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A. Costs to the Firm
We have seen the basis on which the prices of the factors of production and the interest rate are determined. Looked at from the point of view of an individual entrepreneur, payments to factors are money costs. It is clear that we cannot simply rest on the old classical law that prices of products tend, in the long run, to be equal to their costs of production. Costs are not fixed by some Invisible Hand, but are determined precisely by the total force of entrepreneurial demand for factors of production. Basically, as Böhm-Bawerk and the Austrians pointed out, costs conform to prices, and not vice versa. Confusion may arise because, looked at from the point of view of the individual firm rather than of the economist, it appears as if costs (at least in the sense of the prices of factors) are somehow given, and beyond one's control.28 If a firm can command a selling price that will more than cover its costs, it remains in business; if not, it will have to leave. The illusion of externally determined costs is prevalent because, as we shall presently see, most factors can be employed in a wide variety of firms, if not industries. If we take the broader view of the economist, however, the various “costs,” i.e., prices of factors, determined by their various DMVPs in alternative uses, are ultimately determined solely by consumers’ demand for all uses. It must not be forgotten, furthermore, that changes in demand and selling price will change the prices and incomes of specialized factors in the same direction. The “cost curves” so fashionable in current economics assume fixed factor prices, thereby ignoring their variability, even for the single firm.
It might be noted that, in this work, there is none of that plethora and tangle of “cost curves” which fill the horizon of almost every recent “neoclassical” work in economics.29 This omission has been deliberate, since it is our contention that the cost curves are at best redundant (thus violating the simplicity principle of Occam's Razor), and at worst misleading and erroneous.
As an explanation of the pricing of factors and the allocation of output it is obvious that cost curves add nothing new to discussion in terms of marginal productivity. At best, the two are reversible. This can be clearly seen in such texts as E.T. Weiler's The Economic System and George J. Stigler's Theory of Price.30 But, in addition, the shift brings with it many grave deficiencies and errors. This is revealed in the very passage in which Stigler explains the reasons for his switch from a perfunctory discussion of productivity to a lengthy treatment of cost curves:
The law of variable proportions has now been explored sufficiently to permit a transition to the cost curves of the individual firm. The fundamentally new element in the discussion will, of course, be the introduction of prices of the productive services. The transition is made here only for the case of competition—that is, the prices of the productive services are constant because the firm does not buy enough of any service to affect its price.31
But by introducing given prices of productive services, the contemporary theorist really abandons any attempt to explain these prices. This is one of the cardinal errors of the currently fashionable theory of the firm. It is highly superficial. One of the aspects of this superficiality is the assumption that prices of productive services are given, without any attempt to explain them. To furnish an explanation, marginal productivity analysis is necessary.
Marginal productivity analysis and the profit motive are sufficient to explain the prices of productive factors and their allocation to various firms and industries in the economy. Furthermore, there are in production theory two important and interesting concepts involving periods of time. One is what we may call the “immediate run”—the market prices of commodities and factors on the basis of given stocks and speculative demands and given consumer valuations. The immediate run is important, since it provides an explanation of the actual market prices of all goods at any time. The other important concept is that of the “final price,” or the long-run equilibrium price, i.e., the price that would be established in the ERE. This is important because it reveals the direction in which the immediate-run market prices tend to move. It also permits the analytic isolation of interest, as compared to profit and loss, in entrepreneurial incomes. In the ERE all factors will receive their discounted marginal value product, and interest will be pure time preference; there will be no profit and loss.
The interesting phases, then, are the immediate run and the long run. Yet cost-curve analysis deals almost exclusively with a hybrid intermediate phase known as the “short run.” In this short run, “costs” are sharply divided into two categories: fixed (which must be incurred regardless of the amount produced) and variable (which vary with output). This whole construction is a highly artificial one. There is no actual “fixity” of costs. Any alleged fixity depends purely on the length of time involved. In fact, suppose that production is zero. The “cost-curve theorists” would have us believe that even at zero output there are fixed costs that must be incurred: rent of land, payment of management, etc. However, it is clear that if data are frozen—as they should be in such an analysis—and the entrepreneurs expect a situation of zero output to continue indefinitely, these “fixed” costs would become “variable” and disappear very quickly. The rent contract for land would be terminated, and management fired, as the firm closed its doors.
There are no “fixed” costs; rather there are different degrees of variability for different productive factors. Some factors are best used in a certain quantity over a certain range of output, while others yield best results over other ranges of output. The result is not a dichotomy into “fixed” and “variable” costs, but a condition of many degrees of variability for the various factors.32
Even if none of these difficulties existed, it is hard to see why the “short run” should be picked out for detailed analysis, when it is merely one way station, or rather a series of way stations, between the important periods of time: the immediate run and the long run. Analytically, the cost-curve approach is at best of little interest.33
With these caveats, let us now turn to an analysis of the costs of the firm. Let us consider what will happen to costs at alternate hypothetical levels of output. There are two elements that determine the behavior of average costs, i.e., total costs per unit output.
(a) There are “physical costs”—the amounts of factors that must be purchased in order to obtain a certain physical quantity of output. These are the obverse of “physical productivity”— the amounts of the physical product that can be produced with various amounts of factors. This is a technological problem. Here the question is not marginal productivity, where one factor is varied while others remain constant in quantity. Here we concentrate on the scale of output when all factors are permitted to vary. Where all factors and the product are completely divisible, a proportionate increase in the quantities of all the factors must lead to an equally proportionate increase in physical output.34 This may be called the law of “constant returns to scale.”
(b) The second determinant of average costs is factor prices. “Pure competition” theorists assume that these prices remain unchanged with a changing scale of output, but this is impossible.35 As any firm's scale of output increases, it necessarily bids factors of production away from other firms, raising their prices in the process. And this is particularly true for labor and land factors, which cannot be increased in supply via new production. The increase in factor prices as output increases, combined with constant physical costs, raises the average money cost per unit output. We may therefore conclude that if factors and product were perfectly divisible, average cost would always be increasing.
In the productive world, perfect divisibility does not always, or even usually, obtain. Units of factors and of output are indivisible, i.e., they are not purely divisible into very small units. First, the product may be indivisible. Thus, suppose that three units of factor A + 2 units of factor B may combine to produce one refrigerator. Now it may be true that 6A + 4B will produce two refrigerators, according to our law of returns to scale. But it is also true that 4A + 3B will not produce one-and-a-fraction refrigerators. There are bound to be gaps where an increased supply of factors will not lead to an increased product, because of the technological indivisibility of the unit product.
In the areas of the gaps, average costs increase rapidly, since new factors are being hired with no product forthcoming; then, when expenditures on factors are increased sufficiently to produce more of the product, there is a precipitate decline in average cost compared to the situation during the gap. As a result, no businessman will knowingly invest in the area of the gaps. To invest more without yielding a product is sheer waste, and so businessmen will invest only in the trough points outside the gap areas.36
Secondly, and more important, the productive factors may be indivisible. Because of this indivisibility, it is not possible simply to double or halve the quantities of input of every one of the productive services simultaneously. Each factor has its own technological unit size. As a result, almost all business decisions take place in zones in which many factors have to remain constant while others (the more divisible ones) may vary. And these relative divisibilities and indivisibilities are due, not to variations in periods of time, but to the technological size of the various units. In any productive operation there will be many varieties of indivisibility.
Professor Stigler presents the example of a railroad track, a factor capable of handling up to 200 trains a day.37 The track is most efficiently utilized when train runs total precisely 200 a day. This is the technologically “ideal” output and may be the one for which the track was designed. Now what happens when output is below 200? Suppose output is only 100 per day. The divisible factors of production will then be cut in half by the owners of the railroad. Thus, if engineers are divisible, the railroad will hire half as many engineers or hire its engineers for half their usual number of hours. But (and this is the critical point here) the railroad cannot cut the track in half and operate on half a track. The technological unit of “track” being what it is, the number of tracks has to remain at one. Conversely, when output increases to 200 again, other productive services may be doubled, but the quantity of track remains the same.38
What happens should output increase to 250 trains a day—a 25-percent increase over the planned quantity? Divisible services such as engineers may be increased by one-fourth; but the track must either remain at one—and be overutilized—or be increased to two. If it is increased, the tracks will again be underutilized at 250, because the “ideal” output from the point of view of utilizing the tracks is now 400.
When an important indivisible factor is becoming less and less underutilized, the tendency will be for “increasing returns,” for decreasing average costs as output increases. When an important indivisible factor is becoming more and more overutilized, there is a tendency for increasing average costs.
In some spheres of production, indivisibilities may be such that full utilization of one indivisible factor requires full utilization of all.39 In that case, all the indivisible factors move together and can be lumped together for our purposes; they become the equivalent of one indivisible factor, such as the railroad track. In such cases again, average costs will first decline with an increase in output, as the increased output remedies an underutilization of the lumped indivisible factors. After the technologically most efficient point is reached, however, costs will increase, given the indivisible factors. The tendency for costs to decline will, in addition, be offset by the rise in factor prices caused by the increase in output.
In the overwhelming majority of cases, however, each factor will differ from the others in size and degree of divisibility. As a consequence, any size or combination chosen might utilize one indivisible factor most efficiently, but at the expense of not utilizing some other indivisible factor at peak efficiency. Suppose we consider a hypothetical schedule of average money cost at each alternative output. When we start at a very low level of output, all the indivisible factors will be underutilized. Then, as we expand production, average costs will decrease unless offset by the price rise for those divisible factors needed to expand production. As soon as one of the indivisible factors is fully utilized and becomes overworked, average costs will rise sharply. Later, a tendency toward decreasing costs sets in again as another underutilized factor becomes more fully utilized. The result is an alternating series of decreases and increases in average costs as output increases. Eventually, a point will be reached at which more indivisible factors will be overutilized than underutilized, and from then on the general trend of average cost as output increases will be upward. Before that point, the trend will be downward.
Mingling with these influences from the technological side of costs are the continuing rises in factor prices, which also become more important as output increases.
In sum, as Mises states:
Other things being equal, the more the production of a certain article increases, the more factors of production must be withdrawn from other employments in which they would have been used for the production of other articles. Hence—other things being equal—average production costs increase with the increase in the quantity produced. But this general law is by sections superseded by the phenomenon that not all factors of production are perfectly divisible and that, as far as they can be divided, they are not divisible in such a way that full utilization of one of them results in full utilization of the other imperfectly divisible factors.40
Some indivisible factors, such as the railroad track, can be available in only one particular size. Other indivisible factors, such as machinery, can be built in various sizes. Cannot a small factory, then, use small-scale machinery which will be just as efficient as large-scale machinery in a larger factory, and would this not eliminate indivisibilities and result in constant costs? No, for here too, one particular size will probably be most efficient. Below the most efficient size, operating the machine will be more costly. Thus, as Stigler says, “fitting together of the parts of a ten-horsepower motor does not require ten times the labor necessary to fit those of a one-horsepower motor. Similarly, a truck requires one driver, whether it has a half-ton or two-ton capacity.”41
It is also true that an oversized machine will be more costly than the optimum. But this will be no limitation on the size of the firm, for a large firm can simply use several (smaller) optimum-sized machines instead of one huge machine.
Labor is usually treated as a perfectly divisible factor, as one that varies directly with the size of the output. But this is not true. As we have seen, the truck driver is not divisible into fractions. Further, management tends to be an indivisible production factor. So also salesmen, advertising, cost of borrowing, research expenditures, and even insurance for actuarial risk. There are certain basic costs in borrowing which simply arise from investigating, paperwork, etc. These will tend to be proportionately smaller the larger the size—another indivisibility, with returns increasing over a certain area. Also, the broader the coverage, the lower insurance premiums will be.42
Then there are the well-known gains from the increase in the division of labor with larger outputs. The benefits from the division of labor may be considered indivisible. They arise from the specialized machines that must first be used with a larger product, and similarly from the increased labor skills of specialists. Here too, however, there is a point beyond which no further specialization is possible or where specialization is subject to increasing costs. Management has usually been stressed as particularly subject to overutilization. Even more important is the factor of ultimate-decision-making ability, which cannot be enlarged to the extent that management can.
What any given firm's size and output will be is therefore subject to a host of conflicting determinants, some impelling a limitation, some an expansion, of size. At what point any firm will settle depends on the concrete data of the actual case and cannot be decided by economic analysis. Only the actual entrepreneur, through the give and take of the market, can decide where the maximum-profit size is and can set the firm at that point. This is the task of the businessman and not of the economist.43
Furthermore, the cost-curve diagrams, so simple and smooth in the textbooks, misinterpret real conditions. We have seen that there are a whole host of determinants which tend at any point toward increasing and toward decreasing costs. It is, of course, true that an entrepreneur will seek to produce at the point of maximum profit, i.e., of maximum net returns over costs. But the factors that influence his decision are too numerous and their interactions too complex to be captured in cost-curve diagrams.
It is clear to almost everyone that the optimum size of a firm in some industries is larger than in others. The economic optimum for a steel plant is larger than the optimum barbershop. In industries where large-scale firms have demonstrated the most efficiency, however, many people have worried a great deal about an alleged tendency for decreasing costs to continue permanently and therefore for “monopoly” to result from ever-larger firms. It should be obvious, however, that there is no infinite tendency for ever-larger size; this is clear from the very fact that every firm, at any time, always has a finite size and that, therefore, an economic limit must have been imposed upon it from some direction. Furthermore, we have seen that the general rule of operating in a zone of diminishing marginal productivity for each factor, as well as the tendency for product prices to decline and factor prices to increase as output increases, establishes limits on the size of each firm. And, as a neglected point, we shall see that ultimate limits are set on the relative size of the firm by the necessity for markets to exist in every factor, in order to make it possible for the firm to calculate its profits and losses.44
Money costs will equal opportunity costs to the businessman only when he plans an investment in factors. To the extent that his money costs are “sunk” in any production process, they are committed irrevocably, and any future plans must consider them as irretrievably spent.45 The businessman's market-supply curve will depend on his present opportunity cost, not his past money cost. For the businessman sells his goods at any price that will more than cover any further costs that must be incurred in selling them. As capital goods move toward final output in any stage of the production structure, more and more investment has been sunk into the process. Therefore, the marginal cost of further production (roughly the opportunity cost) becomes ever lower as the product moves toward final output and sale. This is the simple meaning of the usual cost-curve morass. When, for example, some costs are not “fixed,” but irrevocable from the point of view of further short-run production, they are not included in the businessman's estimated costs of such further production. As we have seen above, the sale of immediate stock completely ready for sale is virtually “costless,” since there are no further costs for its production—in the immediate run.46 In the ERE, of course, all costs and investments will be adjusted, and irrevocably incurred costs will present no problem. In the ERE average money costs for all firms will equal the price of the product minus pure interest return to the capitalist-entrepreneurs, and also, as we shall see, minus the return to the “discounted marginal productivity of the owner,” a factor which does not enter into the firm's money costs.47,48
- 28. Hence, when the economist considers only the single firm (as in recent years), he goes completely astray by ignoring the generality of economic interrelations. To analyze means-ends relations logically, as economics does, requires taking all relations into account. Failure to do so, either by treating the single firm only or by treating unreal holistic aggregates or by taking refuge in the irrelevant mathematics of the Lausanne “general equilibrium” school, is equivalent to abandoning economics.
- 29. Many beginning students come away with the impression that economics consists of an indigestible brew of “cost curves” to be memorized by rote and drawn neatly on the blackboard.
- 30. E.T. Weiler, The Economic System (New York: Macmillan & Co., 1952), pp. 141–61; Stigler, Theory of Price, pp. 126ff.
- 31. Stigler, Theory of Price, p. 126.
- 32. Robbins points out that the length of a period of productive activity depends upon the expectations of entrepreneurs concerning the permanence of a change and the technical obstacles to a change. Robbins, “Remarks upon Certain Aspects of the Theory of Costs,” pp. 17–18.
- 33. For a critique of cost-curve theory, see the articles by Robbins, Thirlby, and Gabor and Pearce cited above, especially Gabor and Pearce, “A New Approach to the Theory of the Firm.” Also see Milton Friedman, “Survey of the Empirical Evidence on Economies of Scale: Comment” in Business Concentration and Price Policy (Princeton, N.J.: National Bureau of Economic Research, 1955), pp. 230–38; Armen Alchian, “Costs and Outputs” in The Allocation of Economic Resources (Stanford: Stanford University Press, 1959), pp. 23–40; F.A. Hayek, “Unions, Inflation, and Prices” in Philip D. Bradley, ed., The Public Stake in Union Power (Charlottesville: University of Virginia Press, 1959), pp. 55 f.; Hayek, Pure Theory of Capital, pp. 14, 20–21; Harrod, “Theory of Imperfect Competition Revised” in Economic Essays, pp. 139–87; G. Warren Nutter, “Competition: Direct and Devious,” American Economic Review, Papers and Proceedings, May, 1954, pp. 69ff.; Scott, Natural Resources: The Economics of Conservation, p. 5.
- 34. This law follows from the natural law that every quantitatively observable cause-effect relation can be duplicated. For example, if x + 2y + 3em>z are necessary and sufficient to form 1p, another set will form another p, so that 2x + 4y + 6z will yield 2p.
- 35. See chapter 10 for more on the theory of pure competition.
- 36. For example, suppose that 1,000 gold ounces invested in factors yield 100 units of product and that 1,100 ounces yield 101 units. All the points in the gap between 1,000 and 1,100 will yield no more than 100 units. The excess of investment over 1,000 and under 1,100 ounces is clearly sheer waste, and no businessman will invest within the gap. Instead, investments will be made at such trough points for average cost as 1,000 and 1,100.
- 37. Stigler, Theory of Price, pp. 132ff.
- 38. We are not discussing the fact that the railroad could, of course, cut down or increase the mileage of its track by including less or more geographic area in its service. The example assumes a given geographic area in which the railroad operates.
- 40. Ibid., p. 340.
- 41. Stigler, Theory of Price, p. 136.
- 42. It is particularly important not to limit possible efficiencies from large-scale production to narrow technological factors such as the “size of the plant.” There are also efficiencies derived from the organization of a firm owning several plants—e.g., management utilization, specialization, efficiency of large-scale purchasing and selling, research expenditures, etc. Cf. George G. Hagedorn, Studies on Concentration (New York: National Association of Manufacturers, 1951), pp. 14 ff.
- 43. See Friedman, “Survey of the Empirical Evidence on Economies of Scale: Comment,” pp. 230–38.
- 44. For a good, largely empirical, study of size of firm, see George G. Hagedorn, Business Size and the Public Interest (New York: National Association of Manufacturers, 1949). Also see idem, Studies on Concentration, and John G. McLean and Robert W. Haigh, “How Business Corporations Grow,” Harvard Business Review, November–December, 1954, pp. 81–93.
- 45. Plans are relevant, not only in the ERE, but also to all decisions on maintenance or replacement, as well as additions to capital goods when they wear out or fall into disrepair.
- 46. It is costless only if no rise in the price of the good is foreseen for the near future. If it is, then there will arise the opportunity cost of forgoing a higher price. Hence, if there is no hope of a higher price, the businessman will sell, however low the price (adjusting for the costs of selling minus the costs of continued storage).
- 47. Conventional “cost-curve” analysis depicts average cost and demand curves as tangential in the ERE—i.e., that price = average cost. But (aside from the unreality of assuming smooth curves rather than discontinuous angles), interest return—as well as return to the owner's decision-making ability—will accrue to the entrepreneurs even in the ERE. Hence, no such tangency can arise. See chapter 10 below for the implications of this revision for “monopolistic competition” theory.
- 48. For further readings on cost, see G.F. Thirlby, “The Marginal Cost Controversy: A Note on Mr. Coase's Model,” Economica, February, 1947, pp. 48–53; F.A. Fetter's classic “The Passing of the Old Rent Concept,” p. 439; R.H. Coase, “Business Organization and the Accountant,” The Accountant, October l–November 26, 1938; and idem, “Full Costs, Cost Changes, and Prices” in Business Concentration and Price Policy, pp. 392–94; John E. Hodges, “Some Economic Implications of Cost-Plus Pricing,” Southwestern Social Science Quarterly, December, 1954, pp. 225–34; I.F. Pearce, “A Study in Price Policy,” Economica, May, 1956, pp. 114–27; I.F. Pearce and Lloyd R. Amey, “Price Policy with a Branded Product,” Review of Economic Studies, Vol. XXIV (1956–57), No. 1, pp. 49–60; James S. Earley, “Recent Developments in Cost Accounting and the ‘Marginal Analysis’ ,” Journal of Political Economy, June, 1955, pp. 227–42; and David Green, Jr., “A Moral to the Direct-Costing Controversy,” Journal of Business, July, 1960, pp. 218–26.