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Deadweight Loss in Oligopoly: a New Approach Author(S): Alan J. Daskin Source: Southern Economic Journal, Vol. 58, No. 1, (Jul., 1991), Pp

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Deadweight Loss in Oligopoly: a New Approach Author(S): Alan J. Daskin Source: Southern Economic Journal, Vol. 58, No. 1, (Jul., 1991), Pp Deadweight Loss in Oligopoly: A New Approach Author(s): Alan J. Daskin Source: Southern Economic Journal, Vol. 58, No. 1, (Jul., 1991), pp. 171-185 Published by: Southern Economic Association Stable URL: http://www.jstor.org/stable/1060041 Accessed: 23/04/2008 13:45 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=sea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We enable the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. http://www.jstor.org Deadweight Loss in Oligopoly:A New Approach* ALAN J. DASKIN Boston University Boston, Massachusetts I. Introduction Ever since Harberger's[18] pioneeringarticle, researchershave attemptedto estimatethe welfare loss resultingfrom the exercise of marketpower. Despite nearlyfour decades of work in this area, however, surprisinglyfew researchersdisagree with Harberger'sfinding that deadweight loss is quite small. While many dispute his claim that deadweightloss in manufacturingamounts to only about 0.1% of GNP, few estimates exceed more than 1-3% of the value of output.' Some of the higher estimates, moreover,include losses of a broadernature than the purelyallocative losses on which Harbergerfocuses. In this paper I use a generalizationof a recent model of oligopoly to estimatethe magnitude of deadweight loss in the U.S. manufacturingsector. While the exact magnitudeof the losses depends on several parameters,the estimates indicatethat deadweightloss may be considerably higher than earlier work suggests, ranging from roughly 6-10% of the value of shipments if demandis inelastic to over 20% if demandis elastic. The theoretical model used to derive the empiricalestimates below is an explicit model of oligopoly, rather than an extension of the basic model of monopoly on which Harbergerbases his work. While much of the existing work in this area extends Harberger'sbasic framework,the predominanceof oligopolistic marketstructures in many industriesjustifies an approachbased on a model of oligopoly. The particularmodel I use is flexible enoughto allow for the exercise of dif- ferent degrees of marketpower in differentindustries. Moreover, unlike most previousempirical work in this area, the model allows for differencesin both costs and conduct among firms within any particularindustry. Section II provides a brief (and deliberatelyselective) review of the literaturedesigned to motivate the particularapproach I have taken. (For a more complete review, see Scherer and Ross [25].) In section III, I develop the theoreticalmodel used to estimate deadweightloss in an industry.The theoreticalmodel extends and generalizesthe oligopoly models of Dixit and Stern [14] and Clarke and Davies [4], which trace their lineage to work of Cowling and Waterson[8]. Section IV adapts the theoretical model for use with availabledata on U.S. manufacturing,and section V presents and discusses empiricalestimates of the model. A brief conclusion follows. *I would like to thankMyong-Hun Chang, Stephen Rhoades, MarthaSchary, John Wolken, an anonymousreferee, the editor, and seminar participantsat the Departmentof Justice, the SouthernEconomic Association meetings, and Boston University for helpful discussions on earlier versions of this paper. I, of course, bear full responsibilityfor any errors. 1. Kamerschen[20] and Cowling and Mueller [5] are two notableexceptions. 171 172 Alan J. Daskin II. A Brief (and Selective) Review of the Literature Much of the work in this area stems from Harberger'swell-known deadweight loss triangle. In its simplest textbook form, the intuitionbehind Harberger'sanalysis is straightforward:Firms' decisions to set price above marginal cost reduce consumer surplus and increase firms' profits relative to their levels in a competitive environment.The differencebetween the increase in pro- ducer surplus and the reductionin consumersurplus represents pure deadweightloss ratherthan redistributionfrom consumersto producers. If demand is linear and long-runmarginal costs are constant-and equal for the monopo- list and the hypothetical competitive industry-the deadweightloss for a monopolist (DWL) is given by DWL = (1/2)(Ap)(Aq), where Ap = Pm - Pc and Aq = qm -q denote the deviations from competitive pricing and output that result from the monopolist's exercise of marketpower. (Subscriptsnt and c denote monopoly and competition, respectively.) Harbergerand others then rewriteDWL in terms of observablevariables. Letting r/ denote the absolute value of demand elasticity, we can rewriteDWL as DWL = (1/2)>r2rl/R, where -r is the monopolist's excess profits and R is the firm's revenue. Using this framework and several empirical assumptions, Harberger[18] estimates that deadweight loss in the U.S. manufacturingsector was on the orderof 0.1 percentof GNP in the late 1920s. Many later researchers, while using the same basic model, criticize Harberger'sempirical assumptions.Much of their criticism focuses on his assumptionthat r7 = 1 for all industries, his failureto account for the interdependenceof Ap and Aq (throughthe demandfunction), and his estimationof excess profits. (For summariesof some of this work, see Waterson[33], Clarke[3], and Schererand Ross [25].) Cowling and Mueller [5; 6] and Cowling, Stonemanet al. [7] attemptto correct for these problems-and others-and suggest that welfare losses are considerablyhigher than had been suggested by Harberger.2Although Cowling and Mueller estimate welfare losses attributableto individualfirms ratherthan industries, they ultimatelyderive their estimates of allocative losses by startingfrom the same basic theoreticalstructure as Harberger;i.e., they look at a "welfare loss triangle" whose area is (1/2)(Api)(Aqi) for an individualfirm i [5, 729]. Given their other assumptions,such estimates of welfareloss reduceto simple functionsof the firm'sexcess profits. Holt [19], however, points out that such "Lernerequation loss estimates," as he calls them, are appropriateonly for a monopoly with lineardemand and constantcosts. They are inappropri- ate estimates for the welfare loss from the exercise of marketpower in an oligopoly. In particular, he criticizes Cowling and Mueller's focus on individualfirms and shows that the summationof 2. Cowling and Mueller also look at a broaderrange of losses than those consideredin most of the earlier litera- ture, including, e.g., losses due to advertising.In this section, I focus on their approachto allocativeloss only. In a recent paper, Shinjo and Doi [29] apply Cowling and Mueller'sapproach to estimatewelfare losses in Japan.Among their other findings, they conclude [29, 252] that "aggregateWL [welfareloss] as a percent of nationalincome is found similar to the orderof magnitudereported for the U.S. and Europeancountries." DEADWEIGHTLOSS IN OLIGOPOLY:A NEW APPROACH 173 such estimates across all firms in an industrydoes not lead to an accurateestimate of welfarelosses for the industry.3In general, Holt notes [19, 289] that "[t]he precise relationshipbetween industry profits and welfare losses depends on the numberof firms, the natureof cost asymmetries, and the source of monopoly power in the industry."(See also Schmalensee[26].)4 Masson and Shaanan[21] also argue that it is more appropriateto model the industryrather than the firm.5They acknowledge, however, that they do so at the cost of losing individualfirm differences. In particular,their analysis precludesconsideration of differencesin firms' costs. Recent papers by Gisser [15], Dickson [11], Daskin [10], and Willner [35] model the indus- try ratherthan individual firms using a dominant-firmsmodel, while Dickson and Yu [13] use a more general model to estimate welfare losses in Canadianmanufacturing. The model outlined below also considers welfare loss at the industrylevel, thereby avoid- ing aggregationproblems inherentin a firm-levelapproach. The model is more general than the dominant-firmsmodels noted above, however, allowing a broaderrange of oligopoly solutions. In addition, the model is flexible enough to allow for cost asymmetriesamong firms within an industry.Finally, unlike Dickson and Yu's model, the model below allows for differentbehavior among firms within an industry. III. The Theoretical Model In this section I develop the theoreticalmodel to be used to estimate deadweightloss in an in- dustry. Since the model derives from a model in Dixit and Stem [14] (henceforthD-S), I first summarizethe salient featuresof their model.6To do so, firstdefine the following notation: X = total industryoutput; n = the numberof firms in the industry; xi = output of firm i (i = 1, 2, ..., n); si = xi/X = the marketshare of
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