragraph appears here as a footnote in the original.—TR.

188 Principles of Economics

tural produce for manufactures will be uneconomic for both nations.

It is, of course, true that in the trade of individuals, and still more in the commerce between whole peoples, the values goods actually have for men can generally be observed to be subject to constant fluctuations. These fluctuations occur principally because new quantities of goods are continually coming into the hands of the various economizing individuals through the production process. As a result, the foundations for economic exchanges are constantly changing, and we therefore observe the phenomenon of a perpetual succession of exchange transactions. But even in this chain of transactions we can, by observing closely, find points of rest at particular times, for particular persons, and with particular kinds of goods. At these points of rest, no exchange of goods takes place because an economic limit to exchange has already been reached.

Another observation made earlier concerned the gradually diminishing economic gains obtained by given economizing individuals from the exploitation of a given opportunity for trade. The first trading contacts of economizing individuals are usually the most advantageous economically. It is usually only later that opportunities for trade that promise smaller economic gains are also exploited. This is true not only of trade between individuals but also of the commerce between whole nations. If two peoples whose ports or boundaries were always or for some time previous closed to mutual intercourse open them suddenly to trade, or even if only some previous impediments to trade are removed, a very lively trade in goods develops immediately. For the number of trading opportunities to be exploited and the economic gains to be made are at first very great. Later, trade moves in the channel of normally profitable business. But if the full gains from the new trade are sometimes not immediately forthcoming, the reason is that the other two prerequisites of economic exchange, knowledge of the trading opportunities and power to carry through exchange operations recognized to be economic, are ordinarily acquired by the participants only after a certain period of time. Some of the most strenuous efforts of trading nations are directed toward removing impediments to trade in both these categories (by careful

The Theory of Exchange 189

study of the commercial situation, by the construction of good roads and other means of transport and communication, etc.).

Before I close this discussion of the foundations and limits of economic exchange, I wish to direct attention to an important factor that must be taken into consideration if the principles expounded in this chapter are to be correctly interpreted. I refer to the economic sacrifices that exchange operations demand.

If men and their possessions (the economies of individuals7) were not separated in space, and if the mutual transfer of command of goods between one economizing individual and another did not therefore generally require the shipping of goods and many other economic sacrifices, the full economic gains resulting from an exchange transaction would accrue to the two participants. But such cases are very rare. Cases are indeed conceivable in which the economic sacrifices of an exchange operation fall to a minimum neglected in practical life. But it is not easy to find an actual case in which an exchange operation can be performed without any economic sacrifices at all, even if they are confined only to the loss of time. Freight costs, loading charges, tolls, excise taxes, premiums for marine and other insurance, costs of correspondence, commissions and other sales costs, brokerage charges, weighages, packaging costs, storage charges, the entire cost of the commercial banking system, even the expenses of traders8 and all their employees, etc., are nothing but the various economic sacrifices which are required for the conduct of exchange operations and which absorb a portion of the economic gains resulting from the exploitation of existing exchange opportunities. Indeed, these economic sacrifices often render exchange impossible when it would be possible if only these “expenses,” in the general economic sense of the term, did not exist.

Economic development tends to reduce these economic sacrifices, with the result that even between the most distant lands

7“die menschlichen Wirthschaften”—TR.

8Carey’s portrayal of merchants as economic parasites because they claim a portion of the gain arising from the exploitation of the available opportunities for economic exchange transactions (op. cit., III, 23–25) is based on his erroneous ideas about the productivity of trade.

190 Principles of Economics

more and more economic exchanges become possible which previously could not have taken place.

Implicit in what has been said is an explanation of the source from which all the thousands of persons who are intermediaries in trade derive their incomes. Because they do not contribute directly to the physical augmentation of goods, their activity has often been considered unproductive. But an economic exchange contributes, as we have seen, to the better satisfaction of human needs and to the increase of the wealth of the participants just as effectively as a physical increase of economic goods. All persons who mediate exchange are therefore—provided always that the exchange operations are economic—just as productive as the farmer or manufacturer. For the end of economy is not the physical augmentation of goods but always the fullest possible satisfaction of human needs. Trades people contribute no less to the attainment of this end than persons who were, for a long time, and from a very one-sided point of view, exclusively called productive.

CHAPTER V

THE THEORY

OF PRICE

However much prices, or in other words, the quantities of goods actually exchanged, may impress themselves on our senses, and on this account form the usual

object of scientific investigation, they are by no means the most fundamental feature of the economic phenomenon of exchange. This central feature lies rather in the better provision two persons can make for the satisfaction of their needs by means of trade. Economizing individuals strive to better their economic positions as much as possible. To this end they engage in economic activity in general. And to this end also, whenever it can be attained by means of trade, they exchange goods. Prices are only incidental manifestations of these activities, symptoms of an economic equilibrium between the economies of individuals.

191

192 Principles of Economics

If the locks between two still bodies of water at different levels are opened, the surface will become ruffled with waves that will gradually subside until the water is still once more. The waves are only symptoms of the operation of the forces we call gravity and friction. The prices of goods, which are symptoms of an economic equilibrium in the distribution of possessions between the economies of individuals, resemble these waves. The force that drives them to the surface is the ultimate and general cause of all economic activity, the endeavor of men to satisfy their needs as completely as possible, to better their economic positions. But since prices are the only phenomena of the process that are directly perceptible, since their magnitudes can be measured exactly, and since daily living brings them unceasingly before our eyes, it was easy to commit the error of regarding the magnitude of price as the essential feature of an exchange, and as a result of this mistake, to commit the further error of regarding the quantities of goods in an exchange as equivalents. The result was incalculable damage to our science since writers in the field of price theory lost themselves in attempts to solve the problem of discovering the causes of an alleged equality between two quantities of goods.1 Some found the cause in equal quantities of labor expended on the goods. Others found it in equal costs of production. And a dispute even arose as to whether the goods are given for each other because they are equivalents, or whether they are equivalents because they are exchanged. But such an equality of the values of two quantities of goods (an equality in the objective sense) nowhere has any real existence.

The error on which these theories were based becomes immediately apparent as soon as we free ourselves from the one-sidedness that previously prevailed in the observation of price phenomena. The only quantities of goods that can be called equivalents (in the objective sense of the term) are quantities which, at a given point in time, can be exchanged at will— that is, in such a way that if one of two quantities of goods is offered, the other can be acquired for it, and vice versa. But equivalents of this sort are nowhere present in human economic

1See Appendix F (p. 305) for the material originally appearing at this point as a footnote.—TR.

The Theory of Price 193

life. If goods were equivalents in this sense, there would be no reason, market conditions remaining unchanged, why every exchange should not be capable of reversal. Suppose A had exchanged his house for B’s farm or for a sum of 20,000 Thalers. If these goods had become equivalents in the objective sense of the term as a result of the transaction, or if they had already been equivalents before it took place, there is no reason why the two participants should not be willing to reverse the trade immediately. But experience tells us that in a case of this kind neither of the two would give his consent to such an arrangement.

The same observation can also be made under the most highly developed conditions of trade, and even with respect to the most saleable commodities. Let anyone buy grain on a grain exchange or securities on a stock exchange and try to sell them again before a change in market conditions occurs, or let him try to sell and buy separate units of the same commodity at the same time, and he will easily be convinced that the difference between supply prices and demand prices is no mere accident but a general feature of social economy.

Thus commodities that can be exchanged against each other in certain definite quantities (a sum of money and a quantity of some other economic good, for instance), that can be exchanged for each other at will by a sale or a purchase, in short, commodities that are equivalents in the objective sense of the term, do not exist—even on given markets and at a given point in time. And what is more important, deeper understanding of the causes that lead to the exchange of goods and to human trade in general teaches us that equivalents of this sort are utterly impossible in the very nature of the case and cannot exist in reality at all.

A correct theory of prices cannot, therefore, have the task of explaining an alleged “equality of value” between two quantities of goods when such an equality does not, in truth, exist anywhere. In this setting, the subjective character of value and the nature of exchange would be completely misunderstood. A correct theory of price must instead be directed to showing how economizing men, in their endeavor to satisfy their needs as fully as possible, are led to give goods (that is, definite quan-