《Innovation, Diversity and Diffusion：A Self-Organisation Model》relation of profit rate to industry concentration-American manufacturing, 1936-1940

I. The concentration-profits hypothesis, 294.-II. Industry definition neasure of concentration, and selection of sample, 297.--III. Character and tions of profit data, 305 -IV. Calculation of accounting profit rates, 310 -V. Association of industry profit rates and concentration, 311.-VI. Asso-

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THE QUARTERLY JOURNAL OF ECONOMICS Vol LXV August, 1951 No. 3 RELATION OF PROFIT RATE O INDUSTRY CONCENTRATION AMERICAN MANUFACTURING. 1936-1940 By JOE S.BAIN I. The concentration-profits hypothesis, 294.-II. Industry definition neasure of concentration, and selection of sample, 297.--III. Character and tions of profit data, 305 -IV. Calculation of accounting profit rates, 310 -V. Association of industry profit rates and concentration, 311.-VI. Asso- tion of firm profit rates and industry concentration, 317 -VII. associatie of profit rates with other determinants, 321 vil, Summary, 323 Students of industrial price behavior have recently shown much interest in the concept of workable competition and in the potential association between the workability of competition and the structure of the industry. I Their evident uncertainty about the nature of such a relationship suggests the need for detailed empirical studies which would formulate specific hypotheses on the relations of market structure to market performance and would then test such hypotheses with available evidence. In another place, I have advanced some hypotheses concerning such relationships, emphasizing those of seller concentration, buyer concentration, condition of entry of product differentiation to profits, selling costs, and relative effi- ciency of scale and capacity. This paper reports on the results of a statistical study of one of the relationships in this complex, as found in American manufacturing industries from 1936 through 1940 namely that of the size of profits or profit rates to the degree of seller concentration within industries 3 The Current Status of the Monopoly Problem in the United States, Harvard Law Review, June 1949, pp. 1265-85; M.A.Adelman Effective Competition and the Anti-Trust Laws, "ibid. September 1948, pp. ay 3. I am indebted to the Bureau of Business and Economic Research, Uni- versity of California, Berkeley, for extensive assistance in this study throughout the academic year 1949-50, and to Mr Allan Muir, who undertook substantiall all the work of statistical compilation and calculation and who contributed measurably to the development of statistical analyses. 293

294 QUARTERLY JOURNAL OF ECONOMICS I. THE CO Statement of the hypothesis to be tested involves an initial distinction among industries according to the degree of seller con- centration, recognizing(1) highly concentrated oligopolies, where a very few firms control a high proportion of industry output,(2)less ontrolled by a given number of firms is smaller but where oligopo- listic interdependence must still be presumed to exist, and (3)indus- tries of atomistic structure. The hypothesis in brief is that the average profit rate of firms in oligopolistic industries of a high concentration will tend to be significantly larger than that of firms in less concentrated oligopolies or in industries of atomistic structure. Firms in oligopolie of high seller concentration will tend to earn higher profit rates than all others. s This hypothesis is essentially developed from conven- tional price theory, and the manner of its development may be briefly traced a single firm monopolist or a group of oligopolists operating with effective express or tacit collusion should approach a conventional maximization solution and realize in long-run equilibrium the maxi- mum excess profit aggregate which is permitted by the relation of the industry demand curve to the costs of production and selling and by the conditions of entry 7 Sellers in industries of atomistic structure, or oligopolists who cannot reach or maintain fully effective collusion will not tend to maximize this excess profit aggregate, and 4. Before examining the hypothesis to be tested, let us note that the size of the profit rate for a firm or industry should not be regarded as a sole or an fallible index of the workability of competition. Clearly it is one of sever dimensions of market performance which must be interpreted as a complex in evaluating the workability of competition. Low or normal profits are ordinarily associated with certain model types of competitive equilibrium, and profits chronically much in excess of some normal rate with undesirable restriction of output and adverse income distribution effects. But the existence of a low profit te may be associated with adverse results on other levels(such as chronic excess apacity)and any profit performance must be read in the light of the rate echnical progress, the trend of de unable here to discover any net relation of concentration to the workability competition; we seek simply the relation of concentration to the profit rate, whatever its ultimate significane 5. The major distinction, it may be emphasized, is not between industried olies and all other industrie 6. The term excess profit is used here throughout to refer to a return luding imputed interest costs on equity capital, and no 7. The conventional maximization solution must be construed to ither one where marginal cost equals industry marginal revenue(as where blockaded or alternatively cannot be advantageously forestalled)or one

RELATION OF PROFIT RATE TO INDUSTI 295 with(1) identical entry conditions and(2)an identical industry demand and cost situation, will tend to sell at a lower price and receive a smaller profit. 8 In short, if we hold demand and cos conditions and entry conditions constant, monopoly or effectively allusive oligopoly tends to yield higher profit aggregates and prices in long-run equilibrium than competition or imperfectly-or non- collusive oligopoly Retaining suppositions(1)and(2)above, monopoly or effectively collusive oligopoly will also bring forth a higher excess profit rate on sales. This will be true even where cost and demand conditions are not identical, so long as the opportunity for aggregate profit relative to aggregate sales is the same. The excess profit rate on sales(after deducting all costs, including all paid and imputed interest)should average higher in long-run equilibrium among industries with monop- oly or effectively collusive oligopoly than among others, so far as on the average the relation of industry demand to cost and the conditions of entry are about the same This association should actually hold even in long-run equilibrium only on the average and not in each case. Similarity of demand-cost relations should be found only on the average, as should any similarity of entry conditions. When we leave the static model, the same association should tend to hold on the average through time, but a considerable dispersion of individual profit rates for particular inter- vals could be caused by difference in trends and fluctuations of demand, in the rate of innovation, and so forth. Thus individual industries in the more"competitive' category may have as high as or higher profit rates than individuals in the"monopoly 'category but on the assumption that all other influences on the profit rate f'average-out'' within groups, the group averages over time of excess profit rates on sales should differ in the manner indicated. 9 Average excess profit rates on sales should thus be higher with han without monopoly or effective oligopolistic collusion. This prediction evolves into one that there will be larger profit rates with high seller concentration than with moderate or low seller concentra- tion if we posit a systemati ation between the probability of ORO G s enough lower to forestall entry and thus to maximize the long-run pre American Economic Review, March 1949, pp. 448-64 to or below the competitive level 9. This averaging-out'' should also presumably apply to any effects of any other differences in market structure which may have an independent influence on profit rates

QUARTERLY JOURNAL OF ECONOMICS ffective collusion and the degree of seller concentration within an industry A tentative hypothesis is herewith advanced to that effect. Given this, we arrive at the hypothesis that there will be a systematic difference in average excess profit rates on sales between highly concentrated oligopolies and other industries. This difference should be found, strictly, even if there are on the average identical entry conditions in So far itry tends to be mo difficult in highly concentrated industries, as seems probable, there is a second reason for larger profit rates with higher concentration As the hypothesis is developed to this point, the predicted profit rate differences are explicitly differences in ratios of excess profit to sales. Because data on profit rates on equity are more readily available, let us inquire whether the predicted relationship should also hold for the ratios of profit to equity. The rate of excess profit sales may be expressed (non-operating costs and revenues being sales revenue minus contractual costs minus imputed interest Readily available profit-rate data are largely in the form of rates of return on investment or on equity before deducting imputed interest The relevant equity rate is sales revenue minus contractual cost stockholders'equ This may also be stated as ales revenue minus contractual costs minus imputed interest lus interest rate stockholders'equity These are of course all average rather than marginal rates. between firms or groups of firms, should the same relation hold among 1. That is, in highly concentrated oligopolistic industries, there will on the average be found more effective express or tacit collusion, and in oligopolistic industries of lower concentration as in industries of relativ structure, there will be found on the average less effective or more imperfec ollusion, more profit destructive rivalry of either an open or secret sort, and tht Bain, "Workable Competition in Oligopoly, "loc. cit, pp. 43-44 g. Cf.J. s 2. It is postulated throughout at this point that there is a theo ent of all magnitudes which appear in these ratios; the cha of such measurement al he possible aberrations in accounting measure discussed 06-10 belo appropriate cost 1. At the same appropriate cost valuation used in calculating imputed nterest

RELATION OF PROFIT RATE TO INDUSTRY their rates of return on equity, either gross or net of the interest rate as between their sales rates? For comparisons of individual cases the answer is no, since the ratio of equity to sales will vary among cases. However, so far as there is on the average among groups of firms or industries being compared about the same ratio of equity o sales, their average equity rates should stand in about the same relation as their sales rates. Then, assuming the sales-equity ratio averages the same for industries of different concentration, the postu lated relation of industry concentration to profit rate should hold for rates of return on equity, net or gross of imputed interest, as ell as for sales rates. An additional source of profit-rate variation within groups has been introduced if equity rates are used, but the average relation should be roughly the same The validity of this assumption and of the derived conclusion has been tested by experimental calculations for groups of industries of the relationship of profit rate to concentration, using first the equity rate, second the rate of excess profits on sales, and third the rate of earning before all interest on total investment. There is no significant difference in the findings on group-average relationships by the three methods. The crucial ratios appear to be similar enough so that for statistical purposes the measures are effectively interchangeable hence, subsequent to the experiment, equity rates have been used in all calculations as the only measure of profit In the most convenient form for testing, therefore, the central hypothesis is that there will be higher average profit rates on equity in industries of high concentration than in less concentrated oligo- lies or in industries of atomistic structure. The hypothesis does not suggest the exact degree of concentration which will separate highly concentrated oligopolies from other industries; it is a purpose of this study to determine where such a line, if any, falls. Similarly, no finer distinction is tentatively drawn than between highly con- centrated and other industries, although evidences of associations which might justify finer distinctions must be sought and evaluated II. THE INDUSTRY DEFINITION, THE MEASURE OF CONCENTRATION, AND THE SELECTION OF AN INDUSTRY SAMPLE Given the hypothesis for test, we must first make explicit the definitions of certain terms it employs and see to what extent corre- 5. The assumed motive, it may be noted, is to maximize aggregate profits and not average equity rates. Higher aggregate profits, in a given demand and lower aggregate profits associated with lower prices, but not necessarily a higher equity rate if the equity-sales ratio is sufficiently lower in the low-aggregate-profit

298 QUARTERLY JOURNAL OF ECONOMICS sponding categories and measures found in the available statistic data are congruent with them. The first such concepts for definition are the industry and the degree of industry concentration. For the purpose of such an hypothesis at least, the industry appears to be primarily a concept of demand- it is a group of outputs which to all (or most)of the buyers of each are generally close substitutes for each other and distant substitutes for all other outputs.6 The industry may be viewed in derivative fashion as a group of firms or divisions thereof, so far as the firms or divisions thereof all produce entirely (or, for rough purposes, almost entirely) within the close-substitute output group. The degree of industry concentration to which our hypothesis refers is the degree of concentration within an industry so defined -e.g the proportion of the combined production volume of such a group of close substitute outputs supplied by one, four eight, or twenty firms To test our hypothesis, we need to identify a number of such industries, obtain a measure of concentration within each of them and obtain also a measure of profit rates earned in producing their outputs. Ideally we might wish to make up theoretically significant industries de novo from the most basic data, and to calculate con- centration measures for them, but the magnitude of such a task has made this impossible for the present. As a result, we are forced to refer to already available groupings of firms or outputs and available measures of concentration within them, and to decide which of these groupings correspond approximately to theoretical industries as defined, or more generally for which groupings the received con ntration measures represent the true theoretical concentration affecting the outputs included. We may then select a sample of such groupings and related concentration measures in terms of which our For the time interval to be studied, 1936-40, the most compre- hensive available data identifying industries and measuring their concentration refer to about 340 manufacturing"industries"identi- fied in the Census of Manufactures for 1935. In addition there are concentration measures available for 1937 for about half of the 3600-odd manufactured"products which the Census recognizes as making up its"industries. Our general problem involves first deciding for which such "industries"or "products"the received group of outputs tied together by high eros elasticities of demand inter se which 7. Butit is quite possible for a firm or even a plant to produce simultaneously

RELATION OF PROFIT RATE TO INDUSTRY 299 concentration measures are theoretically significant. Since profit-rate data are seldom available for firms operating within a sphere so narrow ensus "product, however, we must we are even T to match profit data with concentration measures, confine ourselves to seeking"significant""Census industries To what extent do Census"industries"correspond to theoretical industries as defined? So far as they tend to represent different groups of outputs serving different needs of users-like firearms or fertilizers-they may tend to correspond, but they may also deviate in important respects from theoretical industries. First, although the Census industry occasionally includes only a single group of close substitute outputs-as in the cigarette industry--it commonly includes several technologically related output groups, identifiable as Census products, within each of which there is evidently close substitution but between which there is or may be slight inter-group substitutability for buyers. " The steel industry, ,which includes armor plate, axles, concrete reinforcing bars, etc. is a case in point several or many theoretical industries are potentially included in this Census industry. Second, the Census industry may be so defined as to exclude entirely close substitutes for the outputs which it includes. When the cane sugar industry is defined so as to exclude beet sugar, this is very obviously the case. Third, the Census industry, because it always includes the entire national supply of the products it contains, frequently may lump together several local or regional industries producing a given commodity, i. e, several output groups which have poor intergroup substitutability at going prices because of transport costs. This is evidently true of bakery roducts or common brick. If a Census industry is not guilty of any of these deviations from the theoretical norm, of course, it will tend o approximate a theoretical industry in that it will include a single group of close substitute outputs and exclude no close substitut for the Remembering these potential discrepancies between theoretical and Census industries, we have analyzed the 340 Census industries in search of the answers to two questions. First, which of them correspond closely to theoretical industries, so that their concentra tion measures obviously qualify as theoretically significant? Second, since there are few of these, for which other Census industries are the received concentration measures theoretically significant in that the Census industry concentration is representative of the true con- centrations for the several theoretical industries which the Census industry may contain? Obviously suspect is the Census industry which includes several

300 QUARTERLY JOURNAL OF ECONOMICS potentially close-substitute output groups which are actually poor substitutes because of geographical market segmentation. The Census industry then includes several theoretical industries, and its concentration measure will tend to represent that in each of the local industries only in the event that each of the principal firms is diversi- fied among all areas so as to control roughly the same proportion of each local market. If the various firms specialize in given areas, must be assumed in the absence of information on the point, the Census industry concentration figure will tend to understate ths true concentrations for the component theoretical industries. Thue we have rejected out of hand Census industries(and related concen- tration measures) for which the data have revealed significant geo- graphical market segmentation but no evidence of balanced inter-area diversification by firms. Our sample has thus been drawn only from industries where all principal sellers tend to reach all major market areas alike Geographical difficulties aside, however, which Census industrie have appropriate scope in terms of the potential substitutability of ncluded and excluded outputs? This is a difficult decision to make Lacking the crucial data on cross-elasticities of demand, we may either make a large number of horseback judgments, or accept either the Census“ industry” or the Census‘ product” definition as an approximation to what we seek. To avoid reliance on personal judgment in selecting a sample, we have assumed in general that geographical factors aside a theoretical industry is found in the case of each Census industry either in this "industry"'or in the individual Census products which it includes. Thus with the firearms industry which includes the Census products pistols, rifles, and shotguns, we assume that either there is a firearms industry in the theoretical sense there are pistol, rifle, and shotgun industries in the theoretical sense. Geographical difficulties aside, the theoretical industry we seek is assumed to be no broader than the Census industry- which is thus presumed to exclude no close substitutes-and no narrow than the Census product. We have avoided making a decision as to whether the true industry is the Census"industry"or the Census product. Each Census industry is thus generally viewed as com prising either a theoretical industry or a com aplex of several theoretical industries This last judgment has been modified only in a very few cases where there was conclusive evidence that close-substitute outputs were excluded from the Census industry-for classification establishing three sugar industries was not honored. In

RELATION OF PROFIT RATE TO INDUSTRY such cases, the Census industry has been rejected from the sample he ground that to overstate the true concentration for the theoretical industry within which the outputs in question fell. The same policy has been followed where there was evidence of a significant supply of imports of close substitute outputs, automatically excluded from Census data For almost all Census industry, however, we have followed the assumption that, geographical difficulties aside, either the industries or their component products represent theoretical industries, but that we do not know which do. We thus do not specifically identify the theoretical industry in most instances. If this is the case, how can we decide whether or not a Census industry concentration measure, computed for the aggregate output of such an industry will tend to represent the concentration measure for the theoretical dustry or industries putatively contained? This question may be analyzed on the assumption, which will not be reiterated throughout that we are dealing only with industries which are free of geographical market segmentation and have not been found overly narrow in definition Occasionally, of course, we find a Census industry with but a single product, and thus by assumption a simple theoretical industry for which the concentration measure may be accepted at face value. This is the case, for example, with matches, locomotives, and ciga rettes. In most cases, however, we have a number of products within the Census industry, and the issue must be faced. Its resolution is quite simple- we need only to identify those Census industries for which the concentration measure is roughly the same both for the Census industry and for each of its principal products. For in these the industry concentration measure will tend to represent the true theoretical concentration for the industry or component industries in question regardless of whether Census product or Census industry is the theoretical entity. The Census industry concentration measure vill in effect be interchangeable with the component product con centration measures when, and only when, there is within the Census ndustry a sort of symmetrically balanced diversification among all products by all firms, instead of narrower product specialization by firms. If there is specialization by firms among products, the aggre- gate concentration measure for the Census industry will generally be lower than the concentration measures for the individual products. 8 8. Thus if in industry X there are three products, a, b, and c, and of each of these firm I produces 60 per cent, firm 2, 30 per cent, and firm 3, 10 per cent he concentration figure for the aggregated output of the industry will be the

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