Explaining the Concentration-Profitability Paradox - SSRN

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Explaining the Concentration-Profitability Paradox Jan Keil* December 2016 This paper explains an empirical paradox which is often found, but generally ignored: a significant negative econometric relationship between profitability and market share concentration. The phenomenon can appear when there is a negative correlation between market share and costs – for example due to economies of scale. I show that concentration becomes an indicator for the cost competitiveness of direct rivals within an industry. Profitability of a given firm is undermined if price correlates positively with average industry costs (Classical natural prices) and frictions like sunk costs make an industry exit expensive for firms. This idea also explains the frequent findings of highly persistent profit rate differentials. (JEL B51, D24, D40, L11) Keywords: Classical Political Economy, Competition theory, industrial organization, industry market share concentration, profitability

hy do so many empirical studies find an inverse relationship be-

W

tween profitability and industry concentration? This article offers

an explanation for the seemingly paradoxical finding. It also presents a rationale for the frequent occurrences of significant negative coefficients of * University of the West Indies at Mona,

Department of Economics, Kingston 7, Jamaica, [email protected]. Helpful comments by two careful anonymous referees from the Review of Political Economy are gratefully acknowledged. I thank Nalisa Marieatte and Chrystal Rhone for valuable input and assistance.

barrier variables and for the stylized fact found in current applied research that the degree of persistence in profit rate differentials tends to be very high in most countries and industries. None of these three phenomena have been completely understood yet. The analysis presented here describes how a firm can be trapped in an industry dominated by cost-competitive rivals. It shows that it can be economically rational for a high cost firm to stay in its industry and accept long periods of below average profitability. This is a possible (but not a necessary) result in industries with a high degree of market share concentration. The rationale is that industry concentration is an indicator for the costcompetitiveness of direct intra-industrial rivals whenever there are increasing returns to scale or any other type of negative correlation between market share and costs. It implies that a higher market share concentration must be associated with lower average industry costs and, if the Classical theory of price holds, with a lower industry output price. If there is some kind of exit barrier in such an industry, the profit rate of a firm with a given market share must be lower than in the case where the firm is located in another industry that only differs by having a lower degree of concentration (and thus higher average industry costs and a higher price). From a Classical point of view it should be unacceptable that competition theory is dominated by the mainstream even more than in other areas in economics. Thus, a goal of this paper is to show that “Classical” explanations can be developed to understand empirical findings that have not been explained by orthodox theories. The illustration here is Classical because it

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assumes 1. simple prices of production that are equal to average industry costs plus a markup for allowing an average firm of the industry to obtain the normal profit rate on capital invested; 2. Classical surplus profit that can be obtained by capitals if their individual costs are below the industry average; 3. the standard method with which Classical and Neo-Ricardian economists determine the value of used fixed capital. The remainder of this article is organized as follows: section I. reviews the empirical literature and previous attempts to explain the paradoxical findings that the analysis in section II. seeks to explain. The study is concluded in section III.

I. A

Literature Review

Econometric Evidence

Early research on the determinants of profit rate differentials (for further summaries see Scherer (1980) or Clarke (1985)) was based on cross-sectional regressions like πi = α + βHHIi + bxi + ei

(1)

where πi is the differential between firm i’s profit rate versus the average of the entire sample of firms. α is the constant, β the regression coefficient of HHIi , the Herfindahl-Hirschman Index of market share concentration of the industry in which firm i is located,1 xi is a vector of control variables such as sales growth and b is the corresponding vector of regression coef1 In

many cases the four-firm, five-firm or another concentration ratio is used.

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ficients. ei is the error term. While the standard is a firm level regression, there are also examples where industries (Holtermann, 1973; Clarke, 1984) or company segments / lines of business (Weiss and Pascoe, 1981; Gale and Branch, 1982) are used as the unit of analysis. Starting with Bain’s (1951) seminal paper, numerous authors found consistently stable and significant positive relations between concentration and profitability (Bain, 1956; Mann, 1966; Collins and Preston, 1969; Weiss, 1974). This was interpreted as empirical support for the “concentration doctrine” (Demsetz, 1973b) – the broadly dominating view among traditional mainstream economists that a positive causal effect of concentration on market power and profitability exists (Clarke, 1985, p. 99). However, studies with supporting evidence either used industry level information or company data without including the market share as a control variable. With the formulation of the efficiency hypothesis, both methods were generally dismissed as leading to obvious spurious results (Demsetz, 1973a, 1974). The efficiency hypothesis states that firms are larger or can obtain greater market shares because they are more efficient (lower costs of production or delivery) or more productive (higher quality products). The market share becomes an indicator of efficiency. Statistically, the market share concentration correlates positively with the market share of a randomly selected individual firm and with the industry average firm size.2 Since a) efficiency is supposed to be reflected in a firm’s market share and b) 2 If, for example, the degree of inequality of the market share distribution and the indus-

try size are both constant, an increase in the average firm size can only result from a smaller number of firms which simultaneously produces a higher level of industry concentration (when measured by concentration ratios or the Herfindahl index.

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the market share correlates positively with concentration, then higher concentration must also be positively related to firm efficiency and average industry efficiency. As higher efficiency is also said to imply higher profitability in the case of a firm and the industry average, the spurious econometric result is a positive relation between firm or industry level profitability and concentration. It follows only from efficiency, not market power, collusion or some other lack of competition: when firms become more efficient, they grow and increase their own market share and the concentration level of their industry while also becoming more profitable (see also Clarke, 1985, pp. 100 or Scherer, 1980). When the market share is not included as a control variable in firm- or segment level regressions (in vector xi in equation 1), the degree of concentration might have a spurious significant positive coefficient just because it captures the positive correlation between market share and profitability that is driven by efficiency. Industry level regressions cannot be saved, since it is not possible to control for the market share. Adding the market share as a control variable to a firm or segment level analysis produces a stable, significantly positive market share coefficient as an own stylized fact of empirical research (e.g. Gale and Branch, 1982; Ravenscraft, 1983; Shepherd, 1972). This is seen as evidence in support of the efficiency hypothesis. The inclusion of the variable reduces the frequency with which significant positive concentration variable coefficients are found. Robust significant positive coefficients become either less and weakly significant, insignificant or even significantly negative (Khalilzadeh-Shirazi, 1974; Hart

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and Morgan, 1977; Ravenscraft, 1983; Gale and Branch, 1982; Amato and Wilder, 1985). Surprisingly, insignificant or mixed results are still often interpreted as “only weak evidence” for the concentration doctrine, which is still assumed to be somewhat valid. Alternatively, findings other than significant positive coefficients are explained by an insufficient quality of industry concentration measures or other variables in the regressions (Kwoka, 1979; Hirsch and Hartmann, 2014). Accordingly, simple structure-conductperformance regressions explaining profit rate differentials are not very popular anymore today. The finding of a significant negative effect of concentration is as frequent as that of a significant positive one or that of an insignificant relation. Table 1 summarizes a selected set of studies that detect a negative relation. They draw upon different concentration measures, profit indicators and samples. For example, Stigler’s (1963) early analysis of the US manufacturing sector for the years 1941-1948 reports how firms in less concentrated industries have higher profit rates. In an influential study, Shepherd (1972) detects a negative non-linear relation in some of his regressions. Samuels and Smyth (1968) reproduce the finding for the UK. It is noteworthy that this is the case even though none of these regressions control for market share. Equally surprising, it even occurs in numerous industry level regressions (see, e.g. Holtermann, 1973; Hart and Morgan, 1977; Clarke, 1984; Geroski, 1981). In very sophisticated studies Gale and Branch (1982) and Ravenscraft (1983) analyze business segments or lines of business within

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companies3 and find highly significant negative coefficients for concentration indicators. Their samples are exceptionally large and also cover nonmanfacturing industries. Ravenscraft (1983) includes 30 control variables such as market share, company diversification or industry export intensity. The persistence of profit research produces similar findings. Authors in this tradition follow Müller (1977, 1986) and model time series processes in firm (or segment) level profit rate differentials. They estimate the autoregressive process4 δit = αi + λi δit−1 + µit

(2)

and compute its unconditional mean

pˆi =

αˆ i 1 − λˆ i

(3)

where δit is the differential of the profit rate of firm i in period t versus the economy-wide average of that period. µit is a random error. The AR parameter λi measures the speed of adjustment to the long-run equilibrium value and represents the profit rate differential’s degree of persistence. pi is the part of the profit differential that is not eroded by the adjustment that the AR process produces throughout time. It is the persisting long-run differential. λi and pi are both of analytic interest. Most studies estimating 3 This

focus allows to allocate micro units to industry level variables in a much more precise way since many firms are active in multiple locations and sectors through separate segments. 4 The AR(1) is most widely used although many authors apply more complex methods: Crespo-Cuaresma and Gschwandtner (2008) allow the AR(1) parameters to vary through time; McMillan and Wohar (2011) include different parameters for below and above average profitability in an asymmetric AR model; among many others, Glen et al. (2003) use an AR(2) process.

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equation 2 test for stationarity and interpret the magnitude of λˆ i or pˆi (see, for example, Glen et al., 2003; Cable and Müller, 2008). Some authors add a second step where pˆi or λˆ i are used as dependent variables in a second cross sectional regression

pˆi = α + βHHIi + bxi + ei

(4)

α is the constant, ei the error term, β the coefficient of the Herfindahl index HHIi (or a concentration ratio), xi a vector of control variables and b the coefficient vector.5 It is noteworthy that many studies which carry out this second step do this in a flawed way. Acquaah (2003), for example approximates the fourfirm concentration ratio from Compustat, which is now known to be an unsuited methodology as the proxy is virtually uncorrelated with the more comprehensive Census concentration measure (Ali et al., 2009). Goddard et al. (2011) and Kambhampati (1995) use industry level regressions or exclude market share as a control variable – with the result that their correlations for the concentration measure are likely to be biased and entirely spurious. Of all studies, only Yurtoglu (2004) finds a positive significant effect in a regression that is not invalid in some obvious way. But he detects it in just 1 out of his 7 reported equations. The equation is also only explaining αˆ i , not pˆi . This makes little sense as a high degree of persistency might just describe how an extremely small differential or even a below 5 An alternative is to simultaneously estimate the impact of explanatory variables (included in vectors xi and zi ) on αˆ and λˆ through the single equation δit = α(xi ) + λ(zi )δit−1 + µit (Gschwandtner, 2012).

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average profit rate prevails for an extended period. Thus, a positive correlation with a concentration measure is not necessarily implying market power or a lack of competition. On the other hand, there are many authors that find significant negative effects of concentration on pˆi (and αˆ i ). This starts with the very first contribution of Müller (1986) who detects a nonlinear negative relation between concentration and estimates of long run profitability. Gschwandtner (2012) finds consistently negative concentration indicator coefficients (in regressions on αˆ i and pˆi ) that are significant in many cases. She reports insignificant negative coefficients for some of her regressions in an earlier paper (Gschwandtner, 2005). Keil (2016b) uses a panel of business segments covering 24,880 original US manufacturing and non-manufacturing observations. The analysis includes non-linearities and barrier-concentration interaction effects. Using instrumental variables to address endogeneity problems, the study shows that concentration is significantly negative in some specifications and in several industry groups. The persistence of profit research has another paradoxical finding. The autoregressive parameter which represents the speed of adjustment of an annual profit differential to the long-run equilibrium value is often found to be of a substantial magnitude. High sample means are found by Waring (1996) with 0.66 for the U.S., by Müller (1990) with 0.78 for one of his samples or by McMillan and Wohar (2011) with 0.61 for the U.K. Usually, a considerable fraction of firms analyzed have highly persistent parameters, close to or exceeding 1, which implies a divergence of profit rates (see e.g. Keil, 2016b).

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The usual explanation for high degrees of profit persistence is a lack of competition, but to just assume this is problematic. Additional regressions must be applied to show that this is a possible explanation by documenting a positive relation between profit persistence and industry concentration (or some other variable for which economic theory predicts a competition impeding effect). However, as described before, concentration is in most cases either insignificant or does not show the “correct” sign. Thus, the findings of large AR parameters are paradoxical, as the common models fail to provide any theoretical rationale. The article presented here offers an explanation. Many analyses also find coefficients of mobility barriers or interaction effects between barrier and concentration variables to be negative – and usually significant in at least some regressions reported. The studies rely on different time periods, industry samples, estimation techniques and micro units. Authors report negative coefficients for capital intensity (Holtermann, 1973; Geroski, 1981; Ravenscraft, 1983), firm size or minimum efficient scale (Shepherd, 1972; Nickell and Metcalf, 1978; Clarke, 1984; Gschwandtner, 2012; Keil, 2016b), and advertising and/or R&D expenditure intensity (Phillips, 1972; Nickell and Metcalf, 1978; Ravenscraft, 1983; Gschwandtner, 2012; Keil, 2016b). Given Bain’s (1956) broadly accepted theoretical argument for a positive effect of mobility barriers on profitability (see also Stigler, 1968; Spence, 1977; Comanor, 1967), this is yet another paradoxical but common result which must be explained.

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B

Existing Explanatory Attempts

The “perverse” (Hart and Morgan, 1977) or “puzzling” (Hirsch and Hartmann, 2014) finding of a significant negative regression coefficient of concentration variables on profit measures is generally not recognized as a result that requires as much explanation as the other two findings (significantly positive and insignificant coefficients). The present analysis attempts to accomplish precisely this. Given the number of studies with these paradoxical results, and the fact that the respective regressions are usually econometrically more sound6 , it is surprising that few explanatory attempts have been made. Müller (1986, pp. 63-64) sees competition increasing in concentration initially through rising rivalrous expenditures on product differentiation. These expenditures are said to have an inverted U-shape and occur in industries producing heterogeneous output. With higher concentration, a very small number of firms undermines this competition and produces a positive link. It is essentially a common threshold story (just like a simple Cournot model that implies a convex relation between concentration and profitability) in which a second causality runs parallel to the standard concentration-collusion mechanism. However, testing it empirically by isolating industries with product differentiation and adding squared terms of the concentration index (Keil, 2016b) fails to generate any evidence in support of this theory. One explanation offered by Ravenscraft (1983, p. 27) is that larger units 6 For

example, because more precise company segment data or larger samples are used. The finding is also especially frequent in persistence of profit analyses.

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have cost or product quality advantages with the implication of gaining less from collusion than smaller units and thus behaving more competitively. However, this logic is flawed since it is always true that product quality or cost heterogeneity can discourage stronger rivals from colluding with weaker ones. This is equally possible in industries with high and with low concentration. Concentration is misinterpreted as inequality. However, with higher concentration, heterogeneity might be lower in many cases where the fewer remaining firms have equal market shares and may copy each other more rapidly and systematically. Another idea put forward by Ravenscraft (1983) is that the ability to exploit these advantages may depend on the absence of large rivals with similar strengths. While this only offers an explanation of profit differentials of large, not of small firms, it is still an appealing intuition and related to the explanation developed here. Both his ideas provide in any case only a partial answer as the negative effect of concentration is explained but not the significant negative coefficient of barrier variables and barrierconcentration interaction terms or the high degree of persistence (or divergence) of profit rate differentials. Two extensions to the mainstream IO models are sometimes referred to when these paradoxical results are found. The first one is the idea that a lack of competitive pressure leads to X-inefficiency – motivational deficits producing higher costs, lower productivity and lower profits (Stigler, 1976; Leibenstein, 1966). While the concept itself is logically sound and surely backed by substantial empirical evidence, it is not suited to explain the

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concentration-profitability paradox. Just adding this phenomenon means that it exists parallel to the simultaneously still prevailing competition impeding and markup-increasing effect of concentration described in standard IO models. These theories themselves are untouched and it is not at all clear what the nature of the overall effect of concentration of profitability is. The positive and the negative ones might cancel out or the positive effect might dominate. Additional theoretical arguments are also necessary for X-efficiency to weight more and produce a negative correlation between concentration and profitability: that owners have no or little control over management (in the spirit of Berle and Means, 1932; Fama and Jensen, 1983; Jensen and Meckling, 1976) and that capital markets have significant frictions. A negative relation is only possible where managers reap all monopoly power benefits from owners and the latter actually obtain lower returns on their investments than those of competitive firms. The second extension economists refer to is the possibility that maintaining market power involves costs, such as excess capacity (Spence, 1977), untapped financial resources (fight-back potential) or low pricing strategies to discourage entry. While there should be little doubt that monopolies face such a problem to at least some degree, this line of research predicts an insignificant or weakly positive relation between concentration and profitability, but does not explain a significant negative one. If the costs of defending a monopoly exceeded the financial benefits from the exploitation of monopoly power, rational company owners would simply chose not to defend the monopoly in the first place.

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Another class of more recent models initiated by Jovanovic (1982) and developed by Ericson and Pakes (1995) and others are based on dynamic stochastic games. This endogenizes market shares and concentration. Mainstream textbook IO models of imperfect competition are pushed somewhat closer to the dynamic Classical (and Austrian) competition theory promoted here. The analytic interest of the approach is also related to this study since it covers the effect of mobility barriers on profitability as well as entry and exit behavior of firms. One special case is described where higher mobility barriers may reduce concentration, which in turn results in lower profitability (Amir and Lambson, 2007). While this might sound like a possible explanation for the negative barrier variable coefficient, the direct relation between concentration and profitability is not analyzed. Standard Cournot, Stackelberg or game theoretic competition models with incomplete information are assumed in every period (once stochastic state variables are determined). Thus, it is never the case that the direct effect of concentration on profitability is analyzed in any new way. The common Neoclassical models used still describe a positive relation between concentration and profitability. The concentration doctrine is valid and marginal costs, demand elasticities etc. continue to be essential in determining model outcomes. While barriers may have negative effects on profitability, it is not possible to explain the negative concentration-profitability relation that appears even when barriers are included as control variables. Although it would be interesting to elaborate the possibility of Classical versions of these dynamic stochastic models, it is not necessary to make the point of this article – to

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explain the negative impact of concentration. The subsection on exit costs relates to the works by Dixit (1989) and Lambson (1992) who explain profit rate differentials, entry and exit decisions. They develop essentially equivalent exit rule criteria. However, their analysis has a different focus and deals with stochastic shocks, hysteresis phenomena in different economic applications and barriers to mobility. The main focus of the analysis here is to explain the effect of changes in concentration on profit rates. A barrier is just an additional variable that the model requires to take some value.

II.

A “Lock-in” Model

Almost all existing IO models are Neoclassical or have been fully assimilated into the mainstream. The industry output price results from (1) marginal costs associated with well-behaved Cobb-Douglas production functions, (2) the price elasticity of demand and other demand curve parameters, (3) exogenously predetermined characteristics of oligopolistic firms such as the mutual conjectural variations and/or 4. the set of rules of some highly abstract and counterfactual game. The explanation offered here does not rely on any Neoclassical assumptions and methodology at all. It is “Classical” in the sense that a) prices are prices of production or natural prices that are based on the industry average costs of production and capital intensity while allowing the average capital of the industry to obtain the uniform normal rate of profit; b) individual capital can obtain simple Classical surplus profits (or losses) if the 15

individual costs of production are below (or above) the industry average; c) real, physical time is analyzed and not abstract game time or instantaneous jumps when it comes to the adjustment (or a lack thereof) of profit rate differentials towards the normal rate of return; d) equilibrium prices of fixed capital vintages are determined by costs of production and depreciation in the standard Classical and Neo-Ricardian way. The explanation derived in this paper incorporates the efficiency hypothesis in the simplest possible way – by assuming an inverse relation between market share and variable costs unit. In subsection A I show that this implies an inverse relation between concentration and industry average costs. A second model ingredient is the Classical equilibrium price in subsection C. Since prices of production are proportional to average industry costs, an inverse concentration-price relation results from this inverse relation between concentration and industry average costs. The initially assumed negative correlation between firm size and variable costs is then shown (in subsection D) to imply that larger firms obtain Classical surplus profit and smaller ones below average rates of return. Because more concentration is associated with lower average industry costs, a firm with a given fixed market share (and individual cost level) will obtain lower profits when the degree of concentration is higher (and industry average costs lower). Subsection E introduces fixed capital and sunk costs that constitute an exit barrier. I show that if the loss from an industry exit is large enough, it can trap a firm in an industry and cause profit rate differentials to stay constant or grow through the lifetime of fixed assets.

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A

Inverse Size-Cost Relation

The “efficiency hypothesis” is not only found in Chicago School theory (Demsetz, 1973a, 1974) but also in the dynamic Austrian (Schumpeter, 1942; Hill and Deeds, 1996) and Classical (Steedman, 1984; Shaikh, 2008) approaches. They all predict that superior efficiency allows firms to be more profitable, reach stronger sales growth and capture market shares from competitors. The Classical way to think about higher efficiency is in terms of lower costs of production, which means that there is a negative market share-cost relation. I assume this to be the case here. For the analysis at hand it is not relevant how this analysis how this relation comes about. It could, for example be due simply to increasing returns to scale. It could equally be a statistical correlation that results from some firms being “lucky” or successful innovators managing to lower costs and increase market share. Moreover it does not matter if the relation is present in the use of all inputs or only the variable ones. For the sake of simplicity I restrict this inverse size-cost relation to variable costs only.7 The inverse market share-cost relation explains the stylized fact of the positive significant relation between the size of an individual firm’s market share and profitability. It also implies that industry average costs decline as the market share concentration increases. Keeping everything else equal, larger firms have simultaneously lower costs and produce a greater share of total industry output. The more output produced by lower cost firms, the 7 While

relaxing this assumption is immaterial to the predictions of the model, it would raise the degree of model complexity.

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lower the average industry costs. THEOREM: If there is a negative linear size-variable costs relation, the result must be a negative linear relation between concentration (measured by the Herfindahl-Hirschmann Index, HHI) and industry average variable unit costs (computed as the arithmetic mean). PROOF: Assume variable unit costs of an individual firm i (ci ) are linearly inversely related to sales,

ci (yi ) = a − byi

(5)

where yi are sales of firm i and a and b are positive constants.8 The average ¯ on a product unit basis are given by variable unit costs for the industry (c) the costs of the individual firms in the industry, weighted by their respective market shares, c¯ =

N  X y

i

Y

i=1

where Y are industry sales (Y =

 (a − byi )

PN

i=1 yi )

and

yi Y

(6)

is the market share of firm i.

c¯ is just the average cost of all single units sold. It can easily be rewritten as # N  N "  X X yi2 yi c¯ = a − b Y Y i=1

or c¯ = a

i=1

N X y i=1

(7)

i

Y

− bY

N " 2# X y i=1

8a

i Y2

(8)

contains a (maximum) variable cost term and b captures the elasticity of variable costs with respect to scale.

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The expression simplifies9 to

c¯ = a − bY ∗ HHI

(9)

Industry average (variable) costs decline linearly as concentration increases. Note that fixed costs can still be present (see below) and that the result also holds when these fixed costs involve increasing (or even slightly decreasing) returns to scale. However, fixed costs are treated as being constant for all scales in order to simplify the analysis as much as possible.

B

Endogeneous or Exogeneous Demand

One must note that industry size impacts costs in equation 9 with exactly the same elasticity as concentration does. Therefore one must consider the potential effects of concentration on total industry output which could in turn would influence average costs through an indirect second order effect. According to one view, there is no difference in Classical and Neoclassical economics when it comes to the recognition of the existence of downward sloping demand curves while, of course, the explanations for it differ (Shaikh, 2012). In the most simple way, industry demand can just be written linearly as Y = α − βp

(10)

where p is price and α and β are positive parameters. This implies that a P yi that the sum of market shares is one ( N i=1 Y = 1) and that the sum of squared   PN yi2 market shares is the Herfindahl index ( i=1 Y 2 = HHI). 9 Recall

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change in HHI will not only directly affect c¯ through equation 9, where an increase in the HHI first produces a lower c¯ in a first step. There will also be a reinforcing indirect effect: the next subsection describes Classical prices which imply a positive link between average industry costs and price. This means that a lower c¯ is associated with a lower p. The lower price increases demand Y through equation 10 in a second step. This higher demand level in turn decreases p even further (again equation 9). According to another (more long-term) view held by Classical economists, demand and supply can be treated as given quantities and not as the functional price-quantity relationships described in standard textbooks (Garegnani, 1983; Salvadori and Signorino, 2013). If this perspective is adopted, equation 9 simplifies to: c¯ = a − bHHI

(11)

The choice between the two views on industry demand is irrelevant for obtaining the basic insight of the paper. If the industry quantity is endogeneously determined through downward sloping demand curves, concentration is even more negatively related to industry price (and firm profit). The only difference is that the magnitude of a reduction of average industry costs due to an increase in concentration is larger. I assume in the following that demand is fixed as in equation 11 for three reasons: (1) predictions are essentially equivalent; (2) the analysis is simplified; (3) the theoretical argument is stronger and more acceptable if one can show that the analysis holds even for “the weaker case” (a smaller absolute effect of concentration changes on industry price and and firm level profits). 20

While the inclusion of downward sloping demand curves is unproblematic here, it creates complications when one tries to explain the concentrationprofitability paradox with Neoclassical models like Cournot competition. Whether an increase in the HHI leads to a lower price depends on both the parameters of scale economies and the demand curve. The price elevating effect of higher concentration due to higher market power may be overcompensated by the price depressing effects of lower costs for larger firms. Since both effects increase profit, a negative effect of concentration on profitability cannot be modeled. This is illustrated in the appendix.

C

Classical Prices of Production

The previous subsections showed how concentration impacts average industry costs if the efficiency hypothesis is assumed to hold. But how does concentration affect the industry equilibrium price? This depends on the relationship between average industry costs and prices. Classical equilibrium prices cover industry average costs and allow the average capital invested in the industry to obtain a uniform “normal” rate of return.10 The price of production of an individual industry can be written in standard form as wl + (1 + r)pa a = p 10 While

(12)

prices are by definition proportional to average industry costs one could also say that “price is strongly correlated with industry average costs” as equilibrium prices in a dynamic world with all frictions will generally never be exactly proportional to industry average costs. Given space limitations, the focus of the study and to better understand the problem at hand, it is useful to make the simplifying but counterfactual assumption that the costs of the technique with the lowest costs (the “regulating capital”) of all generally available techniques is close to or sufficiently correlated with the average costs of existing techniques (in an industry). However, deviations will always exist (Shaikh, 2008).

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where w is the wage rate, l the direct labor input required to produce one output unit, r the normal profit rate, a the vector of variable direct material inputs to produce one output unit, pa the corresponding price vector and p the price of the industry output. A system of such equations can represent the economy as a whole and be solved to calculate the prices of production. Note that at any individual point of time, a firm i has always variable costs above or below those of other firms in the same industry. They generally differ from the average, li , l and ai , a. In the present model this is the case whenever market shares differ. The labor and material inputs in equation 12 represent industry average values, i.e.

wl =

n X y

i

i=1

Y

wli and pa a =

n X y

i

i=1

Y

pa ai

(13)

Writing wl + pa a = c¯

(14)

and inserting it into equation 12 allows to simplify the latter to

p = rpa a + c¯

(15)

To consider the effect that the negative size-cost relation has on prices of production, one just needs to insert equation 11 into 15:

p = rpa a + a − bHHI

(16)

This shows that market share concentration is directly and inversely related 22

to the industry output price. A stronger inverse size-cost correlation means that the price reducing impact of increasing concentration is greater. Classical theory of price and competition describes a rivalry between incumbents in the form of a mutual price underbidding and threats of new firms entering the industry or incumbents augmenting capacities (Shaikh, 2008). This is precisely what ensures that a fall in average industry costs (like the one that must result mathematically from an increase in concentration) will also lower prices and not result in persistent above average profits.

D

Classical Surplus Profit

In this section two questions must be answered. How does the negative effect that concentration has on price translate into firm level profits? How do individual profits relate to the mentioned uniform normal rate of return? To answer both questions a Classical surplus profit theory is applied. The normal rate of profit is always only obtained by the average capital of the industry. Classical surplus profit presupposes the previous outline of prices of production where the latter are proportional to average industry costs and allowing the average capital to obtain the normal profit rate. Any divergence of an individual from the normal profit rate originates from a cost-differential of individual capital relative to the industry average. Lower individual costs imply a positive excess profit. Higher individual costs are associated with a below-average individual profit rate. One uncommon but valid way to look at this is to hold a firm’s market share and individual costs

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constant and vary the industry average costs. I just showed that higher concentration lowers industry average costs. It narrows any possible preexisting cost advantage and increases every cost disadvantage. An increase in concentration thus necessarily reduces the amount of profit a firm with a constant market share makes: The total profit after depreciation, Πi,t that firm i receives in year t is

Πi,t = [p − ci ]yi = [rpa a + c¯ − ci ]yi

(17)

where the term in brackets represents the profit margin. One can see that equilibrium prices allow to obtain the normal profit rate on capital in¯ It is also possible to see from this vested, rpa a and cover average costs, c. equation how any advantage of individual versus average costs results in a ¯ i will then be > 0 and Πi,t > rpa ayi . profit greater than the normal one, as c−c Using equation 11, one can rewrite equation 17 as

Πi,t = [rpa a + (a − bHHI) − ci ]yi

(18)

This reveals how an increase in industry concentration must reduce the profit margin and lead to a lower total profit quantity for an individual firm of a given and fixed size. Firm i’s profit rate πi,t can be written as

πi,t =

[rpa a + (a − bHHIyi ) − ci ]yi pa a

(19)

It will also be lower since the Herfindahl index in the numerator has a neg-

24

ative sign. This is the major and new insight of this paper: higher concentration can have a negative correlation with an individual firm’s profit rate. The logic is that a negative size-cost relation implies that concentration captures the average cost competitiveness of the firms in the industry. Having lower-cost firms in an industry has a negative impact on price. If a firm’s market share is held constant (for example, when one interprets the regression coefficient of the HHI) and its own competitiveness does not change, the presence of the more competitive rivals must result in a lower profit rate for that individual firm.

E

Exit Barriers

So far, the previous subsection’s insight is incomplete. If an incumbent obtains a below average profit rate in an industry with large, highly cost competitive rivals, why would the firm not just exit and migrate to another industry populated by small, high cost rivals? The answer proposed here is that there might be barriers to exit, which causes a negative impact of concentration on profitability to emerge and to persist. Sunk costs in fixed asset investments could produce such barriers. It may result from transaction costs, legal fees, firm specific expenditures that cannot be sold to a third party. This might produce discounts on the value of assets in the resale market or even an inability to sell any of the assets. Sunk costs can be represented easily as some fraction or percentage δ of the total value of fixed assets. This can be interpreted in two ways. The first one is that the total of all existing fixed assets can be sold at a percentage

25

discount, for example at 80% of the remaining aggregate actual value. The second one is that some of the different fixed assets a firm owns cannot be sold at all and are entirely lost while others (for example the same 80%) are liquid and can be sold at their full value. Other types of exit barriers can have the same effect that is described in this subsection. However, the idea that capital structures with large shares of durable fixed capital act as mobility barriers affecting, for example, investments, profits or industrial pricing throughout the business cycle is occasionally articulated by representatives of dynamic Classical competition theories (see e.g. Semmler, 1981, pp. 41-42). Thus, it seems to be a very “natural” solution for a Classical analysis. Including fixed assets into Classical theory of price complicates matters, nevertheless it is a well established practice. I apply the exact standard method dominating the literature. What follows shows that the results obtained above are also valid when fixed capital is present. The part after that describes how fixed assets can constitute a trap that might lock a firm into an industry.

F

Fixed capital

To simplify the following analysis as much as possible, one can assume that all variable (including material) costs occur at the end of the production period so that no return needs to be computed on related capital expenditures (contrary to how this is usually done). This could also be thought of as an industry where production involves only fixed capital and labor (but

26

no material variable inputs such as raw materials). Relaxing this assumption does not change the implications of the workout. However, it becomes unnecessarily more complex and harder to follow. Thus, the sole purpose of the assumption is for analytic simplicity. It means that equation 12 must be written as

p = wl + pa a = c¯

(20)

The simplification allows to isolate fixed capital as the only capital quantity on which the profit rate must be levied. The common method to model fixed capital is as a joint product. With intermediate variable inputs paid at the end of the production period, it can be written in the standard way as

c¯ + (1 + r)Kt = p + Kt+1

(21)

where Kt is the value of fixed capital of vintage t used (technically the expression should read and kt pkt with kt being the fixed capital quantity required to produce one output unit and pkt the corresponding unit price for fixed capital of vintage t). Depreciation is Kt − Kt+1 . One may express equation 21 as c¯ + rKt + (Kt − Kt+1 ) = p

(22)

The sum of the normal return on fixed capital (rKt ) and the depreciation of it (Kt − Kt+1 ) can be written as a capital charge component m

m = rKt + (Kt − Kt+1 ) 27

(23)

Note that this quantity m is a charge on a per output unit basis. Due to the standard Classical equilibrium assumption that all firms use fixed capital in exactly the same way, with equal efficiency, fixed capital intensity and without any type of scale economies, m it is identical for every firm in an industry. It is also constant through time – given the standard assumptions of constant lifetime efficiency of assets and capacity utilization. Thus, m can be derived using the standard and broadly used annuity loan formula (see. e.g. Sraffa, 1960, §75) as

m = K0

r[1 + r]T [1 + r]T − 1

(24)

where r is the normal return, T is the lifetime and K0 the original value of the required fixed assets in the initial period 0 (capital quantity * price, k0 ∗ pk0 ). The annuity factor allows equilibrium prices to be independent of asset life and the return on fixed assets to be constant and equal to the normal rate at every point of time. This determination of m is common practice in Classical theory of price. By inserting equation 23, the equilibrium price equation 22 can be simplified further to

p = m + c¯

(25)

This is just a rearranged and simple version of the standard prices of productions representation for an industry that uses fixed capital (and that pays material variable inputs in the end or has labor as the only variable input). 28

To consider the effect that the negative size-cost relation has on prices of production, one just needs to insert equation (11) in (25):

p = m + a − bHHI

(26)

In this variant of equation 16 concentration is still inversely related to price. It also still holds that an increase in concentration reduces the amount of profit that a firm makes, since equation 17 becomes

Πi,t = [p − ci − dt ]yi = [m + c¯ − ci − dt ]yi = [m + a − bHHI − ci − dt ]yi

(27)

where dt is the depreciation per output unit, dt = Kt − Kt+1 . The HHI has still a negative effect. This equation can also be written as

Πi,t = [m − dt ]yi + [c¯ − ci ]yi

(28)

and divided by Kt to obtain firm i’s return on the quantity of fixed capital invested, ri,t : ri,t =

[m − dt ]yi [c¯ − ci ]yi + = r + si,t Kt Kt

This requires some explanation. The first term,

[m−dt ]yi , Kt

(29) is always equal to

r because the annuity formula implies by design values of dt and Kt that result in profit rates on remaining fixed capital in every period invested being exactly equal to the normal profit rate.11 The second term, si,t , is more interesting. It is the surplus-profit (or loss) that results from a firm 11 See

equation 36 below for the formula to compute Kt .

29

having below (or above) variable average costs. The subscript indicates that it is different for every firm when variable costs differ. It also implies that it is different in every period t. It turns out that any differential between the profit rate on Kt versus the normal rate grows as the asset approaches the end of its lifetime: si,t+1 > si,t if si,t > 0 (si,t+1 < si,t if si,t < 0) because Kt+1 < Kt while the numerator in equation 29 stays constant. Thus, the profit rate on the basis of the value of remaining real assets invested by a firm in the industry, ri,t , is diverging once a profit rate differential occurs. In equilibrium, production processes are repeated and firms must save an accumulated depreciation fund to replace used-up fixed capital, Dt . Several Classical economists describe a “monetary” concept of capital. It accounts for this explicitly and includes the growing Dt in addition to Kt (see, for example, Marx (1992, pp. 251, 261, 529), Shaikh (2015, Appendix 6.4), Torrens, 1818, p. 337). To keep it simple, I follow one interpretation of the issue and assume that the accumulated depreciation fund has the ability to obtain the normal profit rate.12 A firm’s profit rate on total assets, πi,t is just the weighted average of the returns on the shrinking fixed capital stock (ri,t ) and the normal return on the accumulated depreciation fund Dt (r):

πi,t = ri,t

Dt Kt +r Kt + Dt Kt + Dt

12 The

(30)

analysis also holds when the accumulated depreciation fund obtains an interest rate below the normal profit rate. However, this is non-standard and implies a different computation of m and Kt .

30

Using equation 29 the first term can be written as

πi,t = [r + si,t ]

Kt Dt K + Dt Kt Kt +r =r t + si,t = r + si,t (31) Kt + Dt Kt + Dt Kt + Dt Kt + Dt Kt + Dt

πi,t turns out to be constant because the growing |si,t | is exactly countered by the shrinking Kt that caused it to grow. To show this replace si,1 by

¯ i ]yi [c−c Kt

(see equation 29) to yield

πi,t = r +

[c¯ − ci ]yi Kt [c¯ − ci ]yi =r+ Kt Kt + Dt Kt + Dt

(32)

Noting that Kt + Dt = K1 ∀t or D1 = 0, one can write this as

πi,t = πi = r +

[c¯ − ci ]yi = r + si,1 K1

(33)

Any individual difference in costs versus the industry average will result in a constant below (or above) average profit rate on total capital. Profit rate differentials persist when computed on the basis of total capital until fixed capital is depreciated. Clearly, this result also holds when the return on the depreciation fund is an interest rate < r. This provides a rationale for the frequent finding from the persistence of profit literature that concentration indexes correlate in regressions negatively with persistent profit differentials.

31

G

A “Lock-in” effect

The point of including fixed capital in the analysis is to show that it can constitute a barrier to exit which may trap a firm in its industry. Since an industry exit occurs with all the assets a firm has invested in that industry and not just the fraction Kt that is required to produce a single output unit, it makes sense to write the entire value of all fixed assets remaining as κi,t = Kt ∗ yi . THEOREM: The presence of sunk costs in fixed capital investments κi,t constitutes a trap that can lock a firm into an industry such that it can become economically rational to accept persistent below average profitability for a longer period of time. PROOF: A rational firm will stay in its industry when it can make more profit this way than leaving it and investing the proceeds at the normal profit rate. A valid precise decision criterion is to compare the present value of all future cash flows the firm would make when staying and continuing to operate in the industry with the resale value of all its asset if it would exit. The former can be represented by the present value of an annuity bond:

P Vt,i = [m + c¯ − ci ]yi

[1 + r]T −t − 1 r[1 + r]T −t

(34)

where t is the age of the fixed asset. The term in front of the fraction is the total annual cash flow for firm i. P Vt,i is the sum of all these discounted future total cash flows that firm i can obtain when it continues to operate in 32

that industry until fixed capital reached the end of its economic lifetime after T −t years. The resulting number reflects how profitability the particular individual firm with its specific efficiency (that is in turn a function of its market share) can continue to operate in the industry. Since market shares and individual costs differ (ci ), every firm will have a different present value even if one would scale this present value by sales or the capital stock. How much sense an industry exit makes depends on the amount of money that the firm can obtain from selling its assets to other competitors in the industry (this is assuming that proceeds can be invested at the normal profit rate in equilibrium and that the particular fixed assets are only used in that industry13 ). The total asset resale value RVt,i is dependent on the current value fixed assets have in equilibrium κt,i for others (what others are willing to pay for it) and the sunk costs (like transaction costs, fees, etc.) expressed as a discount in percent of κt,i , ∂:

RVt,i = [1 − ∂]κt,i

(35)

The crucial point here is what this value of remaining used fixed capital of a certain vintage is. The determination of m as above implies that Kt and κt,i can be computed as the present value of all fixed capital charges m ∗ yi 13 Like

usual, an interlocked system would make the issue much more complicated.

33

that can be obtained.14 This is again the annuity bond valuation formula

κt,i = m ∗ yi

[1 + r]T −t − 1 r[1 + r]T −t

(36)

This is the standard Classical answer to the problem of how equilibrium prices of fixed capital vintages are to be determined. The price of vintage fixed capital represents the present value of all future fixed capital charges (depreciation plus the average profit charge) that can be derived from the application of the fixed asset in the industry under average conditions of production or by the average capital in the industry. This intuition is straightforward under the strong assumptions of the abstract model here where all firms apply fixed capital in exactly the same way. The idea that the industry average level of efficiency of using an asset determines its value also holds and is standard practice when one relaxes that assumption and allows for heterogeneity in the use of fixed capital.15 The crucial point here is that while the profitability of the option to stay in the industry is a function of 14 This

method yields identical results under equilibrium conditions to the alternative and also standard representation as the remaining debt from an annuity loan (see, e.g. Sraffa, 1960, §83). Of course, different depreciation and fixed capital pricing methods may be supported by a classical economist, like one based on a monetary fixed capital concept or linear depreciation, for example (see, e.g. Keil, 2016a). 15 The logic is equivalent to the Classical idea that average costs of production determine the price of output. It is also not clear why and how fixed capital prices could be determined in an alternative way. A fundamental empirical complication is that developed secondhand markets for capital goods are “inevitably missing” and “almost absent from this world” (Schefold, 2011, pp. 182, 189). But there are also logical complications. Should the price be determined by the highest return that the largest firm in the industry could derive from the fixed asset? But this would be assuming perfectionist Neoclassical capital markets and abstract from real existing frictions and physical time that all are present in Classical equilibrium prices that are just centers of gravity. And what about the fact that returns and rates of depreciations are different in different industries whenever the system is interlocked (the same fixed capital asset is used in a different production process)?

34

the relative costs of production of the particular individual firm, the economics of exiting are determined by the value assets have for others in the industry (minus possible transaction costs). As entering another industry or investing funds in financial assets is expected to yield the normal return, firm i will stay in the industry if it can make more profit from continuing its operations in it than from selling its assets at a discount and reinvesting the money at the normal return. In other words, the present value of future returns from continued participation in its own industry, P Vt,i must be larger than the resale value of the assets, RVt,i . The implication is the decision rule:16      exit if P Vt,i < RVt,i       Firm i in its industry will =  be indifferent if P Vt,i = RVt,i          stay if P Vt,i > RVt,i

In first case there might be small sunk costs (low δ) or a large negative profit differential. This makes a fast adjustment possible where firms exit the industry immediately when they make below average profits. In the third case, sunk costs δ might be very large or the profit differential might be relatively small. For such a firm in this type of industry the loss caused by an “expensive exit” (very low resale value RVt,i ) exceeds the disadvan16 The valuation formulas for P V , RV t,i t,i and Kt,i imply that a differential in percent between any of these three that may exist at one period will be the same at all successive periods unless parameters change. Equivalently, they also imply that P Vt,i = Kt,i for all t if ¯ ci = c.

35

tage of making below average profits in the industry (low present value P Vt,i of future profits when “staying”). In this latter case, the firm is locked into its industry. The implication for econometric work is that one should not be surprised to find significant negative coefficients for barrier, concentration or, barrier-concentration interaction variables when profit rate differentials or persistent profit rate differentials are explained econometrically. Of course, this finding requires necessarily the existence of economies of scale, or some other negative size-cost relation. It equally presupposes that some exit barrier is present in the first place. The precise parameter values of the returns to scale, the demand elasticity parameters, the resale discount of fixed capital and the distribution of market shares must have certain values to constitute a trap. Low sunk costs (small δ) will hardly have an impact on the exit decision of firms. An insensitive response of costs to sales (low value of b) and/or a relatively equal market share distribution will not result in major surplus profits and losses. Thus, the message of this article is more differentiated and not that concentration will always and everywhere lead to lower prices and lower profitability for a firm with a given market share in an industry of a given size. The insight is rather that in some cases such a relation can be expected and that the likelihood of this finding depends on very concrete industry characteristics. It is also needless to say that there are always other factors such as disruptive rapid technological change à la Schumpeter (1942) that is pioneered in Classical economics as the dynamic, evolutionary aspect of competition which is at least as important as the static, equilibrating dimension of it (Salvadori

36

and Signorino, 2013). Such dynamics within and outside an industry can be more important in some cases: reality is always a complex totality of many economic and social laws operating simultaneously. It depends on the concrete situation which of these laws is dominating and observable empirically.

III.

Conclusion

The paper illustrates that a negative relation between sales volume and unit costs implies automatically that industry concentration is an indicator for the cost competitiveness of intra-industrial rivals. A negative impact of fewer, larger and more productive rivals on the industry price is possible in a Classical pricing scenario. The presence of high sunk costs can make an industry exit expensive and trap small, less productive firms in an industry (unless other counteracting effects are present). In this case, a higher market share concentration is associated with lower profitability for a firm with a given market share or sales volume. The analysis shows that over the lifetime of an investment, profit differentials are persistent when computed on the basis of total assets and diverging on the basis of remaining real fixed assets that a firm has in an industry. To our knowledge this analysis is the first to consistently explain common empirical phenomena by predicting negative significant effects of industry concentration and barrier variables on profitability and expecting persistence or even divergence of profit rate differentials in some industries 37

during at least some periods. They are paradoxical for traditional mainstream IO models but are made sense of here by applying a fundamentally different theoretical framework. Of course, space limitations and the focus of the study do not allow to discuss in great detail how sensible all of the standard practices in Classical price theory are that appear in this article. Neither is the model an attempt to make a universal claim that concentration of market shares is never problematic and instead always and everywhere associated with a higher intensity of competition. The analysis does, however, prove that concentration can and is even likely to imply lower profitability and more competition (when this is measured by industry output prices) if a small set of realistic conditions holds. Sunk costs and economies of scale clearly exist in many industries. The article also does point to a larger issue: it shows that there is no theoretical reason to generally assume a simple positive industry concentrationprofitability link. The “quantity theory of competition” of mainstream Neoclassical models, according to which one judges the degree of competition by just looking at the number and size of firms, does not seem to hold.

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Table 1: Studies which find the Concentration-Profitability Paradox Article Keil (2016b)

Micro units 2,109 segments

Period 1973-2010

Industries US man. & non-man.

Profit measure pers. profit rate differential

Concentration measure HHI proxy

Gschwandtner (2012)

190 firms

1984-1999

US man.

pers. profit rate differential

CR4

Gschwandtner (2005)

152 firms

1950-1999

US man.

pers. profit rate differential

CR8

Müller (1986)

551 firms

1950-1972

US man. & non-man.

pers. profit rate differential

HHI proxy

Clarke (1984)

105 industries

1970-1976

UK man.

profit margin

CR5

Ravenscraft (1983)

3,186 segments

1975

US man. & non-man.

ROS

CR4

Gale and Branch (1982)

1,486 segments

1970-1979

US man. & non-man.

ROI

CR2 proxy

52 industries

1968

UK man.

cost margin

CR5

29 product brands

1974-1976

UK man.

cost margin proxy

CR5

76 industries

1958-68

UK man.

profit margin

numer of firms

Holtermann (1973)

industries

1963

UK man.

ROA

CR5

Shepherd (1972)

231 firms

1960-1969

US man.

ROE

CR4

Samuels and Smyth (1968)

186 firms

1954-1963

UK man., distrib., mining

ROA

CR5

firms

1941-1948

US man.

ROA

CR4

Geroski (1981) Nickell and Metcalf (1978) Hart and Morgan (1977)

Stigler (1963)

Table lists a sample of articles that detected a negative relation between concentration and profitability in at least some of their regressions. Segment describes the business segment or line-of-business; HHI the Hirschman-Herfindahl Index; CR4 the four-firm concentration ratio; persistent profit rate differential estimate is the unconditional mean of AR(1) processes that model the deviation of individual profit rates from the average of the sample in the respective year. Each firm or segment represents usually a minimum of 5 and on average about 10 primary observations.

Appendix – Neoclassical competition With equations 5 and 10 still holding, Cournot competitors i’s profits are then given by

πi = yi (

α 1 − y − b[y1 + y2 + ... + yn ] − [a − byi ]) β β i

(37)

Taking first order conditions and rearranging yields

yi =

α β

− a + 2byi 2 β1

n 1 X − yj 2

(38)

j=1,j,i

which simplifies to yi =

α − βa − Y 1 − β2b

(39)

since identical firms, yi = yj ∀i, j. Accordingly, one can write α − βa − Y 1 − 2βb

(40)

α − βa 1 − 2βb + n

(41)

Y =n

This simplifies to Y =n

When all firms have identical size, HHI = n1 . The equation can thus be written in terms of the HHI as

Y=

α − βa 1 + HHI(1 − 2βb)

49

(42)

The effect of increasing concentration in simple quantity competition thus depends on the change in variable unit costs induced by a unit change in output, b and the change in demand induced by a unit change in price, β. If their product is less than 0.5, concentration is negatively related to output and positively to price. For parameter values which do not combine extreme economies of scale with a demand curve that approaches perfect inelasticity this case can be assumed to be almost generally applicable. In fact, a very large b (relative to β) would imply a natural monopoly where marginal costs would be zero or even negative. It is clearer when it comes to profitability. Recall the Lerner index for the Cournot model (and other collusion models) from Cowling and Waterson (1976): L=

p − c0 HHI = p −

(43)

An increase in concentration leads to an increase of the profit margin. Its indirect negative effect on (marginal) costs amplifies this. This shows that it is impossible to produce the inverse concentration-profitability relation in a Cournot competition.17

17 The

use of realistic conjectural variations does not change this result.

50