Chapter 9 — Production: Particular Factor Prices and Productive Incomes
3. Entrepreneurship and Income
D. MARKET CALCULATION AND IMPLICIT EARNINGS
We have seen that a musician or a doctor earns wages without being an employee; the wages of each are implicit in the income that he receives, even though they are received directly from the consumers.
In the real world, each function is not necessarily performed by a different person. The same person can be a landowner and a worker. Similarly, a particular firm, or rather its owner or owners, may own land and participate in the production of capital goods. The owner may also manage his own firm. In practice, the different sources of income can be separated only by referring to these incomes as determined by prices on the market. For example, suppose that a man owns a firm which invests its capital, owns its own ground land, and produces a capital good, and that he manages the plant himself. He receives a net income over a year’s period of 1,000 gold ounces. How can he estimate the different sources of his income? Suppose that he had invested 5,000 gold ounces in the business. He looks around at the economy and finds that what he can pretty well call the ruling rate of interest, toward which the economy is tending, is 5 percent. He then concludes that 250 gold ounces of his net income was implicit interest. Next, he estimates approximately what he would have received in wages of management if he had gone to work for a competing firm rather than engaging in this business. Suppose he estimates that this would have been 500 gold ounces. He then looks to his ground land. What could he have received for the land if he had rented it out instead of using it himself in the business? Let us say that he could have received 400 ounces in rental income for the land.
Now, our owner received a net money income, as landowner-capitalist-laborer-entrepreneur, of 1,000 gold ounces for the year. He then estimates what his costs were, in money terms. These costs are not his explicit money expenses, which have already been deducted to find his net income, but his implicit expenses, i.e., his opportunities forgone by engaging in the business. Adding up these costs, he finds that they total:
250 gold ounces | interest
500 gold ounces | wages
400 gold ounces | rent
= 1150 gold ounces | = total opportunity costs
Thus, the entrepreneur suffered a loss of 150 ounces over the period. If his opportunity costs had been less than 1,000, he would have gained an entrepreneurial profit. It is true that such estimates are not precise. The estimates of what he would have received can never be wholly accurate. But this tool of ex post calculation is an indispensable one. It is the only way by which a man can guide his ex ante decisions, his future actions. By means of this calculation, he may realize that he is suffering a loss in this business. If the loss continues much longer, he will be impelled to shift his various resources to other lines of production. It is only by means of such estimates that an owner of more than one type of factor in the firm can determine his gains or losses in any situation and then allocate his resources to strive for the greatest gains.
A very important aspect of such estimates of implicit incomes has been overlooked: there can be no implicit estimates without an explicit market! When an entrepreneur receives income, in other words, he receives a complex of various functional incomes. To isolate them by calculation, there must be in existence an external market to which the entrepreneur can refer. This is an extremely important point, for, as we shall soon see in detail, this furnishes a most important limitation on the relative potential size of a single firm on the market.
For example, suppose we return for a moment to our old hypothetical example in which each firm is owned jointly by all its factor-owners. In that case, there is no separation at all between workers, landowners, capitalists, and entrepreneurs. There would be no way, then, of separating the wage incomes received from the interest or rent incomes or profits received. And now we finally arrive at the reason why the economy cannot consist completely of such firms (called “producers’ cooperatives”). 
. Another reason why an economy of producers’ co-operatives could not calculate is that every original factor would be tied indissolubly to a specific line of production. There can be no calculation where all factors are purely specific.
For, without an external market for wage rates, rents, and interest, there would be no rational way for entrepreneurs to allocate factors in accordance with the wishes of the consumers. No one would know where he could allocate his land or his labor to provide the maximum monetary gains. No entrepreneur would know how to arrange factors in their most value-productive combinations to earn the greatest profit. There could be no efficiency in production because the requisite knowledge would be lacking. The productive system would be in complete chaos, and everyone, whether in his capacity as consumer or as producer, would be injured thereby. It is clear that a world of producers’ co-operatives would break down for any economy but the most primitive, because it could not calculate and therefore could not arrange productive factors to meet the desires of the consumers and hence earn the highest incomes for the producers.
E. VERTICAL INTEGRATION AND THE SIZE OF THE FIRM
In the free economy, there is an explicit time market, labor market, and land-rent market. It is clear that while chaos would ensue from a world of producers’ co-operatives, other critical points even before that would, as it were, introduce little bits of chaos into the productive system. Thus, suppose that workers are separated from capitalists, but that all capitalists own their own ground land. Further, suppose, that for one reason or another, no capitalist will be able to rent out his land to some other firm. In that case, land and a particular capital and production process are indissolubly wedded to each other. There would be no rational way to allocate land in production, since it would have no explicit price anywhere. Since producers would suffer heavy losses, the free market would never establish such a situation. For the free market always tends to conduct affairs so that entrepreneurs make the greatest profit through serving the consumer best and most efficiently. Since absence of calculation creates grave inefficiencies in the system, it also causes heavy losses. Such a situation (absence of calculation) would therefore never be established on a free market, particularly after an advanced economy has already developed calculation and a market.
If this is true for such cases as a world of producers’ co-operatives and the absence of a rent market, it also holds true, on a smaller scale, for “vertical integration” and the size of a firm. Vertical integration occurs when a firm produces not only at one stage of production, but over two or more stages. For example, a firm becomes so large that it buys labor, land, and capital goods of the fifth order, then works on these capital goods, producing other capital goods of the fourth order. In another plant, it then works on the fourth-order capital goods until they become third-order capital goods. It then sells the third-order product.
Vertical integration, of course, lengthens the production period for any firm, i.e., it lengthens the time before the firm can recoup its investment in the production process. The interest return then covers the time for two or more stages rather than one. 
. Vertical integration, we might note, tends to reduce the demand for money (to “turn over” at various stages) and thereby to lower the purchasing power of the monetary unit. For the effect of vertical integration on the analysis of investment and the production structure, see Hayek, Prices and Production, pp. 62–68.
There is a more important question involved, however. This is the role of implicit earnings and calculation in a vertically integrated firm. Let us take the case of the integrated firm mentioned in Figure 65.
Figure 65 depicts a vertically integrated firm; the arrows represent the movement of goods and services (not of money). The firm buys labor and land factors at both the fifth and the fourth stages; it also makes the fourth-stage capital goods itself and uses them in another plant to make a lower-stage good. This movement internal to the firm is expressed by the dotted arrow.
Does such a firm employ calculation within itself, and if so, how? Yes. The firm assumes that it sells itself the fourth-rank capital good. It separates its net income as a producer of fourth-rank capital from its role as producer of third-rank capital. It calculates the net income for each separate division of its enterprise and allocates resources according to the profit or loss made in each division. It is able to make such an internal calculation only because it can refer to an existing explicit market price for the fourth-stage capital good. In other words, a firm can accurately estimate the profit or loss it makes in a stage of its enterprise only by finding out the implicit price of its internal product, and it can do this only if an external market price for that product is established elsewhere.
To illustrate, suppose that a firm is vertically integrated over two stages, with each stage covering one year’s time. The general rate of interest in the economy tends towards 5 percent (per annum). This particular firm, say, the Jones Manufacturing Company, buys and sells its factors as shown in Figure 66.
This vertically integrated firm buys factors at the fifth rank for 100 ounces and original factors at the fourth rank for 15 ounces; it sells the final product at 140 ounces. It seems that it has made a handsome entrepreneurial profit on its operations, but can it find out which stage or stages is making this profitable showing? If there is an external market for the product of the stage that the firm has vertically integrated (stage 4), the Jones Company is able to calculate the profitability of specific stages of its operations. Suppose, for example, that the price of the fourth-order capital good on the external market is 103 ounces. The Jones Company then estimates its implicit price for this intermediate product at what it would have brought on the market if it had been sold there. This price will be about 103 ounces. 
. The implicit price, or opportunity cost of selling to oneself, might be less than the existing market price, since the entry of the Jones Company on the market might have lowered the price of the good, say to 102 ounces. There would be no way at all, however, to estimate the implicit price if there were no external market and external price.
Assuming that the price is estimated at 103, then the total amount of money spent by Jones’ lower-order plant on factors is 15 (explicit, on original factors) plus 103 (implicit, on capital goods) for a total of 118.
Now the Jones Company can calculate the profits or losses made at each stage of its operations. The “higher” stage bought factors for 100 ounces and “sold” them at 103 ounces. It made a 3-percent return on its investment. The lower stage bought its factors for 118 ounces and sold the product for 140 ounces, making a 29-percent return. It is obvious that, instead of enjoying a general profitability, the Jones Company suffered a 2-percent entrepreneurial loss on its earlier stage and gained a 24-percent profit on its later stage. Knowing this, it will shift resources from the higher to the lower stage in accordance with their respective profitabilities — and therefore in accordance with the desires of consumers. Perhaps it will abandon its higher stage altogether, buying the capital good from an external firm and concentrating its resources in the more profitable lower stage.
On the other hand, suppose that there is no external market, i.e., that the Jones Company is the only producer of the intermediate good. In that case, it would have no way of knowing which stage was being conducted profitably and which not. It would therefore have no way of knowing how to allocate factors to the various stages. There would be no way for it to estimate any implicit price or opportunity cost for the capital good at that particular stage. Any estimate would be completely arbitrary and have no meaningful relation to economic conditions.
In short, if there were no market for a product, and all of its exchanges were internal, there would be no way for a firm or for anyone else to determine a price for the good. A firm can estimate an implicit price when an external market exists; but when a market is absent, the good can have no price, whether implicit or explicit. Any figure could be only an arbitrary symbol. Not being able to calculate a price, the firm could not rationally allocate factors and resources from one stage to another.
Since the free market always tends to establish the most efficient and profitable type of production (whether for type of good, method of production, allocation of factors, or size of firm), we must conclude that complete vertical integration for a capital-good product can never be established on the free market (above the primitive level). For every capital good, there must be a definite market in which firms buy and sell that good. It is obvious that this economic law sets a definite maximum to the relative size of any particular firm on the free market. 
. On the size of a firm, see the challenging article by R.H. Coase, “The Nature of the Firm” in George J. Stigler and Kenneth E. Boulding, eds., Readings in Price Theory (Chicago: Richard D. Irwin, 1952), pp. 331–51. In an illuminating passage Coase pointed out that State “planning is imposed on industry, while firms arise voluntarily because they represent a more efficient method of organizing production. In a competitive system there is an ‘optimum’ amount of planning.” Ibid., p. 335 n.
Because of this law, firms cannot merge or cartelize for complete vertical integration of stages or products. Because of this law, there can never be One Big Cartel over the whole economy or mergers until One Big Firm owns all the productive assets in the economy. The force of this law multiplies as the area of the economy increases and as islands of noncalculable chaos swell to the proportions of masses and continents. As the area of incalculability increases, the degrees of irrationality, misallocation, loss, impoverishment, etc., become greater. Under one owner or one cartel for the whole productive system, there would be no possible areas of calculation at all, and therefore complete economic chaos would prevail. 
. Capital goods are stressed here because they are the product for which the calculability problem becomes important. Consumers’ goods per se are no problem, since there are always many consumers buying goods, and therefore consumers’ goods will always have a market.
Economic calculation becomes ever more important as the market economy develops and progresses, as the stages and the complexities of type and variety of capital goods increase. Ever more important for the maintenance of an advanced economy, then, is the preservation of markets for all the capital and other producers’ goods. Our analysis serves to expand the famous discussion of the possibility of economic calculation under socialism, launched by Professor Ludwig von Mises over 40 years ago.
Mises, who has had the last as well as the first word in this debate, has demonstrated irrefutably that a socialist economic system cannot calculate, since it lacks a market, and hence lacks prices for producers’ and especially for capital goods. 
. It is remarkable that so many antisocialist writers have never become aware of this critical point.
Now we see that, paradoxically, the reason why a socialist economy cannot calculate is not specifically because it is socialist! Socialism is that system in which the State forcibly seizes control of all the means of production in the economy. The reason for the impossibility of calculation under socialism is that one agent owns or directs the use of all the resources in the economy. It should be clear that it does not make any difference whether that one agent is the State or one private individual or private cartel. Whichever occurs, there is no possibility of calculation anywhere in the production structure, since production processes would be only internal and without markets. There could be no calculation, and therefore complete economic irrationality and chaos would prevail, whether the single owner is the State or private persons.
The difference between the State and the private case is that our economic law debars people from ever establishing such a system in a free-market society. Far lesser evils prevent entrepreneurs from establishing even islands of incalculability, let alone infinitely compounding such errors by eliminating calculability altogether. But the State does not and cannot follow such guides of profit and loss; its officials are not held back by fear of losses from setting up all-embracing cartels for one or more vertically integrated products. The State is free to embark upon socialism without considering such matters. While there is therefore no possibility of a one-firm economy or even a one-firm vertically integrated product, there is much danger in an attempt at socialism by the State. A further discussion of the State and State intervention will be found in chapter 12 of this book.
A curious legend has become quite popular among the writers on the socialist side of the debate over economic calculation. This runs as follows: Mises, in his original article, asserted “theoretically” that there could be no economic calculation under socialism; Barone proved mathematically that this is false and that calculation is possible; Hayek and Robbins conceded the validity of this proof but then asserted that calculation would not be “practical.” The inference is that the argument of Mises has been disposed of and that all socialism needs is a few practical devices (perhaps calculating machines) or economic advisers to permit calculation and the “counting of the equations.”
This legend is almost completely wrong from start to finish. In the first place, the dichotomy between “theoretical” and “practical” is a false one. In economics, all arguments are theoretical. And, since economics discusses the real world, these theoretical arguments are by their nature “practical” ones as well.
The false dichotomy disposed of, the true nature of the Barone “proof” becomes apparent. It is not so much “theoretical” as irrelevant. The proof-by-listing-of-mathematical-equations is no proof at all. It applies, at best, only to the evenly rotating economy. Obviously, our whole discussion of the calculation problem applies to the real world and to it only. There can be no calculation problem in the ERE because no calculation there is necessary. Obviously, there is no need to calculate profits and losses when all future data are known from the beginning and where there are no profits and losses. In the ERE, the best allocation of resources proceeds automatically. For Barone to demonstrate that the calculation difficulty does not exist in the ERE is not a solution; it is simply a mathematical belaboring of the obvious.  The difficulty of calculation applies to the real world only. 
. Far from being refuted, Mises had already disposed of this argument in his original article. See Hayek, Collectivist Economic Planning, p. 109. Further, Barone’s article was written in 1908, 12 years before Mises’. A careful perusal of Mises’ original article, in fact, reveals that he there disposed of almost all the alleged “solutions” which decades later were brought forth as “new” attempts to refute his argument.
. Part of the confusion stems from an unfortunate position taken by two followers of Mises in this debate — Hayek and Robbins. They argued that a socialist government could not calculate because it simply could not compute the millions of equations that would be necessary. This left them open to the obvious retort that now, with high-speed computers available to the government, this practical objection is no longer relevant. In reality, the job of rational calculation has nothing to do with computing equations. Nobody has to worry about “equations” in real life except mathematical economists. Cf. Lionel Robbins, The Great Depression (New York: Macmillan & Co., 1934), p. 151, and Hayek in Collectivist Economic Planning, pp. 212f.
Chapter 10 — Monopoly and Competition
2. Cartels and Their Consequences
F. THE PROBLEM OF ONE BIG CARTEL
The answer can be obtained by referring to chapter 9, pp. 612ff above, where we saw that the free market placed definite limits on the size of the firm, i.e., the limits of calculability on the market. In order to calculate the profits and losses of each branch, a firm must be able to refer its internal operations to external markets for each of the various factors and intermediate products. When any of these external markets disappears, because all are absorbed within the province of a single firm, calculability disappears, and there is no way for the firm rationally to allocate factors to that specific area. The more these limits are encroached upon, the greater and greater will be the sphere of irrationality, and the more difficult it will be to avoid losses. One big cartel would not be able rationally to allocate producers’ goods at all and hence could not avoid severe losses. Consequently, it could never really be established, and, if tried, would quickly break asunder. […]
What about the factors? Could not their owners be exploited by the cartel? In the first place, the universal cartel, to be effective, would have to include owners of primary land; otherwise whatever gains they might have might be imputed to land. To put it in its strongest terms, then, could a universal cartel of all land and capital goods “exploit” laborers by systematically paying the latter less than their discounted marginal value products? Could not the members of the cartel agree to pay a very low sum to these workers? If that happened, however, there would be created great opportunities for entrepreneurs either to spring up outside the cartel or to break away from the cartel and profit by hiring workers for a higher wage. This competition would have the double effect of (a) breaking up the universal cartel and (b) tending again to yield to the laborers their marginal product. As long as competition is free, unhampered by governmental restrictions, no universal cartel could either exploit labor or remain universal for any length of time.
Further reading :
Critiques of Natural Monopoly Theory