A Pedagogical Treatment of Bilateral Monopoly Author(S): Roger D

A Pedagogical Treatment of Bilateral Monopoly Author(s): Roger D. Blair, David L. Kaserman, Richard E. Romano Source: Southern Economic Journal, Vol. 55, No. 4 (Apr., 1989), pp. 831-841 Published by: Southern Economic Association Stable URL: http://www.jstor.org/stable/1059465 Accessed: 30/09/2010 04:17 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 service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Southern Economic Association is collaborating with JSTOR to digitize, preserve and extend access to Southern Economic Journal. http://www.jstor.org A Pedagogical Treatment of Bilateral Monopoly* ROGER D. BLAIR University of Florida Gainesville, Florida DAVID L. KASERMAN Auburn University Auburn, Alabama RICHARD E. ROMANO University of Florida Gainesville, Florida I. Introduction Most economists are familiar with the concept of bilateral monopoly: an upstream monopolist sells its output to a single downstream buyer that may also be a monopolist in its output market. The theory of bilateral monopoly has a rich history that can be traced to the writings of Cournot [10] and Menger [31].1 Over the 150 or so years that the problem has been under consideration, however, economists have offered a variety of "solutions" ranging from a completely determinate intermediate good price and output to a completely indeterminate solution within a specified range. Interestingly, this historical divergence of opinion concerning the correct outcome under bilateral monopoly still persists. A clear consensus has not yet emerged. Surprisingly, this lack of unanimity exists despite the fact that Bowley [5] provided the theoretically correct solution in 1928.2 Even more surprising, however, is the apparent popularity of the incorrect solution. A recent survey of the population of intermediate microeconomic texts on the authors' bookshelves revealed that over 80 percent of the current treatments of this topic are in error.3 Table I presents the results of that survey. Those authors who present a correct analysis of bilateral monopoly recognize that optimality requires joint profit maximization. This leads them to the correct conclusion regarding the determinate quantity of the intermediate product exchanged. Of the five treatments we have classified *The authors express appreciationto Leonard Cheng, Bob Ekelund, John Mayo, and an anonymous referee for helpful comments on a priordraft of this paper. The usual caveat applies. 1. These early writers did not consider bilateralmonopoly explicitly but, rather,treated the closely related topic of isolated exchange between two individuals. For an excellent discussion of the historicaldevelopment of the theory of bilateralmonopoly, see Machlup and Taber[27]. 2. Machlup and Taber's [27] paper served to remindthe professionof the correctsolution. 3. Not all microeconomics texts treat the subject of bilateralmonopoly. Among those texts that do not examine bilateral monopoly are the following: Becker [4], Browning and Browning [6], David Friedman[14], Hirshleifer [19], Lindsay [26], McCloskey [30], Quirk [34], Russell and Wilkinson [36], and Varian[42]. Of course, there may be others since we have merely a sample on our collective shelves. 831 832 RogerBlair, David Kaserman,and RichardRomano P3 - - CCx Pi - - ^ m P3^^^1 \DQ-CT 0 Xi X2 X3 X=Q MRP = Dx MRxMRQ Figure 1. as correct, however, two (Friedman[15] and Stigler [40]) drawno conclusionabout the inputprice range that will result, and another (Dewey [12]) draws an incorrectconclusion.4 Thus, only two texts (Hendersonand Quandt[17], and Layardand Walters[24]) are both complete and correct.5 Furthermore,none of these authorsprovides an adequaterepresentation of the contractcurve, and little emphasis is placed on the fact that the price of the intermediategood does not function as a rationingdevice but merely serves to divide the jointly maximizedprofits. As for the far more prevalentincorrect treatments of bilateralmonopoly, the majorsource of confusion appearsto be a failureto recognize the importanceof joint profitmaximization through negotiationon both the price and the quantityof the intermediategood. As we shall see below, it is extremely difficultto derive the correctsolution absentthis recognition. We have divided this "Incorrect"group into three parts. The first set includes those treatments that are clearly written and are clearly incorrectin some importantway. The second set includes those treatmentsthat generally fail to recognizethe correctsolution, but whose exposition is so unclear that one cannot be sure whetherthe authorsintended to treat a narrowerproblem.6 4. Dewey [12] also examines a collusive solution to the monopoly - "monopsony"problem. His treatmentis simplified because he assumes constant marginalcost. As a result, the marginalfactor cost equals the input price and there can be no monopsonistic exploitation.Thus, while Dewey is correctgiven the assumedconditions, his treatmentis less interestingthan the other correct treatments. 5. Scherer's treatise [37] also provides a correct treatmentalthough his is not an intermediatemicroeconomics text. 6. Baumol's exposition [3] is included in the "Unclear"group because he treats this problem in an unorthodox way by using utility functions with income and the quantityof the inputas arguments.Such a treatmentassumes that the amountof income to be sharedbetween the partiesis independentof the quantityof the inputexchanged. This assumption is violated in the bilateral monopoly model since total profitdepends upon the amountof the intermediategood traded (and final output produced). Much of what follows appearsto be correct, but the subsequentdiscussion of the joint profit maximizing solution is inappropriatein this model. A PEDAGOGICALTREATMENT OF BILATERALMONOPOLY 833 These typically fail to identify the crucial importanceof joint profitmaximization. They also tend to muddy the issue by using a labor union as the monopolist. This makes it extremelydifficult to tell whether these authors meant to examine a special case where the seller could not guarantee the quantity,presumably because a union's controlover its membersis somewhatincomplete. Finally, our third set is a small group of texts that do not appear to appreciatefully the importanceof joint profit maximization, but suggest or hint that such an outcome might result. None of these treatmentsexamines intermediateproduct price in a generalway. Neither the range of possible prices nor the fact that price serves only to divide profitsis identified. Clearly, then, something is amiss in the theory of bilateralmonopoly. Either the majority of the authors surveyed (and those who reviewed drafts for their publishers)are unawareof the correct solution, or they are unconvinced by the prior analysis. The purpose of this paper is both to serve as a reminder of the correct solution and to present what is, hopefully, a more convincing case for its adoption. For comparisonpurposes, we sketch the more popularanalysis before proceeding to the correct approach. II. Conventional Analysis The conventional analysis is summarizedin Figure 1. For convenience, we assume a fixed input/outputratio equal to one. This assumptionis not critical and, in fact, we relax it in the next section. If the downstreamindustry were competitive in the final outputmarket, the derived demand for the input would equal DQ -CT, where DQ is final product demand and CT is the constant cost of transformingone unit of input x into one unit of output Q. Thus, DQ - CT representsthe average net revenue as a functionof the quantityof x employed. With monopoly in the sale of Q, however, the derived demandfor x will be the curve that is marginalto DQ - CT, which is labelled D, in the graph. Thus, D, representsthe net marginalrevenue product of input x.7 The curve labelled MRx is marginal to Dx and representsthe marginalrevenue associated with selling this intermediategood to a downstreamfirm that has monopoly power in Q but not monopsony power in x. Note, however, that D_ cannot constitutethe downstreamfirm's derived demand in the bilateral monopoly situationbecause a monopsonistis not a price taker and does not have a demand curve. Turningto the cost curves, AC. denotes the upstreammonopolist's average cost of producing input x, and MC. is marginalcost. If the supplierof x were to behave as a perfect competitor, MC. would correspond to its supply curve. Then, if the downstreammonopsonist were hiring this input from such a competitor,MFC. would be the marginalfactor cost of the input. Authors adopting

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