www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember On Industry Struture and Firm Condut in Long Run Equilibrium Prof. Jean-Paul Chavas Department of Agriultural and Applied Eonomis Taylor Hall, University of Wisonsin, Madison, WI 5376 Tel: +-68-6-944 E-mail: jhavas@wis.edu Reeived: September 6, Aepted: September 9, doi:.543/jms.vnp This researh was supported by a USDA grant to the Food System Researh Group, University of Wisonsin, Madison. Abstrat: This paper presents an analysis of long run equilibrium of industry struture and firm ondut allowing for entry and exit, and ost heterogeneity among firms. It investigates the ase of firms ondut/markups that emerges as the stationary equilibrium from long run evolutionary seletion over time. Treating the number of firms as endogenous provides linkages between firms ondut and market struture. The impliations of ost struture for market equilibrium prie, firms ondut and industry onentration are investigated. The effets of fixed ost and entry/exit on long run industry equilibrium are examined. The analysis shows how globalization an help redue the firms exerise of market power, inrease the responsiveness of aggregate supply, and redue prie sensitivity to shoks. It also shows how negleting either entry/exit or adjustments in firm ondut underestimates the aggregate effets of globalization. Keywords: Entry/exit, Long run equilibrium, Heterogeneous firms, Oligopoly.. Introdution The trend toward globalized markets has stimulated muh researh on its eonomi impliations. Globalization is expeted to have two effets on effiieny. First, expanding the sope of a market an fore the least produtive firms to exit and replae them by more produtive firms, thus leading to effiieny gains (e.g., Melitz). These produtivity gains are been found to be large (e.g., Pavnik). The importane of these seletivity effets has stressed the role of entry/exit deisions among heterogeneous firms in industry equilibrium (e.g., Erison and Pakes; Melitz and Ottaviano). Seond, globalization an be assoiated with inreased ompetition. The entry of new firms in an industry an ontribute to reduing the exerise of market power and generate additional pro-ompetitive effiieny gains. The role of imperfet ompetition has been analyzed extensively in previous researh (e.g., Sherer; Tirole; Friedman and Mezzetti). (Note ) But these two effets are not independent: the entry of new firms an generate both produtivity gains and a redution in oligopoly rents. Yet, these two effets have often been examined separately. For example, Melitz, Melitz and Ottaviano, Arkolakis et al., and Feenstra all examine the effets of globalization under entry/exit, but they restrit their analysis to monopolisti ompetition. This neglets possible pro-ompetitive effets of globalization. Alternatively, the effets of market power have been examined by Dixon and Somma, and Muller and Normann for duopoly, and by Dixit (986) and Friedman and Mezzetti for oligopoly. But these studies took the number of firms as given. By assuming an exogenous industry struture, they do not apture pro-ompetitive effets. When globalization is assoiated with inreased ompetition, these pro-ompetitive effets take the form of hanging priing rules that evolve from imperfetly-ompetitive priing (typially in the form of high markups ) toward ompetitive priing (where marginal ost priing applies). This suggests the need to investigate these two effets jointly. In other words, there is a need to examine the joint determination of industry struture and priing rules under entry/exit among heterogeneous firms. This is the main objetive of this paper. Below, we assoiate the hoie of priing rules (markups) with firm ondut. And we fous our attention on long run industry equilibrium. This paper investigates the long run equilibrium of firms in a single-produt industry, treating firm ondut/markups as endogenous and allowing entry/exit of heterogeneous firms. We analyze long run behavior as the stationary outome from evolutionary dynamis. (Note ) We onsider the ase of heterogeneous firms that learn from experimenting with their own ondut and its effet on firm profit. In this ontext, allowing for entry/exit, long run firms ondut and industry equilibrium arise from evolutionary seletion over time. Allowing for entry/exit in the industry, we treat the industry struture as endogenous. (Note 3) This allows various market strutures as well as firm onduts to arise, going ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember from monopoly to oligopoly to ompetitive markets. This provides useful information on the determinants of both firms ondut and industry struture in long run equilibrium. The analysis allows for non-onstant marginal ost and firm heterogeneity involving both fixed ost and variable ost. The ost heterogeneity aross firms an ome from two soures: different prodution tehnology, and/or different aess to market. The first soure means that some firms have aess to improved tehnology that redues their ost of prodution and gives them some omparative advantage. The seond soure means that transation osts vary aross firms. This an be due to loation differenes (e.g., different transportation ost), differential aess to market information, and/or different trade poliy impats (e.g., with quotas, taxes or tariffs/subsidies that vary aross firms). The effets of hanging transation osts are relevant in the ontext of studying the globalization of markets. Indeed, transation osts redue inentives to produe and trade. By reduing the number of market partiipants, they an ontribute to the reation of loal markets that fail to be integrated in a global eonomy. In this ontext, the development of global markets is supported by a redution of transation osts assoiated with lower transportation and information osts, and by a move toward market liberalization poliies. Our analysis provides useful information on how ost strutures an affet priing and industry behavior in global markets. Finally, while there is some anedotal evidene that prie instability may inrease in thin and onentrated markets, it remains unlear when suh relationships may develop. The paper examines how market onentration an affet supply responsiveness and prie sensitivity. This paper makes several ontributions. First, it refines the role played by both fixed ost and non-onstant marginal ost in the long run equilibrium of heterogeneous firms under entry/exit. Seond, the paper investigates the determinants of firms ondut/markup in long run equilibrium. It analyses how the linkages between firms ondut (representing the exerise of market power) and market strutures (represented by the number of ative firms) are affeted by ost strutures and market onditions. In partiular, it examines how Bertrand/ompetitive priing an emerge through evolutionary seletion over time even when the number of ative firms remains relatively small. Third, analyzing the interations between entry/exit and firm ondut in long run equilibrium provides useful information on the eonomis of globalization. It shows how globalization an help redue the firms exerise of market power, inrease the responsiveness of aggregate supply, and redue prie sensitivity to shoks. It also shows how negleting either entry/exit or adjustments in firm ondut underestimates the aggregate effets of globalization. This stresses that a searh for larger gains from globalization should inlude the joint determination of entry/exit and firm ondut/markups. The paper is organized as follows. Setion presents the model. Setion 3 analyzes the long run market equilibrium under entry/exit of heterogeneous firms, with impliations for linkages between firms ondut and market struture. Setion 4 investigates the properties of steady state industry behavior when both the number of ative firms and the exerise of market power are endogenous, with speial attention given to the role of fixed ost. Setion 5 disusses impliations for the eonomis of globalization. Finally, setion 6 presents onluding omments.. The model Consider an industry omposed of firms produing a homogenous produt with an aggregate demand given by the prie dependent demand p(y), where Y denotes aggregate quantity onsumed during a given time period. The quantity Y an be produed by a set M of potential firms, M = {,, m}. The i-th firm produes output y i at ost C i (y i ). Our analysis fouses on the following speifiation. First, we assume that the demand funtion is linear: p(y) = Y, () with <. Seond, we assume that the ost funtion of the i-th firm satisfies: C i (y i ) = i + i y i + ½ y i, for y i >, () =, for y i =, where i denotes fixed ost i > and, i M. Our analysis distinguishes between inative firms (when y i = ) and ative firms (when y i > ). When >, equation () allows for non-onstant marginal ost. This relaxes the assumption of onstant marginal ost that has sometimes been imposed in previous researh (e.g., Melitz). From (), the tehnology faing the i-th firm an exhibit inreasing returns to sale (IRTS)onstant returns to sale (CRTS), or dereasing returns to sale (DRTS) depending on whether < i /y i = i /y i, or > i /y i, respetively. This shows that the ost speifiation in () is flexible in its representation of returns to sale. For example, the tehnology of the i-th firm would exhibit global IRTS when fixed ost i is positive and = ; it would exhibit global CRTS when i = = ; and it would exhibit Published by Siedu Press 3
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember global DRTS when i = and >. Importantly, while is treated as onstant, firm heterogeneity is aptured by the ost parameters i and i. This allows for heterogeneity in both fixed ost i and variable ost (through i ). And the heterogeneity in fixed ost i allows returns to sale to differ aross firms. As the ost parameters ( i i ) vary among the m potential firms, we denote their distribution by the distribution funtion F(, ). Throughout, we assume that the market is large enough to sustain at least one ative firm. Our analysis addresses the determination of firm ondut and industry struture allowing for entry/exit among heterogeneous firms. In this ontext, the speifiation given in ()-() provides a reasonably flexible representation of both supply and demand onditions. We want to allow a generi representation of firms behavior. This an range from ompetition to oligopoly behavior, and to monopoly priing. We start with the lassial Lerner index representing priing behavior. The Lerner index assoiated with the i-th ative firm (with output y i > ) is L i [p(y) - C i (y i )/y i ]/p(y), (3a) i M. Using ompetition as benhmark, the Lerner index L i in (3a) measures the relative prie enhanement obtained due to the i-th firm s exerise of market power. L i = identifies a ompetitive firm where marginal ost priing applies. L i > ours when the i-th firm has market power as prie exeeds its marginal ost. In general, a rise in L i is interpreted as an inrease in the exerise of market power by the i-th firm. Equation (3a) defines the mark-up priing implemented by the i-th firm, refleting its ondut. Below, we will treat this ondut as endogenous and investigate its linkages with industry long run equilibrium. We will work with the losely related representation v i L i /s i -, (3b) where -[lnp(y)/ln(y)]- > is the prie elastiity of demand, and s i y i /Y is the market share of the i-th firm. It follows that ompetitive markets (where L i = ) are assoiated with v i = - for all ative firms. Alternatively, under imperfet ompetition (where L i > ), we have v i > -. Equation (3b) shows expliitly the role played by the prie elastiity of demand and the market share s i. Given L i ( + v i ) s i /, an inrease the Lerner index L i an be assoiated with a rise in the market share s i, a rise in v i, and/or a more inelasti demand (i.e., a deline in ). In general, v i measures departures from marginal ost priing for the i-th firm. As shown by Dixit (986) and others, speifi values of v i an apture firm ondut under alternative strategi games. This inludes v i = -, whih orresponds to Bertrand prie ompetition where there is no antiipated prie response to the i-th firm supply. It also inludes v i =, whih orresponds to a Cournot quantity game where the i-th firm expets no quantity response from other firms to its own supply deision. Finally, it inludes v i = ji y j /y i, whih orresponds to market ollusion where all firms behave as a artel implementing monopoly priing. This shows that v i in (3b) provides a onvenient representation of firms ondut (e.g., Genesove and Mullin). For the i-th ative firmombining (3a) and (3b) yields G i (y i, Y, v i ) p(y) - C i (y i )/y i + y i ( + v i ) [p(y)/y] =, (4a) or, under the speifiation ()-(), G i (y i, Y, v i ) - Y - i - y i - y i ( + v i ) =. (4b) We assume that [ + ( + v i )] >. (Note 4) It follows that G i (y i, Y, v i ) is stritly dereasing in y i. Then, solving equation (4b) for yi gives by y a i (Y, v i ) = [ - Y - i ]/[ + ( + v i )], with assoiated firm profit a a i (Y, v i ) p(y) y i - i - i y a i - ½ (y a i ) = - i + [½ + ( + v i )] [( - Y - i )/( + ( + v i )]. Sine no firm would produe under negative profit, it follows that a i (Y, v i ) for any ative firm. Thus, given Y and v i, the deision of the i-th firm an be written as y + i (Y, v i ) = y a i (Y, v i ) if y a i (Y, v i ) > and a i (Y, v i ), (5a) = otherwise, or, under the speifiation ()-(), y + i (Y, v i ) = [ - Y - i ]/[ + ( + v i )] if i K i (Y i, v i ), (5b) =, otherwise, 4 ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember where [ + ( + v i )] >, and K i (Y i, v i ) - Y i α( vi), with K i / Y < and K i / v i < (= ) ½ α ( v ) when i > (= ), i M. Conditional on Y and on firm ondut v i, equations (5a)-(5b) give the optimal deision of the i-th firm whether it is ative or not. These equations show that the i-th firm would beome inative (with y + i (Y, v i ) = ) when the marginal ost parameter i is suffiiently high (implying that y a i (Y, v i ) ), or if profit a i (Y, v i ) beomes negative (e.g., due to high fixed ost i ). Similarly, the onstraint i K i (Y i, v i ) in (5b) imposes the non-negativity of firm profit: a i (Y, v i ). It gives the intuitive result that the i-th firm would be ative (with y + i (Y, v i ) > ) only if both marginal ost and fixed ost are not too high. Note that (5b) implies that y + i / Y <, (Note 5) and y + i / v i < for all ative firms. Sine equation (5b) identifies whih firm is ative, it an be used to haraterize market equilibrium under firm entry/exit, inluding the equilibrium number of ative firms. (Note 6) Throughout, we take the number m of potential firms and the distribution funtion F(, ) as exogenous. We assume that F(, ) is a ontinuous distribution funtion. This assumption is partiularly onvenient for our analysis (e.g., it was also made by Melitz). It simplifies the haraterization of market equilibrium (see below). With a finite number of firms, F(, ) being a ontinuous funtion means that the ost struture of the i-th firm needs to be haraterized by a neighborhood ( i, i ) R, where F is a mapping from im ( i, i ) to [, ]. For fully ative firms that make positive profit, this makes no substantial differene: ( i i ) in equation (5b) just needs to be reinterpreted as a representative point in ( i, i ) that exatly repliates the behavior of the i-th firm, i M. But it makes a differene for marginal firms. Marginal firms are firms that are trying to enter the industry while exhibiting near-zero profit. They belong to the set jm {j: i(m-j) y + i (Y +, v i ) < Y + < im y + i (Y +, v i ), Y + argmax Y { im y + i (Y, v i ) Y}. Treating F(, ) as a ontinuous funtion amounts to allowing the marginal firm(s) to enter (or exit) the industry slowly by produing only a fration of their fully ative output. By allowing the marginal firm(s) to be partially ative, it means that the number of ative firms an be measured as a real number (instead of an integer). Let the vetor v = (v,, v m ) V m [, ] m represent the ondut of all firms. Thenonditional on v, define market equilibrium as Y * (v) Max Y {Y: Y S(Y, v), Y R + }, (6a) where S(Y, v) is the aggregate prodution defined as (using equation (5b)): S(Y, v) m K( ) i [ - Y - ~ ]/[ + ( + v i )] df( ~ ~ ), (6b) with K() denoting the non-negative profit onstraints { K i (Y, v i ): (, ) ( i, i ), i M}. For a given v, equation (6a) identifies Y * (v) as the largest aggregate demand where feasibility holds, i.e. where aggregate demand does not exeed aggregate supply. F(, ) being a ontinuous distribution funtion, it follows from (6b) that S(Y, v) is ontinuous and dereasing in Y, and that the maximization problem in (6a) has a unique solution Y * (v) satisfying Y * (v) = S(Y * (v), v). For a given v, this implies both the existene and uniqueness of market equilibrium. In turn, from (5a)-(5b) and onditional on v, it follows that the market equilibrium prodution deision of the i-th fully ative firm is given by y * i (v) = y + i (Y * (v), v i ), (7) i M. And the number of ative firms in the industry is represented by the real number n satisfying n * (v) n(y * (v), v), (8a) where n(y, v) m K( ) df(, ), where again K() denotes the non-negative profit onstraints. (8b) Published by Siedu Press 5
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember Allowing for entry/exit of heterogeneous firms, equations (6a) and (8a) define the market equilibrium of the industry, onditional on firms ondut v. This inludes the aggregate quantity Y * (v) given in (6a) as well as the number of ative firms n * (v) given in (8a). The determinants of v will be examined in setions 3-4 below. What are the impliations of the firms ondut v for aggregate welfare? Consider the ase where all ative firms make a positive profit and aggregate welfare is measured by the total surplus: * Y( v) W = p(z) dz - im C i (y * i (v)). Then, using equations (4a) and (7), the welfare impat of a hange in the ondut v i of the i-th ative firm is given by W/v i = jm [p(y) - C j (y j )/y j ] (dy * j /dv i ), evaluated at Y * (v) and {y * i (v): i M}, (9) = if v j = - for all ative firms, < if v i > -, dy * i /dv i <, and v j -, dy * j /dv i for all j i. This gives the well known result that, to the extent that it ontributes to a redution in supply, (Note 7) any inrease in the exerise of market power (as refleted by a rise in v i from -) has adverse effets on aggregate welfare. The presene of these adverse effets helps motivate the analysis of the determinants of firms ondut, as investigated next. 3. The determination of firms ondut The previous setion has investigated how firms ondut v affets market equilibrium. This setion explores the reverse linkages: how industry struture affets firms ondut. Suh linkages are at the ore of the traditional Struture-Condut-Performane approah to industrial organization (e.g., Sherer). We analyze how the number n of ative firms in the industry influenes the firms ability to exerise market power and affet markups (as represented by v). While this setion treats the number of ative firms n as given, note that the joint determination of n and v will be addressed in setion 4 below. We assume that the firms behave non-ooperatively, where eah firm hooses its own ondut independently of others. (Note 8) Under firm heterogeneity, we investigate the ase where firms learn by experimenting with their own ondut and its effet on firm profit. While eah firm an hoose alternative strategies in the short run, our fous is on the long run, as firms deisions about their own ondut evolve toward a steady state equilibrium. We show that the behavior of the firms onverges as eah firm eventually disovers what works best for itself. In analyzing the properties of long run equilibrium ondut, we obtain useful insights into the linkages between industry struture and firms ondut. In presenting our arguments, we will make use of the properties of reations funtions representing interations among ative firms in the industry. Let the set of ative firms be N = {j: y j >, j M} M. Treating N as givenonsider the market learing ondition: Y = y i + x i, where x i ji y j denotes the prodution of all firms but the i-th one. Let I j = for fully ative firms produing a positive output and generating a positive profit, let I j = for inative firms, and let I j (, ) denote the fration of output produed by the partially ative marginal firm(s) (as disussed above). Taking the industry struture N as given, it follows that x i = ji I j y + j (y i + x i, v j ), () whih an be solved for x i, giving the reation funtions x r i (y i, v N-i ), where v N-i = {v j : j i, j N}, i N. Note that x r i (y i, v N-i ) depends on the ondut of all ative firms exept the i-th one. For a given N, the funtion x r i (y i, v N-i ) satisfying () measures the equilibrium reation of other firms, x i, to the deision of the i-th ative firm, y i, i N. In general, the reation funtion x r i (y i, v N-i) depends on y i, its slope x r i (y i, v N-i )/ y i measuring the marginal response of other firms to the i-th firm prodution, i N. (Note 9) We now analyze the determinants of ondut v N = {v j : j N} V N, where the feasible set V N restrits eah v j to be in the interval [-, ]. The questions are: How does firms ondut v N hange over time? And to what values might it onverge in the long run? Denote the i-th firm profit by: i (y i, x i ) p(y i + x i ) y i - C i (y i ). We make the following assumption: Assumption A: At time t, denote the ondut of the n ative firms by v N,t = (v,t,, v n,t ). Assume that the ondut of the i-th firm evolves over time as follows v i,t+ (v N-i,t ) = ( - vi,t ) v i,t + vi,t v + i (v N-i,t ), (a) where 6 ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember v + i (v N-i,t ) argmax vi { i (y * i (v N,t ), x r i (y * i (v N,t ), v N-i,t ): v N,t V N }, (b) with vi,t [, ] for some (, ], i N. Assumption A states that eah ative firm will modify its urrent ondut v i,t in the diretion of inreasing its profit. This seems both intuitive and reasonable. It is quite general. Under non-ooperative behavior, it lets eah ative firm hoose its own ondut. It allows for alternative short-term firm ondut and its evolution over time. And it allows for omplex interations among firms. Below, we fous our attention on long-term equilibrium of firms ondut generated from the evolutionary dynamis in (a)-(b). Under assumption A, firms ondut evolves over time as v N,t+ (v N,t ) (v,t+ (v N-,t ),, v n,t+ (v N-,t )), where v i,t+ (v N-i,t ) is given in (a). For some initial ondition v N,, the forward path of firms ondut is v * N,t (v N, ) = v N,t (v N,t- ( v N, (v N, ))). Assuming that it existsonsider the limit v * (N) (v * (N),, v * n (N)) lim t v * N,t (v N, ). This identifies the long-run ondut of ative firms {v * i (N): i N} in a steady sate equilibrium under free entry/exitonditional on industry struture N. Note that it allows the ondut v * i (N) to vary aross firms. Under (a)-(b) and onditional on the number n of ative firms, the existene, uniqueness and analytial properties of this long run equilibrium are investigated next (See the proof in the Appendix). Proposition : For a given set N of ative firms, assume that A holds. Under the speifiation ()-(), - A long run steady state equilibrium for ondut v N exists and is unique. - The long run steady state equilibrium for v N is given by v * r xi i = (y i, v N-i ), i N. y - The v i * s are the same for all ative firms and satisfy i v * i = v * (n) = - ½ (n + / ) + ½ (n /α ) 4(n ), () i N, with v * /n = -½ + ½ (n /α ). (3) (n /α ) 4(n ) Conditional on n, proposition establishes the existene and uniqueness of a long run equilibrium for firms ondut. And it provides a formal linkage between market struture (as represented by n) and firms ondut (as represented by v * (n)). r i Note that v * i = x (yi, v N-i ) implies that the v * i s are also the onsistent onjetures disussed by Bresnahan, Perry, and yi Dixit (986). Thus, Proposition shows that the long run equilibrium leads to onsistent onjetures among ative firms. Dixon and Somma, and Müeller and Normann obtained similar results in the ontext of duopoly (where n = ). Thus, Proposition generalizes their results to oligopoly situations, with an arbitrary number of heterogeneous firms. It provides an eonomi rational for onsistent onjetures. Indeed, under the speifiation ()-(), Proposition shows that, if more profitable onjetures tend to beome more ommon, idential onsistent onjeture is the unique evolutionary stable strategy. Under assumption A, this applies irrespetive of the firms short-term strategies. In this ontext, idential onsistent onjetures emerge in the long run through evolutionary seletion over time. Equations () and (3) show analytially how the firms ondut v * varies with the strutural parameters ( / ) and the number of ative firms in the industry (n). The relationship between v * and n is of partiular interest as it makes firms ondut depend on industry struture. Equations ()-(3) imply the following results. Corollary : Under the speifiation ()-() with n, a) the firms ondut v * (n) satisfies - v *, with v * = if n =, Published by Siedu Press 7
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember for a finite /, v * as n, for a finite n, v * as / ; for n, v * as /. b) In addition, v * /n satisfies - v * /n, with v * /n = -/( + / ) if n =, for a finite /, v * /n as n, for a finite n, v * /n as /, / implies v * /n -½ + ½ (n - )/ n - for n, - if n <, if n >. Corollary establishes the properties of ondut v * (n) as the number n of ative firms hanges. From a), v * is in general non-positive and bounded between and. It attains its lower bound (v * = ) when the number n of ative firms is large. This orresponds to Bertrand ompetition, where firms antiipate no prie response from hanging supply. And the ondut v * (n) attains its upper bound (v = ) under monopoly (with n = ). In between these two extremes, inreasing the number n of ative firms tends to redue v * (v * /n from b)). This is intuitive: the potential to exerise market power beomes stronger (weaker) when the number of ative firms is smaller (larger). In addition, from Corollary a, the firms ondut v * tends to when / beomes large. This orresponds to ases where marginal ost is rising sharply ( = large) and/or where demand is very prie-responsive (with Y/p = / = large). In suh situations, as long as the number n of ative firms is finite, Cournot priing is (approximately) satisfied irrespetive of industry struture. (Note ) Alternatively, given n, firms ondut v * (n) tends to when / beomes lose to. This inludes ases where marginal ost is onstant ( =, with large supply response), (Note ) and/or where demand exhibits little prie responsiveness (with Y/p = / = small). In suh situations, as long as n, Bertrand ompetition is (approximately) satisfied irrespetive of industry struture. Finally, from Corollary b, the marginal effet of n on v * beomes small (v * /n ) when / is lose to zero and n >. And v * /n when / beomes very large. It means that, when n > hanges in industry struture (i.e.hanges in n) affet firms ondut only in situations where / takes on moderate values (i.e., neither too small nor too large). For example, assuming onstant marginal ost (with ) would basially remove the possibility for firms to exerise market power when n > (Kamien and Shwartz). This stresses the importane of the ost struture in the study of oligopoly behavior. A ontestable market has been assoiated with free entry and exit, idential produers, and potential entrants exhibiting Bertrand priing (Baumol et al.). Note that idential firms are obtained as a speial ase of our model when i and i are the same for all firms. Corollary shows how firms ondut an generate Bertrand ompetition. Bertrand priing (with v = -) an be obtained under at least two senarios. First, from Corollary a, v * = - if the number n of ative firms is suffiiently large. Seond, Bertrand ompetition (v = -) is generated under onstant marginal ost (where ) when n. In either senario, under entry and exit, a ontestable market would arise in long run equilibrium. The first senario (n = large) is the lassial ase of a ompetitive market. The seond senario arises under more general onditions: as long as marginal ost is onstant, it applies under various industry strutures exhibiting at least two ative firms (n ). In ontrast to Baumol et al., note that our approah does not assume Bertrand priing. These results are illustrated in Figure, whih presents the funtion v * (n) for seleted values of the parameters k /. Figure shows how Bertrand priing an apply under general onditions when / is small. This douments how Bertrand/ompetitive priing an arise over time through evolutionary seletion even when the number of ative firms remains relatively small. However, Figure also indiates how firm ondut an depart from Bertrand priing when the ratio / rises. Again, this illustrates how the ost struture an affet the exerise of market power. 4. Industry Behavior In this setion, we explore long run industry behavior with a fous on the joint determination of firms ondut/markup and firm entry/exit under the speifiation given in ()-(). Reall that we allow for ost heterogeneity among firms, where the distribution of the ost parameters (, ) is given by the distribution funtion F(, ). Below, we investigate how hanges in the ost struture affet industry equilibrium. We will fous our attention on hanges in, the mean of fixed ost, and in, the mean of variable ost aross all firms (inluding both ative firms and potential entrants) in the industry. Changes in the mean (or ) are equivalent to hanges in (or ) affeting all firms in the industry. Suh fous will be of interest below as the aggregate effets of hanges in ost affeting a subset of firms 8 ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember are qualitatively similar to the orresponding effets when all firms are affeted. In the next setion, this will allow us to interpret our results in the ontext of evaluating market globalization issues. To simplify our analysis, we assume that the distribution funtion F(, ) is twie differentiable. In this ontext, we analyze long run industry behavior under three senarios: ) the ase where the firms ondut v is exogenous; ) the long run equilibrium ase when v is endogenous under long run equilibrium, but in the absene of fixed ost; and 3) the general ase of endogenous firms ondut in the presene of fixed ost. 4. Case : The ase of exogenous firms ondut First, we onsider long run industry behavior when firms ondut is treated as given. While restritive, the analysis of this senario will provide a stepping-stone toward a more omplete analysis of firm ondut and industry behavior presented below. Using the results of Proposition, we fous our attention on the ase where v i = v for all ative firms. Thenonditional on v, the market equilibrium onditions are given by the aggregate quantity Y * (v) in (6a), and by the number of ative firms n * (v) in (8a). The assoiated equilibrium prie is p * (v) p(y * (v)). From (6a), the aggregate quantity Y * (v) is given by the value Y that satisfies the market equilibrium ondition: Y = S(Y, v). The properties of Y * are presented next. They inlude the effets of hanging ondut v, mean fixed ost, mean variable ost, as well as the demand shifter. See the proof in the Appendix. Lemma : The aggregate quantity Y * (v) in (6a) satisfies a) Y * /v <, b) Y * / <, ) Y * / <, d) Y * / (, / ). Lemma shows the fators influening the market equilibrium aggregate quantity Y * onditional on ondut v. Result a) shows that inreasing v redues industry supply. Interpreting a rise in v as an inrease in market power gives the intuitive result that the exerise of market power implies a redution in aggregate supply. Results b) and ) imply that inreasing either mean fixed ost ( ) or marginal ost ( ) provides a disinentive to produe at the industry level. However, the soures of these adjustments differ. Higher marginal ost has two additive effets: it redues the supply from inumbent firms; and it provides an inentive for firms to exit (see (B8d) in the Appendix). In ontrast, higher fixed ost has only one effet: it just provides an inentive for firms to exit (see (B8) in the Appendix). Indeed, from equation (5b), fixed ost does not affet the behavior of inumbent firms that remain ative and profitable. Finally, result d) shows that an inrease in demand (represented by a rise in ) tends to stimulate the market equilibrium aggregate quantity Y * (v), the marginal impat being bounded between and /. The prie equilibrium p * (v) is given by p * (v) Y * (v). Using Lemma, we obtain the following results. Proposition : The market equilibrium prie p * (v) satisfies a) p * /v >, b) p * / >, ) p * / >, d) p * / (, ). Proposition shows the fators influening the market equilibrium prie p * onditional on ondut v. Result a) shows that inreasing v inreases prie. Intuitively, a rise in market power tends to inrease markup and prie. Results b) and ) imply that inreasing either fixed ost ( ) or marginal ost ( ) ontributes to a higher prie. Finally, result d) shows an inrease in demand (represented by a rise in ) tends to inrease prie, although the marginal prie inrease is bounded between and. The market equilibrium number of ative firms n * (v) n(y * (v), v) is given in equations (8a)-(8b). This gives n * /(v, ) = n/(v, ) + (n/y) ( Y * / (v, )), (4) Published by Siedu Press 9
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember Equation (4) deomposes the effet of (v,, ) on n * into two additive omponents: a diret effet n/(v,, ), holding aggregate output Y onstant; and an indiret effet (n/y)( Y * / (v,, ))apturing the indued adjustment through Y. The properties of n * (v) are presented next. See the proof in the Appendix. Proposition 3: The number of ative firms given by n(y, v) and n * (v) in (8a)-(8b) satisfies a) n/y <, b) n * /v > n/v = in the absene of fixed ost (where i = for all firms), < in the presene of fixed ost (where i > for all firms), ) n * /( ) > n/( ) <, as (n/y)( Y * / ( )) -n/( ), d) < n * / < n/ =-( n/ Y)/. By identifying the fators influening the number of ative firms, Proposition 3 provides useful information on the determinants of entry and exit in the industry (onditional on v). In partiular, result b) illustrates the role of fixed ost. It shows two results. First, in the absene of fixed ost, it states that n * / v >. In this ase, the diret effet in (4) vanishes (with n/ v = ), and a higher v simulating inreased market power always indues entry (as it redues aggregate supply ( Y * / v < ), whih inreases prie). Interestingly, in the presene of fixed ost, n * / v is not neessarily positive (e.g., it an be negative when the negative diret effet, n/v <, dominates the indiret effet in (4)). Seond, result b) shows that n * /v > n/v in general (i.e., with or without fixed ost). It reflets that the indiret effet of v in (4) is always positive, whih tends to make the impat of v on n * more positive. Result ) shows that the effets of ost on the number of ative firms n * an be omplex. It gives three important findings. First, it states that the diret effet n/(, ) is always negative: for a given Y, inreasing ost (either fixed or marginal) provides an inentive for firms to exit the industry. Seond, result ) shows that n * /( ) > n/(, ). This reflets the fat that the indiret effet in (4) is always positive, (n/y)( Y * / ( )) > : a higher ost tends to derease aggregate supply and inrease prie, whih in turn provides an inentive for firms to enter. As a result the net effet of hanging or on the number of ative firms n * an be either negative or positive depending upon whether the diret effet dominates or not. This gives the third finding: n * /(, ) -n/(, as (n/y)( Y * / (, )) ). Under a general ost distribution F(, ) aross firms, this illustrates the omplex determination of long run industry struture under hanging ost struture. It also shows that inreased ost tends to stimulate exit, n * /(, ) <, when the diret effet n/(, ) < dominates in (4). Below, we will all this a normal situation mostly on intuitive ground. (Note ) This will prove relevant in the disussion presented below. Finally, result d) shows that the net effet of expanding demand (as represented by the parameter ) on the number of firms n * (v) is unambiguously positive. And its marginal effet n * / is bounded between and ( n/ Y)/. 4. Case : The ase of endogenous firms ondut in the absene of fixed ost Case has examined the properties of industry behavior holding the firms ondut v onstant. Under entry/exit, it has allowed the number of firms in the industry to adjust in response to hanges in ost or demand. But holding v onstant is restritive: firms ondut/markups an learly hange with the struture of the industry. We now extend the analysis to the ase where ondut v is endogenous. Relying on Proposition, we fous our attention on the long run equilibrium ondut, i.e., on the firms ondut given by v * (n) in equation (). Case restrits the analysis to situations where there is no fixed ost. This provides an important simplifiation. From Proposition 3b, in the absene of fixed ost, the number of ative firms n(y, v) in (8) no longer depends on v. Then, market equilibrium is given by equations (8) and (), where Y = S(Y, v * (n(y)). Define S * (Y) S(Y, v * (n(y))). It ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember follows that the market equilibrium aggregate quantity is the solution Y e to the equation Y = S * (Y). Note that S(Y, v) is dereasing in Y and v. In addition, v * (n) is non-inreasing in n (from Corollary b) and n(y) is dereasing in Y (from Proposition 3a). It follows that S * (Y) is dereasing in Y. Under assumption A, this implies that Y = S * (Y) has a unique solution Y e. Then, the market prie is p e = - Y e, the equilibrium number of firms is n e = n(y e ), and the long run equilibrium ondut is v e = v(n e ). To illustrate the impliationsompare the market equilibrium onditions of ase and ase. They are: Y = S(Y, v), where S(Y, v) is the equilibrium aggregate supply in ase, v being treated as exogenous; and Y = S(Y, v * (n(y))) S * (Y) in ase (i.e., in the absene of fixed ost, and with v * (n) being given in ()). The properties of v * and n have been examined in Corollary and Propositions 3, respetively. We have S * /Y = S/Y + (S/v)(v * /n)(n/y), (5) where S/Y < from equation (B8a) in the Appendix, S/v < from equation (B8b), v * /n from Corollary b, and n/y < from Proposition 3a. This generates the following result. Proposition 4: In the absene of fixed ost ( = ), the equilibrium aggregate supply funtions S(Y, v) and S * (Y) satisfy S * /Y S/Y <. With Y being the aggregate quantity demanded, Proposition 4 an be interpreted in terms of the responsiveness of aggregate supply to hanging demand onditions. It implies that aggregate supply is more responsive (in absolute value) to hanging demand onditions under ase than under ase. It shows that allowing for adjustments in market struture (as represented by n(y)) and in firms ondut (as represented by v * (n) in equation ()) tends to stimulate aggregate supply response. Alternatively, it indiates that negleting the entry/exit proess and the hanging struture of an industry, along with the assoiated hanges in firms ondutan result in underestimating the magnitude of supply adjustments to hanging demand onditions. This stresses the importane of a proper understanding of the entry/exit proess and its linkages with firms ondut. In addition, under ase (where = in the absene of fixed ost), we have S/Y = n /α (v) from (B8a). Then, equation (5) beomes S * /Y = n /α (v) + (S/v)(v * /n)(n/y). (6) This shows how industry struture (as represented by the number n of ative firms) relates to the responsiveness of aggregate supply S * /Y. The first term in (6) indiates that an inrease in n redues S/Y, and thus inreases the responsiveness of aggregate supply. In addition, when n is greater than and large and/or ( / ) is small, then v approahes - (from Corollary a), ( v * / n) approahes (from Corollary b), and the seond term in (6) beomes negligible. In this ase, any inrease in n always stimulates the responsiveness of supply to hanging demand onditions, S * /Y. This result is summarized next. Lemma : In the absene of fixed ost ( = ), when n is large and/or ( / ) is small, then more ompetitive industry strutures (orresponding to an inrease in n) ontribute to stimulating supply response. Next, we onsider the effets of the demand shifter. In the absene of fixed ost, the market equilibrium is given by the value Y e that solves Y = S(Y, v * (n(y))) S * (Y). Applying the impliit funtion theorem yields Y e / = [ - S * / Y]- ( S * / ), = [ - S * / Y]- (- S * / Y)/ (, / ), (7) where S * / = -( S * / Y)/. Equation (7) shows that the marginal impat of the demand shifter on the market equilibrium aggregate quantity Y e, Y e /, is positive and bounded between and (/ ). With p = - Y, this implies p e / = - (Y e / ) (, ). This is intuitive: any inrease in demand (represented by a rise in ) tends to inrease the equilibrium prie p e. From (6), equation (7) also shows how Y e / depends on the struture of the industry (through n) and on firms ondut (through v). In the absene of fixed ost, and when n is large and/or / is Published by Siedu Press
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember small, we have seen that S * /Y < tends to derease with n (from Lemma ). In this ase, Y e / in (7) inreases with n. With p e = - Y e where p e is the equilibrium prie, it follows that p e / = - Y e / dereases with n. These results are summarized next. Proposition 5: In the absene of fixed ost ( = ), a) < p e /, b) when n is large and/or ( / ) is small, then p e / tends to derease with n. In the absene of fixed ost, result a) shows that the equilibrium prie p e inreases with an exogenous rise in demand (represented by an inrease in ). However, the supply response is suh that the indued prie inrease tends to be less than the original shift in demand. Result b) shows that, if in addition n is large and/or / is small, then the marginal prie effet p e / dereases as the number n of ative firms rises. Alternatively, as n delines, this prie responsiveness would inrease. This shows that the responsiveness of prie adjustments to exogenous shoks is inversely related to the number of ative firms in the market. Thus, a dereasing market onentration would ontribute to reduing the prie effet of a hange in. Alternatively, thin or onentrated markets (where n is low) would be haraterized by greater prie sensitivity to market hanges. This disussion indiates that inreasing (dereasing) market onentration would be assoiated with a higher (lower) prie sensitivity to exogenous shoks. 4.3 Case 3: The ase of endogenous firms ondut under fixed ost What happens if we introdue fixed osts in ase? In the presene of fixed osts, the number of ative firms n(y, v) depends in general on the firms ondut v (from Proposition 3b). In this ase, the determination of the equilibrium number of ative firms beomes more omplex. This illustrates the presene of important interations between fixed osts, market struture, and industry behavior. To see that, given n * (v) in (8a) and v*(n) in (), let g(n) n * (v * (n)). Then, the market equilibrium number n e of ative firms must satisfy n e = g(n e ). Assuming that the market is large enough to support at least one ative firm, (Note 3) a suffiient ondition for the equation n = g(n) to have a unique solution for n is that g/ n ( n * / v)( v * / n) <. The ondition g/ n < is always satisfied if v * / n =. This obviously holds in ase above. From Corollary b, the ondition v * / n = also holds under onstant marginal ost ( ) and n >. This indiates how assuming onstant marginal ost an greatly failitate the haraterization of long run market equilibrium. (Note 4) Finally, given v * / n [-, ] from Corollary b, the ondition g/ n < is satisfied if n * / v > -. Thus, in the presene of fixed osts, a suffiient ondition to have a unique solution for the equilibrium number of firms ne is that n * / v > -. (Note 5) Below, we assume that g/ n <. Then, applying the impliit funtion theorem to n = g(n), we obtain the following properties of market equilibrium number ne of firms with respet to mean fixed ost, mean variable ost, and demand shifter. Lemma 3: Assume that g/ n <. In the presene of fixed osts, the market equilibrium number ne of firms satisfies where n e / (,, ) = [ - g/ n] - n * / (,, ), (8) a) n e / = sign{ n * / } >, b) n e / (, ) = sign{ n*/ (, )}. Assuming g/ n <, equation (8) states that n e / (,, ) is of the same as n * / (,, ). Noting that n * / (, -[ n/ Y]/ ) (from Proposition 3d), this generates result a): n e / >. Thus, expanding demand (as represented by a rise in the parameter ) has always a positive effet on the equilibrium number of ative firms ne. Proposition 3 also showed that the effets of hanging mean osts ( ) on n * an be either negative or positive (depending on whether the negative diret effets n/( ) dominate the positive indiret effets ( n/ Y)( Y * / ( )) in (4)). From result b), similar results apply to the equilibrium number ne of firms. In our above disussion, we haraterized as normal a situation where n * / (, ) <. It follows from b) that inreasing mean osts would tend to stimulate exit, n e / (, ) <, under a normal situation. ISSN 93-3965 E-ISSN 93-3973
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember With ne denoting the equilibrium number of firms, the equilibrium aggregate quantity is then given by Y e = Y * (v * (n e )). This gives Y e / (,, ) = Y * / (,, ) + ( Y * / v) ( v * / n) ( n e / (,, )), (9) Equation (9) evaluates the effets of mean fixed ost, mean variable ost, and the demand shifter on the market equilibrium quantity Y e. It deomposes the effets of (,, ) on Y e into two additive effets: the diret effets Y * / (, ), whih hold firm ondut v onstant; and the indiret effets ( Y * / v) ( v * / n) ( n e / (, )), whih apture the endogenous adjustments in firm ondut. The diret effets Y * / (, ) were evaluated in Lemma : Y * / (, /α ), and Y * / (, ) <. The indiret effets involve the interation between three terms: Y * / v refleting the response of aggregate supply to firm ondut; v * / n measuring the response of firm ondut to hanging market struture; and n e / (,, ) apturing the effets of (,, ) on net firm entry/exit. Eah of these responses was analyzed above: Y * / v < in Lemma a; v * / n [-, ] in Corollary b; and n e / (,, ) in Proposition 3 and Lemma 3. Sine n e / > from Lemma 3a, it follows that the indiret effet satisfies ( Y * / v) ( v * / n) ( n e / ), i.e. that the indiret effet of an inrease in the demand shifter α on Y * is always non-negative. However, while n e / ( ) = sign{ n * / ( )} from Lemma 3b, we have seen that n * /( ) an be either positive or negative (as analyzed in Proposition 3). These results are summarized next. Proposition 6: Assume that g/ n <. In the presene of fixed osts, the market equilibrium aggregate quantity Y e satisfies a) Y e / Y * / (, /α ), b) Y e / ( ) Y * / ( ) <, as n * /( ). Result a) gives the intuitive result that inreasing demand always stimulates the equilibrium aggregate quantity: Y e / >. It also implies that Y e / Y * / in general, and that Y e / > Y * / if the indiret effet of is positive. This indiates that negleting the role of entry/exit and firms ondut tends to underestimate the effets of a demand shifter on aggregate quantity. Result b) shows the effets of hanging mean fixed ost and mean variable ost on the market equilibrium quantity Y e. It states that, in the presene of fixed ost, Y e / (, ) < Y * / (, ) < when n * /(, ) <. Reall that we haraterized as normal a situation where n * /(, ) <. Thus, in a normal situation, we obtain the following two impliations: inreasing mean osts (, ) has a negative effet on aggregate quantity Y e ; and this effet is stronger than the diret effet Y * / (, ) in equation (9). (Note 6) Proposition 6 an be used to evaluate the impliations for priing. Given p * = Y * and the market equilibrium prie p e = - Y e, and following (9), we have p e / (, ) = p * / (, ) + ( p * / v) ( v * / n) ( n e / (, )). () This deomposes the marginal effets of (, ) on market equilibrium prie p e, p e / (, ), into two additive parts: diret effets, p * / (, ), holding firm onjeture v onstant; and indiret effets, ( p * / v) ( p * / n) ( n e / (, )), aounting for the endogenous adjustment in firm ondut. Again, note that the indiret effet involves interations between firm ondut adjustments, v*/ n, and entry/exit effets, n e / (, ). The signifiane and importane of these interation effets are further disussed below. Using Proposition 6 and equation (), we obtain the following results. Proposition 7: Assume that g/ n <. In the presene of fixed osts, the market equilibrium prie p e satisfies Published by Siedu Press 3
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember a) p e / p * / (, ), b) p e / (, ) p * / (, ) >, as n * /(, ). Result a) states that the equilibrium prie p e satisfies the following two properties: p e / < ; and p e / p * /. The first property means that, due to the supply response, the indued prie inrease tends to be less than the original shift in demand. The seond property shows that negleting the role of entry/exit and firm ondut tends to overestimate the effets of a demand shifter on the equilibrium prie p e. This stresses the importane of properly aounting for hanging industry struture in market analysis. Result b) shows the effets of mean fixed ost and mean variable ost on market equilibrium prie p e. It states that, in the presene of fixed ost, p e / (, ) > p * / (, ) > when n * /(, ) <. In this ase, the net effet of inreasing ost (, ) on p e is stronger than the orresponding diret effet p * / (, ). One more, this illustrates how negleting the role of entry/exit and firm ondut an underestimate the effets of ost hanges on the equilibrium prie p e. (Note 7) The above results apply in the long run under entry/exit and fixed osts. How do they relate to previous literature? Below, we disuss senarios where a simpler haraterization of market equilibrium applies even in the presene of fixed osts. They involve the ondition v * /n =. Note that v * /n = means that v * does not depend on n at least loally. This has an important impliation: when v * /n =, then the analysis developed in ase above holds loally. It follows that under senarios where v * /n =, all our market equilibrium results obtained under ase apply, with or without fixed osts. These senarios are further disussed below. In Corollary, we have investigated the determinants of v * and v * /n in long run equilibrium. First, from Corollary, we have shown that v * (Cournot priing) and v * /n when n is finite and /. It follows that, under sharply inreasing marginal ost ( ) and/or a very elasti demand ( Y/p = / ), the effet of n on v * also vanishes: v * /n. Under suh irumstanes, the market equilibrium is obtained by solving Y = S(Y, ) for Y e, with n e = n * () = n(y e, ). This result applies with or without fixed ost. Seond, Bertrand priing is obtained from Corollary when n is large. Indeed, from Corollary, n implies that v * and v * /n. This holds in the presene of fixed ost and for any finite /. This is the lassial ase where ompetitive behavior is obtained when the number of firms is suffiiently large. Under suh irumstanes, the market equilibrium quantity Y e is obtained by solving Y = S(Y, ), and the market equilibrium number of firms is n e = n * ( ) = n(y e, ) from (8). Third, from Corollary, we have shown that v * onverges to Bertrand ompetition (v -) and v * /n when / and n >. It means that, when there are more than two ative firms in the industry, and marginal ost is onstant ( ) or demand is very inelasti ( Y/p = / ), then the effet of n on v * vanishes: v * /n. Under suh irumstanes, market equilibrium is simple. Again, it is obtained by solving Y = S(Y, ), yielding Y e as the market equilibrium aggregate quantity. The assoiated equilibrium number of firms is n e = n * ( ) = n(y e, ). This result applies with or without fixed osts. And with n >, it does not require the number of firms to be large. This senario represents a situation where Bertrand ompetition arises even if the number of firms is relatively small. By identifying an alternative way of generating ompetitive behavior, it provides useful insights on how globalization (leading to an inrease in n) an lead an industry to behave more ompetitively in the long run. 5. Impliations for the eonomis of globalization 4 ISSN 93-3965 E-ISSN 93-3973