6. Attempt at a Definite Theory of the Value of Goods. Criticism of Walras’ Presentation

6—Attempt at a definite theory of the value of goods. Criticism of Walras’s presentation

Let us first of all try to imagine what an economy must be like, if the equations (20)-(24) (or the alternative equations given in the footnote to p. 152) are to reflect the true play of economic phenomena. This requires, of course, that within the whole economy only one single consumption good, for instance corn, is produced. Wages, ground-rent and capital-interest are all received in the form of goods, that is to say, in corn, and the capital itself consists of corn and the installations and tools necessary for the production of corn, which, however, we imagine as being so simple that they can be produced by the economies in question themselves and are of short duration. Durable goods are not produced at all. The economy must be a completely stationary one.

Let us now suppose that beside this economy there exists another, where in the same way another commodity—again, a single commodity only; for instance, linen—is produced. Exchange between the two economies is completely free, but capital and labour cannot be transferred from one to the other. For each of these two economies there would then exist a system of equiiibrium equations similar to system (20)-(24). The constants of the equations—the number of workers, the area of land and the capital—as well as the form of the function of productivity p (or q) are, however, different for both economies. Let the above-mentioned magnitudes be A₁, B₁, K₁ and p₁ for one economy and A₂, B₂, K₂ and p₂ for the other. When these magnitudes are inserted in equations (20)-(24) instead of A, B, K and p, we obtain from each of these equilibrium systems, by elimination of the remaining unknowns,¹ first the length of the period of production t in question, then the values of the magnitudes l, r and z which we require to know. If these values are t₁, l₁, r₁ and z₁ for the first economy and t₂, l₂, r₂ and z₂ for the second, then A₁l₁ + B₁r₁ + K₁z₁ and A₂l₂ + B₂r₂ + K₂z₂ respectively express the quantities of goods which are produced every year in the two economies. Since, furthermore, the distribution of capital property and landed property within each economy must be assumed to be constant, we know now how much of this production falls to each person’s share. Of these quantities of goods, one part of the yearly production of one economy is exchanged for one part of the yearly production of the other economy. And this exchange takes place exactly according to the laws of exchange developed previously. If, for instance, some proportion of exchange (the price on both sides) is first of all assumed at random, then each of the owners of corn—that is to say, each worker, landowner and capitalist of the first economy—offers, at this price, a certain quantity of the corn which has fallen to his share for the year in exchange for a corresponding quantity of linen—i.e. just so much that the ratio of the marginal utilities of corn and linen (appropriate to the quantities of corn and linen which have been consumed during the year) is made equal to the ratio of the prices, that is, the proportion of exchange. By addition of these partial quantities, we obtain the yearly supply of corn and the yearly demand for linen on the part of the owners of corn—at the price in question. In exactly the same way a total supply of linen and a total demand for corn arise on the other side, at the same price. If supply of, and demand for, the one commodity are equal, and consequently also equal with regard to the other commodity, equilibrium is attained; if not, a shifting of prices must take place. But this change has obviously no influence on the proportion of production on both sides. The problem of international trade, of which we have here presented the simplest pattern, is therefore, in fact, much less complicated than that of internal trade. Before long an average proportion of exchange will establish itself. Afterwards, this proportion is maintained practically unaltered from year to year, and is characterized by the fact that for every member of both economies the proportionality between marginal utility and price of both commodities is fulfilled. In this case, of course, it is not necessary that each individual member should appear in the exchange market. Without essential change in the proportions, the exchange can be transacted by all the capitalists, or by a few of them; so that wage, ground-rent and capital-interest, too, can be paid in both kinds of goods or in any conventional medium of exchange (for instance, paper money), provided only the above-mentioned proportion of marginal utility is thereby realized as the final result.

But if we now imagine that both economies are united in a single economy, so that the existing workers, natural resources and capitals of both can now be used indiscriminately in the one or the other production of goods, then at first sight everything seems fluid. If we wish to make use of two equilibrium systems here, the difficulty arises that the magnitudes A₁, A₂, B₁, B₂, K₁, K₂ can no longer be assumed to be known; to begin with, we only know the sums A₁ + A₂ = A; B₁ + B₂ = B. As for the capitals K₁ and K₂, neither they themselves nor their sum are known, strictly speaking. The national capital, in so far as it is free, consists here of two commodities, and its value can therefore only be determined after having found out their prices—that is to say, can only be expressed in one of these or in some other conventional medium of exchange.

But, on the other hand, it is obvious that in this case two different rates of wage, rates of rent and rates of interest can no longer exist, but wage, rent and interest on both sides will become approximately equal (in so far as the labour force and natural resources can be assumed to be uniform).

Let us first try to give an account of how these changes would come about after abolition of the boundary-line between the two economies. Let us suppose that at first l₁ and l₂, r₁ and r₂, z₁ and z₂ are still different. If l₁ > l₂, the workers will gradually go over from the linen business to the corn business: A₁ increases; A₂, on the other hand, decreases. And vice versa: if, when the boundary-line is abolished, r₁, for instance, is smaller than r₂, part of the land used for the cultivation of corn will gradually be employed for the production of linen. B₁decreases and B₂ increases. Finally, if z₁, for instance, is at first smaller than z₂, the capital engaged in the production of corn, in proportion as it becomes free (which occurs by production itself), will be partly invested in the production of linen. Since this capital appears first in the form of corn, some of the workers in the linen business will consequently, if no account is taken of previous exchanges, now receive their wages directly in corn. However, this does not make any difference to them, provided the proportion of exchange between linen and corn remains unchanged. But this proportion of exchange cannot remain unaffected by the changes which have taken place either. If, therefore, taking corn as the standard of value, the price of linen has fallen, the capitalists, whose free capital consists mainly of linen, must increase the number of pieces in their capital stock if they wish to restore to it the same value; if, on the contrary, the price has risen, they can, without loss, decrease this number and consume part themselves. But it is very probable that all the capitalists will increase the number of pieces in their capital stock, at least for some time. In general, this freer and therefore more appropriate employment of productive forces must necessarily lead to higher productivity within both branches of business, and this increased productivity will facilitate the formation of new capital, until finally the stationary situation is again reached—only this time with more capital and probably a higher average level of ground-rent and wages (but not necessarily a higher average level of the rate of interest).

To pursue all these changes in detail is quite impossible, especially as they take place in an infinite number of different ways. We can, however, determine without difficulty the position of equilibrium finally attained, with the help of our equations set forth above—but only if we assume that the present capital is a known magnitude.

First of all the two initial equations

with their derivatives¹ in respect of t₁, h₁, t₂ and h₂ (altogether six equations), must be fulfilled.

The magnitudes l, r and z are now equal on both sides. On the other hand, we assume here for each branch of the business, according to the nature of things, a special form of the productivity function p = F(t,h) (which we assume to be known), as well as a different length of the most profitable period of production and a different proportion of the use of land (number of hectares per worker or, vice versa, number of workers per hectare). We therefore have, for the time being, six independent equations with the seven unknowns t₁, t₂, h₁h₂, l, r and z.

In the equations still remaining

the six new unknowns A₁, A₂, B₁, B₂, K₁ and K₂ occur, but for their determination we still have the equations

A₁ + A₂ = A

B₁ + B₂ = B

K₁ + K₂ = K

where A, B and K stand for the number of workers, area of land and capital existing within the whole economy, the latter expressed in terms of corn. We therefore have altogether thirteen equations with the same number of unknowns,¹but only on the assumption that the proportion of exchange of both commodities is known.

Here, p₁ and p₂ express values, that is to say, they give the exchange value of the yearly production (as functions of t and h). But, of course, in the first instance only the number or quantity of the products in question is, in fact, established by the functions of productivity, which were assumed to be known on both sides. Since now the corn has been taken as our standard of value, p₁—the value of the production of corn (per year and worker)—is dependent merely on t₁ and h₁; the function p₂, on the other hand, includes, in so far as it is supposed to give the exchange value of the production of linen, another factor π, namely the proportion of exchange of both commodities or the uniform price of linen expressed in terms of corn.¹ But this proportion of exchange cannot be assumed to be known here; rather, our task is to show how it is determined by the interplay of all the economic forces. We therefore still have one unknown in excess of the number of equations and need one more of the above-mentioned independent equations, if the problem is to be completely solved.

To find this, we must imagine ourselves placed on the market of exchange of both commodities, and we must lay down the condition that on this market, too, there is equilibrium—equilibrium between supply and demand or, what is here the same, equilibrium between production and consumption.

This can come about, for instance, in the following way. At each level of l, r and z the yearly income of every single member of the economy, in addition to other factors, is definitely fixed. If, for instance, the individual in question is a worker himself, and if he possesses b hectares of land and has invested in the production capital of the value k, then his yearly income e is expressed by e = l + br + kz. This income he uses, according to our fundamental assumption, to the last penny (or rather to the last part of corn) for his yearly consumption of corn and linen. We therefore obtain

e = x + πy

when x and y respectively stand for his yearly consumption of these goods.² But these quantities must now fulfil the law of marginal utility, so that, if f( ) and g( ) stand for the marginal utility functions related to the quantity of the yearly consumption,

f (x) : g(y) = 1 : π

Since the forms of the functions f( ) and g( ) must be assumed to be known, x and y can be determined from the last two equations, that is to say, can be expressed in terms of l, r, z and π. When this operation is carried through for each member of the economy,¹ we have also found the total consumption of, or demand for, the goods concerned, and, according to what has been said above,

X = Σx = A₁p₁

The yearly consumption of corn on the part of the total economy must correspond to the yearly production of corn. In the same way, with regard to the consumption and production of linen,

One of these equations, however, can be derived from the other; for we obtain from these

A₁p₁ + A₂p₂ = Σx + πΣy = Σe = Al + Br + Kz

On the other hand, as is evident, we obtain by addition of our initial equations of production, or by multiplying them by A₁ and A₂,

The one or the other of the above equations gives us, consequently, the hitherto missing relation between our unknown magnitudes. If A₁ and A₂ are already eliminated, we can instead use the equation

Or we could imagine each of the two branches of production as complete in itself, so that the yearly production is in the first instance simply distributed among the members as wage, rent and interest, and the supplies on both sides are partly exchanged later, p₁ as well as p₂ are then to be thought of as numbers of pieces. Wage and rent, likewise expressed in terms of number of pieces of the commodity in question, are connected by the relations

l₁ = πl₂, r₁ = πr₂

and if the capital invested on both sides is in the first instance valued in terms of the commodities concerned, then

K₁ + πK₂ = K

in which K, as before, expresses the known value of the total national capital (valued in corn). If now, for instance, the individual mentioned above uses b₁ hectares in the corn business and b₂ in the linen business, or invests the capitals k₁ and k₂ and has himself worked about eight months in the corn business and four months in the linen business, then he receives each year

and

All these individual quantities are then brought to the cornlinen market and are partly exchanged against each other. The equilibrium price, found according to the rules of exchange, appears now as a known function of l₁, l₂, r₁, r₂ and z, but must equal π, by which means the missing relation is found. Both methods, obviously, lead to the same result, and we can lay down as the final result of our investigation the rule:

If an economy comprises the production, distribution and consumption of only two commodities, the proportion of exchange between them is given by the following conditions: (1) that wage, rent and interest during production of both commodities must be equal; (2) that at the level of wages and rent attained, interest becomes a maximum (or, in general, at the attained level of two of these three magnitudes, the third becomes a maximum); (3) that the existing capital must just suffice to employ the existing number of workers and to rent the existing area of land, and; (4) that the two commodities are distributed among all members of the economy directly or after a preceding exchange, in such a way that the ratio of the marginal utilities of the quantities consumed yearly becomes everywhere equal to the ratio of exchange of the goods.

We have now reached the end of our investigation; for if the theory developed here has gone to the root of economic phenomena, all complications of the problem will find their solution by suitable combinations of equations of the kind laid down above, at least in so far as it is a question of a stationary economy. Let us glance at these complications as they occur in real economic life.

1. Production and consumption in a modern economy comprise not only two commodities, but hundreds of them, even if only the main kinds of goods are reckoned ; and within every class of goods there is usually a large number of different qualities and specialities.

However, this circumstance will only make necessary a larger number of equations. With every new commodity which must be taken into consideration, six new unknowns enter the problem, according to our above-mentioned scheme; since for each commodity the most profitable period of production and proportion of the use of land, the number of workers, area of land and capital employed in its production, and finally the exchange value of the commodity are to be determined. If there are n goods and one of them is taken as the standard of value, the number of unknowns will consequently be 6n + 2.¹ For their determination the laws of production give, as can easily be seen, 5n + 3 independent equations, whilst the missing n—1 equations are obtained from the laws of exchange—for instance, by means of a formula expressing the fact that, at the n— 1 prices of the goods, which must be determined and expressed in terms of one of them, the quantity of each commodity yearly consumed or demanded must be equal to its yearly production, and by taking into consideration that only n—1 of the n equations laid down in this way are independent.²

2. Labour and forces of land were each assumed as a homogeneous mass.

This is, of course, not correct. For certain productions there is at any time only a very limited number of workers who are employable at all, since the business requires either special abilities or a longer training. In order that this circumstance may be taken into consideration, the existing workers must be divided into groups, and the wage for each group, which can then be very different for the various groups, must be ascertained separately. But once the boundary-lines of these groups are drawn, the number of independent conditioning equations (Bedingungsgleichungen) will here obviously increase also to the same extent as the number of the unknowns.¹

As for natural resources, we come first of all to the well-known fact of the difference of landed property with regard to fertility, situation, etc. But, in addition to this, there are natural resources of an entirely different kind: agricultural landed property, fish-ponds, woods, ore-bearing tracts, waterfalls, etc. For each of these kinds, a special uniform measure must, of course, be chosen.

Finally, in my opinion, produced goods also, in so far as they are continuing sources of rent, should be taken into consideration here. In the stationary economy such goods are not produced at all, but kept in the same good condition.² The capital investment in question itself belongs to past time and need no longer be considered. The net interest on this capital has consequently the precise character of a rent, since necessary repairs and maintenance work, as well as running costs, are imposed on the capitalist who uses these goods.

On the other hand, it cannot be right to do as Böhm-Bawerk does and try to exclude means of improving the soil, as soon as they have ‘grown together’ with the land, from the sphere of capital. In the same way, improvements, such as fertilization and the like, which suffice for only a few harvests and must consequently replace the invested capital after a short time, belong obviously to agriculturally-employed capital in the narrower sense, as do tools, labour, draught animals and food-producing animals, etc.

Dwelling-houses, too, must in my opinion be added to rent-goods. Dwellings—just as much as food, clothes, heating, etc.—belong to the needs which must be satisfied from the economic point of view. Why, then, should the service of giving shelter which dwelling-houses provide not be put in the same category as the economic services of fields, meadows, woods, fish-ponds, etc.? From the point of view of the stationary economy there is scarcely any substantial difference left between them.

The boundary-line between rent-goods and capitals in the narrower sense can, I grant, only be established empirically, and even then only approximately. Practically, however, the difference is a highly important one. The volume of circulating capital determines the level of wage, rent and capital-interest. Upon these the highly durable goods merely exercise the same influence as, say, the size of the cultivated area of land. But their capital value is, at least in the stationary economy, an entirely secondary phenomenon and has for the exchange values of consumable goods no importance whatsoever.

For production, we have consequently to consider—once this boundary-line is drawn—not merely the capital K and the different groups of workers A^I, A^II, A^III, A^IV, etc., but also the different groups of rent-goods B^I, B^II, B^III, B^IV, etc., each with its different quantity-unit and rent of this unit. Each new group becomes the source of new unknowns but also the source of the necessary number of new independent equations.

3. It was assumed that the production of a new commodity in all its different stages is done in one single business. In reality this is practically never the case. The raw materials and means of production are usually produced in special firms; the same factory often supplies tools and machines for several different branches of business, and, on the other hand, half-finished products and raw materials coming from quite different sources are put together and further worked up in a single business, etc. Viewed prospectively or retrospectively, the businesses branch out or meet.

This circumstance would create no special difficulties if the production of each separate commodity could be followed through the various businesses, and if we could find out what quantity of labour, capital and natural resources (or of services of the other rent-goods) has been engaged in the completion of this particular commodity. If this is not possible, and if, consequently, the production of two or more commodities forms more or less an indissoluble whole, then, if we are to treat the problem mathematically, these goods must be united in one single group; because then they pay for the labour, capital and rent-goods used in their production not separately, but all together. In the equations of exchange, however, they are to be treated separately again (in so far as two or more of them cannot replace each other).

4. The supply of labour was treated as a constant magnitude. This is not quite correct even if the number of workers remains the same; for the daily working-time can, in certain circumstances, vary, or several days or weeks of the year can be spent in idleness—not only because of lack of employment during certain seasons, but also because the worker may allow himself more leisure when wages are more abundant. That is to say, a labourer’s ability to work or his time, unlike most rent-goods, is of value to its possessor, even when it is not used productively.

If, therefore, we do not (with L. Walras) use the word ‘production’ in such a general sense that even a person’s use of his spare time, a walk, etc., is regarded and treated as ‘production,’ it obviously becomes necessary to consider the yearly working-time, and consequently the yearly production, of a worker as itself a function of the wage. It must be remarked in this connexion, however, that, even if the working-time of the individual worker possibly decreases when wages rise, yet, on the other hand, people who have previously lived in idleness are now tempted or rather forced by the higher price of labour to become workers themselves. Moreover, men will be able to work harder in the shorter working-time because of the greater abundance of food, etc. It cannot therefore be decided a priori to what extent, in given circumstances, a rise or fall in wages would increase or reduce the effective supply of labour. Each individual case must be investigated separately.

5. Finally, our assumption of a stationary economy represents only the simplest case which is theoretically conceivable, but which never quite comes to pass in reality. In exceptional cases, such as our own century, for instance, there can even occur a progression of society so great that this hypothesis does not correspond even approximately to reality. In any case the theory must, in order to be complete, not only be able to treat the statics but also the dynamics of economic phenomena; it must not only take into consideration the equilibrium of economic forces, but also the disturbance of this equilibrium caused by their changes.

The number of workers, or, more generally, of the population, can be increased by a rise in the birth rate or by immigration, and can be decreased by exceptionally heavy mortality or by emigration. The sum of rent goods, including the cultivated area of land, can be increased by industry and decreased by neglect respectively. Lastly, the national income carusuffer changes in several ways. The transformation of capital in the narrower sense into rent-goods or even into working ability (its sacrifice for purposes of education) is here to be emphasized as such a change, and, what is more, as a change of the greatest importance.

If in all these relationships a certain rate of progression may be assumed to be given, then it is clear that equations of production and exchange can be laid down. We have then, so to speak, a problem of dynamic equilibrium instead of a problem of static equilibrium with which to deal.¹

It would be quite a different matter to try to lay down laws for determining the rate of progression itself. I personally make no attempt in this direction.² How far present-day political economy still is from being able to treat these situations in an exact way, becomes clear if we consider the fact that economists are still by no means agreed as to the extent to which such a progression of society is advantageous or not. In particular, so far as I know, the question has never been raised in economic writings, what size of population is economically most profitable when the amount of capital, size of the area of land, etc., are given. If, therefore, these problems are to be solved according to the principle of the greatest utility, it is obviously a serious drawback that there is not even common agreement in what direction economic advantage or disadvantage in fact lies. If, on the other hand, we assume that changes of population are not regulated according to the principle of what is economically most advantageous (in the widest sense of the word), but are regulated now and for ever merely by blind natural instincts, then at least we are on firm ground. In that case, however, we should have no alternative but to accept Ricardo’s doctrine of the natural wage—that is to say, the smallest possible wage—as a fact beyond dispute. Altogether, population questions are unfortunately still neglected by the economists of practically all schools. This is regrettable from the theoretical point of view, but still more regrettable, of course, from the practical point of view.

Even if we take no account of the unfortunate state of affairs last mentioned and look at the problem as a purely statical one, the foregoing enumeration shows that the list of complications is a very considerable one. But it is clear, when treating concrete problems of reality, as soon as the required facts are more or less at hand, all necessary simplifications will follow automatically. The practical business man has, after all, to consider as far as possible all circumstances which influence the conditions of production and sale of his commodity. If he cannot possibly penetrate, or does not need to see at a glance, all phenomena of the market, this may be regarded as proof that, for the theoretical treatment of the problems which he has in fact to solve, at first only a comparatively small number of the pertinent magnitudes need be inserted in the calculation.

Above all, we should, in this case, have to define more precisely the still somewhat hazy concept of the length of the period of production within the individual main businesses—for instance, agriculture, the textile industry, the iron industry, etc.—and to find out the increase in this period which has resulted from the improvements introduced from time to time, in so far as they have really required a larger investment of capital. Once such information is available for the main fields of economic life, the counting procedure and, with it, the a posteriori investigation of the theory can start. It must be remembered, however, that the results of the theory can only remain valid on the assumption of completely free competition.

The doctrine set forth here has much in common with the theory presented in Léon Walras’s Élements d’économie politique pure. There, too, equations of production are laid down and combined with the equations of exchange previously obtained. But, as was remarked above, Walras calls ‘capital’ and treats as ‘capital’ only durable goods, but not raw materials and half-finished products and not the means of subsistence of workers. What the owner of the circulating capital advances to the workers, landowners, etc., is therefore not treated by Walras as capital at all. It is therefore implicitly assumed by Walras that workers and other producers maintain themselves during production and receive remuneration for their productive services from the proceeds of the products in question only after completion of the production. This is obviously incorrect. In this interpretation the true rôle of capital in production is completely overlooked. A necessary consequence of this is the peculiar fact that these equations of production and exchange can give no information at all about the level of the rate of interest. If only durable goods are regarded as capital, then a certain rent is fixed for each group of these by the above-mentioned equations, but not the capital value of the goods itself, nor, consequently, the rate of interest either, ‘le taux du revenu net.’ This is explicitly admitted by Walras; but he asserts that, in order to determine the level of interest, it is necessary to turn from the investigation of a stationary economy to the investigation of a progressive one, where new interest-bearing capital goods are produced, whose capital value can be determined from the production costs. This is certainly incorrect. In the stationary economy, too—even if we assume that all the means of production are indestructible—a rate of interest of the circulating capital will undoubtedly establish itself, precisely because the lengthier methods of production prove more profitable. Walras’s theory of production and capital consequently rests upon incorrect assumptions and cannot be regarded as definitive. However much it may—in several respects—testify to its author’s acuteness, the- real essence of the matter has not become clear to him. The merit of having taken the decisive step forward belongs in this field to Jevons and, above all, to Böhm-Bawerk.¹

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¹ Throughout this chapter I shall use as fundamental the excellent works of Böhm-Bawerk, especially his Positive Theorie des Kapitals, which, I may be allowed to assume, is known to most readers.

² Positive Theorie des Kapitals, p. 24.

¹ Inversion of this seeming paradox produces the question, How is it that goods which can yield, according to their nature, an infinite number of useful services, above all landed property, possess nevertheless only a finite capital value ?

¹Principles of Economics, p. 124. Adam Smith’s remark (Wealth of Nations, vol. II, chapter I), that houses let to a tenant and similar goods can only be reckoned as private capital for the simple reason that rent must always be taken from any other source of income, is meaningless. The same is, after all, true of every money income and, generally speaking, of every income which arises from exchange. If a craftsman or a business-man reckons his landlord as customer, his income is drawn from the landlord’s, just as the landlord’s is drawn from his.

² Op. cit., p. 70.

³ Op. cit., p. 76.

¹ Böhm-Bawerk, op. cit., p. 73.

¹ It must not be overlooked that the role of the capitalist and that of the worker can also be united in one and the same person.

² Op. cit., p. 75.

¹ We say intentionally, ‘up to the moment of consumption’; for it is after all of little importance whether the duration of life of capital is or is not theoretically prolonged by several hours, days or even weeks. The economic sign that goods cease to be capital-goods is, as I see it, this—that they, so to speak, have passed into the lawful possession of the consumers; that is to say, are exchanged for some capitalistic equivalent: labour, the use of land, other capital-goods or money. Nevertheless, the consumers—or the persons so named by us for the sake of simplicity—can in this case partly deny themselves the consumption goods which now belong to them lawfully and use them as new capital-goods. We have already dealt with the position of durable consumption goods.

¹ According to Böhm-Bawerk the productive undertakings designed to improve landed property in so far as they preserve an independent character and do not become completely absorbed in the landed property (e.g. dams, pipes, etc.), ought to be called capital. But of what importance is this independent character here? When it is a question of the level of interest or wages, these goods have exactly the same importance as landed property itself, provided only they are sufficiently durable.

² Money has in this case a remarkable double position. For the community as a whole it is a rent-commodity; what is more, rent (the utility of money) received by the community is many times in excess of the amount of the usual money interest. For the single possessor it is a capital-good.

¹ It is, in my opinion, even more comprehensive than the problem itself, in that it also includes interest phenomena where no interest-bearing capital exists any longer (as in the case of a consumption loan).

¹ In his book Principii di economia pura (p. 301), M. Pantaleoni opposes Böhm-Bawerk in saying that, if it were true that a present commodity possessed a higher marginal utility than a future commodity, the loan would in fact be a purposeless transaction, because like would merely be exchanged against like. The superficiality of this objection is obvious after what has been said above.

¹ If this were not the case, one would hear little of times of famine and distress, and so on. Nothing seems easier than to do as Joseph and Pharaoh did and, when the harvest is good, put aside the surplus for use when the harvest is bad. But the practical solution of this problem soon proves to be a very difficult one, not only because of the improvidence of individuals, but first and foremost because of the cost and inconvenience of the storage itself.

¹ Here, obviously, we are speaking only of the well-thought-out and ‘motivated’ productivity theory of a writer like Thünen. Böhm-Bawerk has a much easier task with most of the other so-called productivity theorists, who were often not even able to distinguish between product of capital and interest on capital. I shall not even mention the incredible superficialities of a writer like Carey. Böhm-Bawerk rightly says of this author, that ‘his theory belongs to those which not only discredit their author, but also the study which is betrayed into accepting them so faithfully; and this not because of its errors, but because of the unpardonable nature of the mistakes by which it errs.’ (Kritik und Geschichte der Kapitalzinstheorie, p. 179.)

¹ The usual explanation of capital-value of durable, produced goods, such as a dwelling-house, by reference to the costs of production and reproduction, is, of course, unscientific and amounts to mixing up and lumping together cause and effect.

¹Positive Theorie des Kapitales, p. 301.

² Particularly as regards the question of the ‘use of money,’ the Use theory can be applied with success. When we so apply it we are generally disturbed by the fact that a borrowed sum of money is ‘used’ by the debtor once only, and for the most part immediately after the receipt of the loan. In fact, however, he uses the money at least twice, once for the purchase, and once for the sale of goods; and in this case the circulation of the money which has taken place in the meantime generally enables him to sell the purchased commodity at a profit later on. This becomes especially clear if one looks at the simplest case where no real production is involved but the money merely serves for the exchange—that is to say, for the economically more advantageous distribution of the existing goods. If we assume that this sum constitutes the only money in circulation within the economy in question, then the situation which we have met before in the case of the exchange of several commodities arises, and we can follow the identical moneys right up to the time of the repayment of the loan. In this case at any rate, interest appears first not in the form of money but in the form of goods.

¹ Strictly speaking, however, as was indicated above, interest on a consumption loan does not belong to the sphere of true capital interest, since here the loaned ‘capital’ continues to exist not as a material commodity but merely as a claim and the repayment takes place by a new formation of capital on the part of the debtor (or by diminution of already existing capital).

¹ Adam Smith (Wealth of Nations, vol. II, Introduction) tried to explain the need for capital formation by the division of labour, since the latter can only come about if the subsistence of the workers concerned is already assured by the accumulation of a given supply of food. But this seems to me to be a false conclusion. Division of labour by itself does not lengthen the period of production, but shortens it, and therefore does not in fact make necessary new capital formation (but does make necessary a certain concentration of the already existing capital). On the other hand, however, as is well known, division of labour is one of the most powerful instruments of production: many round-about methods of production which would otherwise not be sufficiently remunerative, become so by division of labour; and to this extent, of course, the possibility of division of labour becomes indirectly an effectual cause of the adoption of these round-about methods and consequently of the accumulation of new capital.

¹ For several reasons, the constancy of these changes is still more evident if the average proportions within a certain branch of business, considered as a whole, are examined.

¹ Loc. cit., p. 95.

² Whether a capital-good, for example a dwelling-house, will presumably last only 50 or even 100 years, makes, on the assumption of a rate of interest of 5 per cent, a difference of not quite 9 per cent (8 · 72 per cent) to its present-day capital value; whether it lasts 200 instead of 100 years makes a difference of less than 0·7 per cent; whether it lasts for ever instead of for 200 years, makes absolutely no difference, since only the minute difference in value of 0-0057 per cent is involved (i.e. instead of perhaps 100,000 M the house would then be worth 100,005 M 70 Pf.).

¹ The neglect of this important distinction is, in my opinion (indicated above), one of the fundamental mistakes in Böhm-Bawerk’s presentation, which is otherwise so clear. We shall see in due course how he was led by it to criticize in a quite mistaken way Jevons’s theory of interest.

¹ That in this case a maximum and not a minimum of l occurs, can, with reference to the conditions of the problem, easily be proved. Compare the following geometrical illustration.

¹ Strictly speaking, this is, of course, only correct if the month can be regarded as an infinitely small part of the whole process of production. As regards this whole subject, cf. my essay ‘Kapitalzins und Arbeitslohn’ in Conrads Jahrbücher, December 1893, p. 868 ff.

¹ No account is, of course, taken here of brokerage, etc., and a single rate of interest is assumed for the whole capital market.

¹ We can easily convince ourselves of the truth of this, either by examining equations (13) and (14), or, still more easily, by considering the relevant diagram.

² This gradation of production can, of course, be very easily adopted by individual producers as well. Agriculture and, still more, market-gardening are examples.

¹ The figures of the third column, divided by the number of years of the period of production in question, represent the interest, calculated for half the level of wages; for the necessary advance of capital for each worker over a period of x years is of the yearly wage, and the annual profit from one worker constitutes the interest on this sum. For example, if the period is one of six years, we obtain

² Loc. cit., p. 415.

¹ Here, however, we must remember the situation mentioned on p. 128 ff. Certainly, when competition is free, a rate of wage of 500 fl. comes about in the way described above, and at this rate the six-year period of production is seen to be the most profitable for each individual capitalist. If, however, the capitalists, regardless of this, agree to adopt and keep to a seven-year period, then the wage would have to fall to about 430 fl., and at this rate of wage the seven-year period will now yield a net profit of more than 16 per cent. The profit would be still more huge if an eight-year period were adopted, and so forth.

¹ Böhm-Bawerk gives in a note (p. 419) ‘the mathematical proof of this somewhat paradoxical thesis,’ assuming a ‘five-year production divided into sections of one year each.’ If, however, we assume—as in other contexts he himself does—a continuous gradation of production and wage-payment, then what was assumed above becomes self-evident; for a production of n years will then require for every worker, as was pointed out above, an advance of capital of yearly wages. A production of n + 1 years consequently requires an advance of yearly wages, and the difference between these figures is precisely half the yearly wage.

¹ The passage on p. 226 ff. quoted by Böhm-Bawerk refers to the capital-labour market, where capitalists and workers offer to each other, within certain limits, their ‘goods’ ‘at any price,’ and where, therefore, the proportion of exchange (the wage) simply becomes equal to the proportion of the existing quantities.

¹ That is to say, the capital formerly employed was per worker; the capital now employed is consequently , and the difference between these expressions amounts to .

¹ This must in the end be the case, since, if t increases, even the expression α + β log nat t increases beyond all limits.

² This must not be confused with his well-known but mistaken speculations about the so-called natural wage.

¹ Or vice versa: If the workers themselves are entrepreneurs, it must be assumed that the rate of interest is given and that the wage is still to be determined.

¹ If a certain capital k is invested, and then t years elapse before the product—which all this time has grown in value—is sold, we obtain

s = k(1 + z)^t

where s is the final value of the product and z the average yearly rate of interest. This rate of interest becomes a maximum when

By division of these equations we obtain

Since, now, log nat (1 + z) expresses the ‘instantaneous’ rate of interest, where z is the yearly rate of interest, Jevons’s rule could be completed in such a way that, when interest becomes a maximum, the ‘natural’ rate of interest must ultimately correspond to the present rate of interest. (For small values of z, log nat (1 + z) is approximately equal to z.)

If, on the other hand, we assume that production is continuous, we obtain from the two equations in the footnote on p. 123, as can easily be seen,

or

Here, too, it is most advantageous to extend the period of production up to the point at which the (paid out or received) interest (instantaneous rate of interest) is equal to ‘the rate of increase of produce divided by the whole produce,’ according to Jevons’s formula except that in this case the amount of wages which has to be paid each moment must be subtracted from the gross increase of produce.

¹ But only, as I understand it, if we exclude predominantly durable goods (such as buildings, streets, railways, etc.), with which we shall deal soon.

² For the time being we shall leave out of account the services of the remaining ‘rent-goods.’

¹ In passing, we may show that what Böhm-Bawerk has to say about the influence of ground-rent on capital-interest can scarcely be right.

Böhm-Bawerk asserts (loc. cit., p. 438) that the advance of capital to landowners (ground-rent) has an effect on the level of the rate of interest precisely analogous to the effect of the existence of the consumption loan (discussed by him before). ‘The fact that the landowners, too, compete for consumption loans,’ he continues, ‘takes a portion of the means of subsistence out of the market, and a result of this is that the investment of capital in production decreases; investment must call a halt at a higher level of surplus returns; and in this way the rate of interest is at last maintained on a higher level.’

But Böhm-Bawerk forgets the tremendous difference which is made by the fact that the applicants for consumption loans pay interest on the advance of capital which has been made to them, whilst the landowners do not. In other words, the portion of capital paid out as ground-rent together with the portion of capital used in the production itself (paid out as wages) yields interest in the form of the net profit of production. Consequently it is not enough that the capital diminished by ground-rent remains ‘at a higher level of surplus returns.’ When in these circumstances the rate of interest is forced up, the case examined above must occur, where (leaving out of account the services of the land) an increase of productive capital would lead to an absolutely lower net profit and a decrease of capital would consequently yield an absolutely greater net profit. That this is really the case in the present state of production, is scarcely credible. It seems to me most probable that if ground-rent were abolished, that is to say, if the services of the land were free, capitalists would obtain a higher interest on their capital. But what would happen if—as Böhm-Bawerk supposes by way of example—the taxation of ground-rent reached a confiscatory level or private ownership of land were even abolished, is less easy to decide. Actually, however, ground-rent would not be abolished, but would be paid by the capitalists exactly as before; only the state would have replaced the private owner of landed property.

¹ At the very beginning, of course, we could equally well have set down the equation

and its derivatives in respect of t and n

and combined them with equations (23*) and (24), which latter is to be replaced by .

However, we have preferred to use as starting-point the production of one worker supported by the forces of nature.

¹ This elimination can be done quite easily for l, r and z (even without knowing the form of the function of p). h is then replaced simply by in equations (20), (21) and (22).

¹ Analogous to equations (21) and (22).

¹ The unknowns which were introduced last can, it is evident, be eliminated very easily. By this means we obtain between t₁, t₂, h₁, h₂, l and r and between the known magnitudes A, B and K one single relation, namely

which in conjunction with the first six equations, is sufficient for the determination of the still remaining unknowns t₁, t₂, h₁, h₂, l, r and z.

¹ When q₂ = F(t₂, h₂) expresses the number of pieces of linen produced (per year and worker), then p₂ = π . q₂ = π. F(t₂, h₂).

² It is in this case totally indifferent in what form he originally receives his income, whether in the form of corn or linen or both, since linen is always expressed, at the equilibrium price π, in terms of corn.

¹ It is clear that, if a really numerical treatment of the problems should ever be attempted, the consumers would have to be divided into larger groups, whose consumption of, or demand for, the various goods could be found out empirically at each level of prices.

¹ Namely t₁ . . . t_n, h₁ . . . h_n, A₁ . . . A_nB₁ . . . B_n, K₁ ... K_n, the l’s, r’s and z’s for all productions, and finally the n − 1 proportions of exchange—independent of each other—of the n goods. In the way indicated on p. 132, footnote 1, the 3n magnitudes A₁ . . . A_n, B₁ . . . B_n, K₁ . . . K_n can easily be eliminated, and in this way the number of the unknowns of the problem is reduced to 3n + 2.

² When in this case two or more goods can partly replace each other, the marginal utility of any one of them will, of course, not only be a function of the yearly consumed quantity of this commodity, but of all the goods in question.

¹ If workers from the different groups are employed in the same production, the equations in question become, of course, even more complicated, especially as the proportion of workers of different categories would often have to be ascertained according to the principle of the greatest possible profit (difference between male, female and young workers, etc.). Similarly with regard to different qualities of land and to rent-goods altogether.

² The replacement of completely worn out goods of this kind by new ones need not be excluded, of course, but can be regarded as repair of a greater complex of goods. According to the conception stated above, the difference between rent-goods and capital-goods consists in the fact that the sum of the former is independent of the length of the period of production of consumption goods.

¹ The production of new rent-goods, for instance, must then be treated in the same way as the production of consumable goods, in which case, however, the sum of the circulating capital no longer remains unchanged. Instead, the condition is added that the newly produced rent-goods must yield as rent the usual capital-interest on the costs of production.

² We could, of course—as L. Walras does—think of the yearly savings, and consequently the increase of capital, under otherwise unchanging circumstances, as a function of the level of interest, provided we keep in mind that a rise in the rate of interest can not only give cause for an increase in savings, but can also, in certain circumstances, have the contrary effect, and vice versa. But then the population must necessarily be assumed to be stationary or at least its yearly change must be assumed to be given; for obviously—to take an example—the number of children in a family is of much greater importance for the eventual formation or consumption of capital by that family, than the level of the rate of interest.

¹ In the second edition of his work, Walras, commenting on Böhm-Bawerk’s theories, raises the objection that capital-interest can only establish itself on the market and that he has tried in vain to find mention of this market in Böhm-Bawerk’s writings. Walras probably knows only the extract from Böhm-Bawerk’s book in the Revue d’économie politique which he mentions, because it is precisely this market which is presented in sketches in the last chapter of the Positive Theorie des Kapitals, although the services of the land are left unconsidered. I have tried, in what has been said above, to supply what was wanting here.

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¹ If we are to take into consideration compound interest instead of simple interest, it will be best to set out from equation (12). However (on the assumption of immediate interest) this equation then takes the form

which afterwards is combined with its first derivative in respect of t:

For sufficiently small values of z and values of t which are not too great, the first expression turns into

as when calculating simple interest.