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VERTICAL INTEGRATION AND CONTROL By ROBERT SHIELDS HANSEN A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1978
Copyright 1978 by Robert Shields Hansen
To my wife, Nora, our daughter, Rebecca and to the memory of Edward Mark Hansen
ACKNOWLEDGEMENTS I would like to first acknowledge those economists whose general influence contributed to the preparation of this dissertation. My appreciation is extended to Fred Arditti, Sanford Berg, Roger Blair, Ronnie Davis, Richard Elnicki, Arnold Heggestad, Max Langham, the late Rafael Lusky, Yorem Peles, Blaine Roberts, and Frank Sloan. Also, financial support extended by the Public Policy Research Center at the University of Florida is gratefully acknowledged. Many of the aspects encountered in this dissertation were clarified through conversations with Sanford Berg. I gratefully acknowledge Sandy for these dialogues. When I undertook the task of integrating observed meter pricing behavior, encountered in the innumerable meter pricing arrangement cases, with the economic theory of durable goods, I had the good fortune to be at the University of Florida during the perion in which Blaine Roberts was instructing there. Blaine gave many hours, of his time to reviewing my work, and he expended an even greater number of hours in lengthy disucssions relating to virtually all of the microeconomic theory underlying this dissertation. I thank Blaine for extending to me his time and expertise. To the sum of these debts, I must acknowledge an even greater one. The origin of this dissertation be traced back to initial discussions TV
with Roger Blair. Moreover, as the thoughts and ideas in the dissertation were crystal i zing, it was through repeated and patient discussion of them with Roger that they obtained their state presented in this dissertation. Also in clarifying my exposition, Roger's help was indispensable to completing the dissertation. I gratefully acknowledge Roger's generous support, without which the dissertation would have been impossible. v
TABLE OF CONTENTS Page ACKNOWLEDGEMENTS i v ABSTRACT vii CHAPTER I VERTICAL INTERGRATION AND CONTROL: INTERMEDIATE MONOPOLY 1 Introduction 1 The Incentive to Vertically Integrate 2 The Impact of Vertical Integration 5 Forms of Vertical Integration 13 Summary 28 II METER PRICING AND PRICE DISCRIMINATION 31 Introduction 31 Price Discrimination and Meter Pricing: An Overview 34 Price Discrimination and Meter Pricing: A Second View 44 Price Discrimination and Meter Pricing. A Final View 60 III VARIABLE SERVICE FLOW DURABLES AND TWO-PART RENTAL ARRANGEMENTS 63 Introduction 63 Variable Service Flow Producer Durables 64 Two-Part Leasing 72 Price Discrimination 79 IV TYING ARRANGEMENTS AND ANTITRUST POLICY ISSUES 84 Introduction 84 Tying Arrangements: Definitions and Selected Vertical Controls 88 Tying Arrangements: Two Examples, Metering and Packaging 92 Tying Arrangements: The Policy Issues 101 Summary 107 BIBLIOGRAPHY... 109 BIOGRAPHICAL SKETCH 114 vi
Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy VERTICAL INTEGRATION AND CONTROL By Robert Shields Hansen August 1978 Chairman: Roger D. Blair Major Department: Economics The focus of the dissertation is upon the substantive equivalence between various contractual forms of vertical integration and vertical merger. Particular emphasis is placed upon the examination of the non-time meter leasing arrangement; a type of vertical pricing subsumed under the legal heading of "tying arrangements." Chapter I reviews the theory of Vertical Integration and establishes the analytical equivalence between the various forms of vertical integration: Vertical Merger, Full-Line Forcing, RestrictedLine Forcing, Lump-Sum Pricing, and Product Royal i ties. Chapter II reexamines the conventional conclusion that the meter lease form of tying arrangement is price discriminatory. Because of an incorrect construction of the economics of meter pricing, this conclusion is shown to be false, and is, therefore, rejected. VI 1
By i ncorporati nq the ability for durable goods to provide variable per-period service flows, Chapter III contributes to the developing economic theory of durable goods. Durable good sale, vertically integrated service sale, and meter leasing arrangements are examined, and are shown to be viable service marketing policies in both a monopolistically and comepti ti vely structured durable goods industry. In Chapter IV, the meter pricing tying arrangement is distinguished from the previously discussed types of tying arrangements, and the implications of this distinction for antitrust policy are discussed. VI 1 1
CHAPTER I VERTICAL INTEGRATION AND CONTROL: INTERMEDIATE MONOPOLY Introduction "Vertical intearation" subsumes the variety of combinations or agreements arrived at between exchanging economic entities. The form that integration takes can vary ranging from a simple spot exchange to a permanent bond between the entities. Equally varied are the identities that the exchanging entities may take (for example, individuals, firms, processes, etc.). Vertical integration is indeed ubiquitous, but depending upon the context within which it is analyzed, the general omnipresence of vertical integration gives way to greater specificity of definition. Consequently, different yet compatible explanations for vertical integration, as well as insights into its impact, may be found within the vertical integration literature.^ This diversity may be quickly exemplified by briefly indicating the role of vertical integration within the familiar bilateral monopoly and costly exchange contexts. Economists have examined vertical integration within the context of comparative exchange advantage (Coase, 1937), economic progress (J. Robinson, 1933, appendix), bilateral monopoly (Zeuthen, 1933) and economies of scale (E. A. G. Robinson, 1958). 1
2 In the bilateral monopoly case, where two independent monopol ists are confronted through exchange, the formerly independent monopolists achieve the joint-profit maximizing solution when they agree to verti2 cally integrate. The vertical integration, perhaps in the form of vertical merger, then facilitates overall profit maximization. Within the second context, one discussed by Coase (1937), the cost of exchange between the vertically related entities becomes the determinant of the form the integration takes. In particular, when different forms of vertical integration are possible, the exchanging parties may be expected to adoot that form v/hich minimizes exchange costs, ceterus pari bus Within this latter context, the role of integration is to facilitate a reduction in the costs of coordinating economic activity. Within the present and subsequent chapters the context within which vertical integration is examined is narrowed to vertical integration by an intermediate good monopolist. Through adopting this focus the present chapter examines various yet equivalent forms of vertical integration. Prior to that discussion, the incentive for an intermediate monopolist to integrate, and the impact of that integration are briefly reviewed. The Incentive to Vertically Integrate Most discussions of this incentive begin with the intermediate monopolist intially in a disintegrated position. This firm's product Vertical integration within the bilateral monopoly context is reviewed by Machlup and Taber (1960). 3 This incentive to integrate has been the focus of many of the recent contributions to the vertical integration literature. See, for example, Arrow (1975), Blair and Kaserman (1978a), and Williamson (1971).
3 is jointly employed with other competitively supplied intermediate goods by a competitive downstream industry, and the latter is engaged in the production of a final good. Consideration is then upon the profitability of vertical integration by the monopolist. That the profitabilty of vertical integration exists within this context has been recognized by Burstein (1960a), McKenzie (1951), and Vernon and Graham (1971). The recognition of this possibility represents a modification of the conclusion implied in Bork's (1954) influential contribution to the literature. This latter conclusion, that essentially the monopolist has no incentive to vertically integrate, is valid only for a limiting case.^ The more general condition is obtained through appeal to the economics of production and derived demand. Downstream producers are assumed to behave rationally. Consequently, they seek to produce their final output in a manner which reduces cost to the lowest possible level. This result occurs, for any level of production, once the downstream producers cannot further adjust the quantities of their inputs employed without raising total cost. At this particular employment combination, an additional dollar expended for the additional employment of any of the inputs yields identically 5 the same contribution to final output. To see that this efficiency The limiting case requires the presence of fixed proportions in downstream production. 5 This is merely an alternative statement of the equality of the marginal product to factor price ratio's obtained from equating input marginal rates of technical substitution to relative input prices.
or cost-minimization condition will be met, suppose that it is not. In that case the producer can reduce by a dollar's worth the quantity of the less contributive input, then increase by less than a dollar's worth the employment of the more contributive input, and still produce the same level of output. In short, the cost of producing the same level of output is reduced through a substitution between the inputs; the more contributive being substituted for the less contributive. When this condition is combined with intermediate good monopoly, the incentive to integrate becomes immediately apparent. When downstream producers pay a monopoly price for one of their inputs, a dollar's worth of this input, evaluated at the monopoly price, is less contributive to final good production than is a dollar's worth of this input evaluated at its production cost. Consequently, for any level of output each and every downstream producer will employ relatively less of the input when it is monopolized than when it is not. Alternatively, since the input monopolist will evaluate a dollar's worth of this input at its lower unit cost, through achieving vertical integration, the monopolist can produce the same competitive level of output at a lower total cost. This cost reducing effect, a substitution effect, provides a minimum measure of the profitability of g vertical integration. Furthermore, since this minimum profitability exists for all downstream producers, greatest minimum profitability is g Vernon and Graham (1971) note this minimum profitability explicitly in their discussion of vertical integration. Its existence requires the presence of substitution possibilities in the production process.
obtained when the entire downstream industry is integrated. ^ These results establish the general case for the profitability of vertical integration. With the recognition of this incentive to vertically integrate, Warren-Boul ton (1974) focused upon the postintegration impact of vertical integration. In particular, he attempted to determine whether the impact of vertical integration could be assessed unambiguously in social welfare terms. The Impact of Vertical Integration Welfare Effects Warren-Boul ton's (1974) analysis of the welfare effects of vertical integration could only produce an ambiguous welfare effect. In general, this ambiguity should be expected. The total effect of vertical integration and monopolization may be divided into two components, a substitution effect and a monopolization effect. Through the former, reviewed above, there is always a reduction in social cost, a social dividend, while the latter effect can reduce welfare through possible reductions in consumer surplus. Final Price Effects A monopolization effect is present when integration raises product price. Through computer simulation, Warren-Boul ton did find that vertical integration and monopolization results in an increase in product ^This is discussed by Schmalensee (1973), who included profit lost from incomplete integration in the monopolists' cost function.
b price. To do so, he assumed a downstream industry production function of the Constant Elasticity of Substitution form, as well as a constant O elasticity of demand for product. These results can be obtained within a less restricted context. By postulating linear homogeneity in the downstream industry production function and admitting a demand function of the non-increasing elasticity type, it can be demonstrated that vertical integration and monopolization will always result in product price increases for the C.E.S. case.^ To obtain this result it is not necessary to examine product price directly. First recall that the profitability of vertical integration and monopolization is due to the presence of downstream substitution possibilities. When these are technologically absent, integrated profitability can be obtained through simple monopoly pricing of the intermediate good, and the pre and postintegration product prices are identical.^ Now if the introduction of substitution possibilities The assumption of an industry level production avoids the aggregation probl em. Thi s may be exemplified by the existence of several downstream producers of a homogeneous product with identical production functions of the constant returns to scale form. Such an aggregate function is assumed throughout most of the subsequent discussion. For the constant cost case, vertical results in a final price increase whenever marginal production cost due to integration of the postintegration demand elasticity. integration and monopolization the percentage decline in exceeded by the reciprocal preintegration final price i s If i s is p D =mCp, and postintegration final price is Pj, where Pj=mCj n j 1 then pfv 1 implies that, mCj me D 1 I Throughout me. the discussion, I and D subscripts denote solution values for the integrated and disintegrated cases respecti vely. a di ^For an early discussion of this case, see Burstein (1960a). scussion of the implications of this case see Bork (1954). For
7 induces a fall in this monopoly price for the intermediate good, then all that needs to be demonstrated is that this price fall results in a reduction of final good unit production cost. Since this latter result always holds, what needs to be established is that increased substitution possibilities in downstream production will result in a lowering of the simple intermediate good monopoly price. ^ Consider the case when input one is monopolized. Monopoly profits are obtained when the input price, p-| satisfies Pi = c l e ll e n _1 ( 1 ) where c-| is unit production cost, and e^ is the elasticity of (derived) demand for the monopolized input. Hicks (1970) has shown that this elasticity equals e^ = (l-k-j)a + k-j n where o is the elasticity of substi tution between the inputs, n is the elasticity of final good demand, and k-j is the proportion of final good production cost paid to the monopolist. By substituting into (1) for e,-|, and totally differentiating, the following result can be obtained; dp 1 P 1 (i-k) < 0, where g > 0. da g Consequently, increased substitutability between the factors ( 2 ) necessarily implies that final good price will increase when the vertically 1 3 integrated monopoly solution is obtained. ^Throughout it is assumed that rate of substitution between the inputs is held at the factor price ratio. 1 2 Here k-|=p-|X^/pq, where p and q are final good price and output, and x-| is the quantity of the monopolized input employed. 1 3 Expression (2) is fully derived in Hansen (1978a).
8 When downstream input substitution possibilities are enhanced, the degree of intermediate good monopoly power is reduced 1 4 This is to be expected, for while other intermediate goods may not be perfect substitutes for the monopolized product, they are partial substitutes. Consequently, there is not uniqueness of the monopolized input in the substitution sense. The presence of the partial substitutes are indeed a competitive force mitigating input monopoly power. 15 The input monopolist is subjected to competitive pressures which, absent vertical control, are met with monopoly price reductions. These price reductions translate into a decline in input monopoly profits. To enhance this profitability, the monopolist must eliminate the competitive force introduced by the partial substitutes, and this is precisely what vertical integration achieves. Through vertical integration, the input monopolist obtains control over the downstream employment decision, which, in turn, is control over final good supply and price. Graphical Summary These results are depicted graphically in Figure 1.1, where for simplicity, final good production is assumed to require the employment of only two inputs, x-j and x^. Product demand and marginal revenue are 14 Adopting Lerner's (1943) measure of monopoly power, elasticity reciprocal, this is not merely a restatement of rule of derived demand. The demand for anything is likely elastic, the more easily substitutes for that thing can be Marshall's rule applies to the partial ae^/So,, while the applies to the total effect, de-|-,/da-,, of Â’increased substitutability the monopolized intermediate good. the demand Marshall 's first to be more obtained, above discussion on There is a type of product differentiation here, technological differentiation. When the inputs are technically indistinguishable in the production process, they are perfect substitutes. This extreme case
9 indicated by ar and mr respectively, and income effects are assumed to be negligible. Two cases which exhaust the possibilities are discussed; fixed and variable proportions. Fixed Proportions When the downstream production technique is characterized by constant input-output ratios, vertical integration by the monopolist may not affect product price and output levels. Furthermore, under these conditions, there does not exist additional profitability to vertical integration. This may be seen in the Figure where the input-output ratios have been set to one.^ For the integrated monopolist, average and marginal production cost is biven by ACj = c.j + c^, where c, and c 2 are the constant costs of obtaining inputs x-j and x 2 respecti vely. Equating marginal revenue to marginal cost, mr^ = c ] + c 2> the quantity of the final good produced by the integrated firm is q^ with final price P r Integrated profitability is then given by (p ACj)qj of substitutability would represent complete elimination of monopoly power. Alternatively, when the inputs are unrelated in production, competitive pressures on the monopolized input are absent. 16 Even under fixed proportions incentives to achieve vertical integration can exist. Blair and Kaserman (1978a) discuss the role of vertical integration when fixed proportions and uncertainty are present and find potential incentives to vertically integrate. Gould (1977) points out that the benefits of heretofore unexploited (latent) downstream monopsony power will produce integration incentive. This is a harmless assumption. The input units are simply redefined. Thus, if to produce a measure of brass requires two measures of zinc and three of copper, define single units as one, two and three measures respectively. The proportions are then fixed one to one. Generally, throughout the remainder of the chapter, it will be assumed that associated with the vertically integrated solution is the linear expansion path whereby all input-input, and input-output ratios are set to one. Thus comparisons
To obtain integrated profitability from the disintegrated position, the monopolist will equate input one marginal cost, c-j to input one marginal revenue, thus determining the input level and monopoly price. This, in turn, determines final output and price. For the fixed proportions case, input one marginal revenue is simply final good marginal reveune netted for the constant cost for the competitive factor. Thus, the input monopolist equates this net marginal revenue, net mr = mr-c^, to his marginal cost, c-j which implies mr^. = +c 2 the integrated maximum profitabil ity condition. This may be seen in Figure 1.1 by shifting the price axis origin to C 2 Their ar, mr and AC j are netted for c^. It is apparent that the resulting solution is identical to the "A" vertically integrated solution (where p^ = Pj c 2 ). When the input-output ratios are technologically fixed, the monopolist can control precisely the quantity of all inputs employed, as well as the entire downstream industry supply. Consequently, the technical relation between the inputs permits the monopolist to obtain integrated profitability through simple monopoly pricing of its input. When variable proportions are present, the monopolist loses a degree of freedom due to substitution possibilities. It is not surprising, therefore, to find that supplemental vertical controls can enhance profitability. Variable Proportions Consistent with the previously noted price effect, in Figure 1.1, product price for the variable proportions case, p Q is lower than intebetween the fixed versus variable proportions case are based upon identically the same expansion path, postintegration. Generally they may not be identical, but are assumed so here for comparative purposes.
Price 0 ~======~~i----r----~AC 0 ~-----'k----t-----------.:::-AC I = c, + C2 mr Figure l. l 11 or Quantity
12 grated final price, p p where, p D = (PqX-j Q + c 2 x 2D )/q D is the average cost to downstream producers of purchasing the intermediate goods. But the average social cost of producing this level of output is C D = ( c l x i d + c 2 x 2D^ q DÂ’ the sum the avera 9 e cost for purchase of the competitively supplied input, plu's the average cost of producing the monopolized intermediate good. Average social production cost is thus lowered from AC^ to ACj via vertical integration. As depicted the postintegration monopoly output level is below the disintegrated level of output. Because of this output reduction, there is a loss in consumer surplus which is approximated by the vertically stripped shaded region. The social dividend resulting from vertical integration is given by the horizontally striped shaded region and equals the reduction in the total cost of producing the monopolized level of final output. The net social welfare effect of vertical integration is then the difference of these two effects. The total effect is negative when the consumer surplus lost exceeds the gain resulting from input employment efficiency.^ This completes the review of the incentives for and impact of vertical integration. The results obtained are now summarized. 1 8 The impact of vertical integration due to the monopolization effect may be dampened by other factors not here considered. Warren-Boul ton (1974) did examine two such effects. One effect mitigating the price effect is the presence of potential entrants for the downstream industry. The effectiveness of the potential entrants upon limiting the exercise of monopoly power may be inhibited if the potential entrants require the monopolized intermediate good in their production. For one discussion see Schmalensee (1973). A second dampening effect may exist if the prices of the remaining inputs are reduced ex post, below preintegration levels. From the substitution effect resulting from the vertical integration the quantities of the remaining inputs employed may be increased or decreased. Any subsequent monopolization will generally result in a reduction in demand for inputs employed. If a net reduction in demand for any of the remaining inputs results in an input price decrease,, postintegration
13 (1) In the presence of substitution possibilities in the downstream production process, an intermediate monopolist will increase profitability through vertical integration. (2) The impact of integration with subsequent monopolization cannot be unambiguously assessed in social welfare terms. (3) When more than two inputs are employed, when product demand elasticity is non-increasing, and when the production function is of the C.F.S. variety, the price effect of vertical integration is unambiguously positive. With it now apparent that vertical integration is profitable in the unilateral intermediate monopoly case, the review turns to examine selected forms which the vertically integrated solution can take. Forms of Vertical Integration The above discussion makes apparent the object of vertical integration; achieving integrated profitability through control over the downstream production-employment decisions. To achieve this control, the input monopolist may employ one of several different forms of vertical integration. Common among these are vertical merger and fullline forcing. Less common, but potentially equivalent, are restrictedline forcing, lump-sum pricing, as well as product royalties. 19 marginal production cost can be reduced. Warren-Boul ton s computer simulation for the C.E.S. case obtained the result that final price may decrease if this external effect is significant enough. This external effect may be attended by monopsony effects. For a discussion of the latter see Gould (1977). 19 As a practical matter the actual choice of the form the vertical control takes will be affected by potentially differing net benefits from the various forms. When transactions costs are present, each vertical
14 Demonstrated in subsequent pages is the equivalence of these forms. To facilitate this review, it is assumed that the input monopolist has indeed consummated a vertical merger with the entire downstream industry, which is, in turn, monopolized. From this persepctive, it is shown that integrated profitability may be achieved with appropriate vertical controls within the vertically divisionalized firm. Vertical Merger The integrated firm may simple maximize profits on final good production. To establish this reference solution let p = h(q), h' < 0, be the product demand function where p is product price and q is final output. Demand elasticity, n, is then given by n = h/qh > 1. For the firm, the linearly homogeneous production function is given by q = f(x-j ,x n ) where the x^ are the input quantities (i = l,...,n), 20 and subscripts on f indicate the usual first and second derivatives. n Monopoly profit, n = pq I c.x., is maximized when the familiar i=l 1 1 first-order conditions are satisfied, mr i f i i = c., and mrj = Pj(^-) ,(i=l ,n). (3) form may be associated with different profitabilities depending upon implementation and control costs. But the actual choice of form is conceptually straightforward and is therefore not examined further. 20 For the fixed proportions case the production takes the form X 1 x 2 q = min(Â— Â— Â’ Â— ) (and thus q = x-j/B-j = x^B 2 in equilibrium), where B-j B 1 B. and Bo are the fixed input-output ratios. In the above discussion 3, and $2 are generally set to one.
The 21 where the are the constant costs of obtaining the inputs. firm will simultaneously employ the inputs up to where their respective 22 marginal revenue products equal their respective purchase prices. It is also a familiar result that mr^ = mCj at the profit maximizing 23 output level, where me is the marginal cost of final good production. To examine the nature of the vertical controls, the firm is now vertically divisionalized. The approach is similar to that adopted by Hirshleifer (1956).^ Full-Line Forcing ^ Joint sales agency Initially, the firm is vertically divisionalized into a single upstream intermediate good procurement division and a downstream production division. The firm's profit center is located in the procurement division where successful divisionalization requires attaining entire integrated 21 Substituting the solutions in (3) into the profit function, integrated profits are IIj = P jP j/n j 22 Dividing the ith by jth equation in (3) and rearranging yields the cost minimizing condition = f j j / c j = mc j23 In the fixed proportions case, q=x.($.=l, i=l,...,n), hence profit n 1 n is n = pq (E$. c.)q, marginal cost equals E c., and marginal revenue i 3 1 i=lB, 1 1 1 equals marginal cost yields Pj(i Â— ) = mCj 24 Hirshleifer (1956) examines a multi product downstream division but does not employ information embedded in the downstream production function Nor did Hirshleifer examine the alternate methods to the transfer pricing problem, the solutions to which achieve integrated profitability. 25 Full -line forcing defines the case where all inputs in the downstream division must be purchased solely from the upstream division. For an early discussion see Burstein (1960a). Note, however, that final consumers, hence indifference analysis, are not directly relevant to this intermediate monopoly case.
16 profitability at the procurement stage. The production division, quite possibly multiplant in organization, is therefore restricted to earn no more than a normal economic profit. The procurement division seeks internal transfer prices p^ to maximize joint procurement profitability, n,, where 3 n n, = Z (p, C,)x. ( i =1 ,n) (4) J i=l 1 1 1 There are two methods to obtain the solution depending upon whether the input demand functions are in direct or inverse form. With input demand functions in direct form, p^ = p^ (x.. ,x n ) input procurement profit is maximized when 311. 3p. f = p i c i + .1 *j 3^ = < i=1 ">Â• 3X, -l 'I j., "J (5) The partial derivatives inside the summation sign capture the input Â•pr demand interrelationships. These demand interrelations may be expressed in terms of the quantity crossand own-demand elasticities. That is, 27 n E x J 3x Pi n E J k i M j=l J ""J which by substitution into (5) yields ( i =1 ... ,n). ( 6 ) 1 pd 1 + kÂ— i j=i k -J-) = c. (i=l ,. ,n). ji (7) 26 It is these input demand relations that generate the need for vertical control by the unilateral monopolist. In a sense, the case of disintegrated unilateral monopoly is analogous to a non optimal multiproduct firm solution, where the firm is selling all but one commodity at cost to the same users. 27 These quantity elasticities are ratios of proportional input price changes to respective proportional input quantity changes. The definition is consistent with Hicks (1970). For a discussion of their derivation, see Hansen (1978b).
17 These conditions are quite general and remain independent of the production technology. To obtain the correct transfer prices, the procurement division will require information about the quantity elasticity measures (l/e^ = 8PjX^/9x^Pj) as well as the respective revenue shares for each of the inputs (k. = p.x./ E p.x.). It is shown below that when J J J j 1 J J the downstream production technology is taken into account, precise values for the respective transfer prices may be obtained. When the procurement division employs the inverse input demand functions, x^ = x^ (p^. ,p n ) n. is maximized when an. 3X. 0, (i=l. ,,,.n). (8) The terms inside the summation sign may be expressed in price elasticity form, then rearranged, to yield the necessary conditions n p i (1 + F~e^ Â— E k i 1 k i e ii j=l J e ij e jj ) = c i (i=l ,.. ,n). (9) 28 The simultaneous solution to (9) requires information on respective input shares and the relevant price elasticities (e. = 8x p ./9p .x ) .' ^ J T J J In general, this information may not be known. When information embedded in the downstream production process is used, however the transfer prices may be determined precisely. When production is linearly homogeneous, the price and quantity elasticities may be expressed as 28 These are ratios of input quantity percentage changes to proportional input price changes.
18 Â“ = k i (c ji and e ji Â‘ k i (0 ij Â‘ n) Â’ (k>J=1 n)> J ( 10 ) where the c^. are the partial elasticities of complementarity and the 29 a., are the partial elasticities of substitution between the inputs. Substituting the relevant elasticity values from (1) into (7) and (9), then simplifying, yields the profit maximizing transfer prices 0 j xr tt ) (i-1 ,n) V HD Multiple sales agency The divisionalized firm may further subdivide the procurement division into separate input procurement divisions, making each a separate profit center. For this further divisionalization to achieve integrated profitability, the different procurement divisions must behave cooperatively. Input procurement division i profit, = (p^ c^)x^, is maximized when dx i dp p i (1 + -W7 x i -Â— ) c i = 0, (i-1 ,.. ,n) ( 12 ) i r i To evaluate the derivative, either the direct or inverse input demand function may be used. Using the direct input demand function. where x. Ji d fi ^ dx i Pi n Â£ j=l T ji Â£ ij is an interdi vi sional -, (j=l ,. ,n) output variational measure. (13) 29 These measures of factor substitution are distinguished by Hicks (1970). Their relation to the problem of derived demand is clarified by Hansen (1978b).
19 30 t j .j = dXjX^/dx^Xj. Cooperative profit maximizing by the procurement divisions requires that all divisions adjust their outputs in equal proportions, thus x.. = 1. Using this result and substituting for J 1 / e Â• Â• from (10), (13) reduces to 1 /n Substituting this into (12), yields the transfer prices given by (11). When the separate divisions employ inverse input demand functions, the relevant measure inside (12) is dx i Pi E e .t > (j l.,,,.n) (14) j=l 1J JT 31 where t.^ is now an interdivisional price variational measure. Interdivisional cooperation requires t^ =1. By substituting for e^j from (10), (14) reduces to -1/q. Again substituting into (12), the transfer prices given by (11) are obtained. These results are not particularly surprising. Having demonstrated that the correct transfer prices can be obtained through alternative and somewhat cumbersome means, the final solution in all cases points directly to a simple approach to the transfer pricing problem. The nondi visional ized firm maximizes profit when the equations in (3) are satisfied, mr^ = c^(i=l,2). Furthermore, when the divisionalized firm, using transfer prices p.. requires the production division to 30 The x are the conjectural -variation terms found in the differentiated oligopoly literature. For a discussion of them see Hicks (1935). 31 tj n = dpjP^/dp.p.. These price variational measures have been applied in an oligopoly framework by Stigler (1940).
20 32 produce competitively, the resulting downstream first-order conditions are then P I f i = P i (15) Solving (15) and (3) for p^ yields the correct transfer price given by ( 11 ). The full -line forcing solution is relatively straightforward. One of the first authors to recognize its applicability and equivalence to vertical merger was Burstein (1960a). The solution requires the upstream division to simultaneously and by the same multiple raise all input prices until they equal the value of the marginal product for the respective inputs. Thus, whereas the nondivisionalized integrated firm employs input quantities up to the level where their respective marginal factor cost equals their marginal revenue product, the vertically divisionalized firm obtains the total profit by internally transferring these same input quantities at prices equal to the value of their respective marginal products. It is now apparent that integrated profitability can be realized through vertical divisionalization of the integrated firm. The correct transfer prices that generate this solution are the input procurement 33 unit costs each multiplied by a factor of proportionality. 32 The downstream quantity adjusting plants maximize profits II = pq Ep^x^, obtaining the first-order conditions, 9II/3x^ = 0, yields (15). 33 This result is to be expected. When all intermediate good prices are increased in equal multiples, relative input prices remain unaltered. As all input prices are thus raised, changes in final output and input employment will be proportional Alternatively, the downstream response to the proportional increase in prices is entirely abosrbed by a propor-
21 To obtain the correct factor of proportional ity, n/(n 1), product demand elasticity at the monopoly level of output must be known. 34 Restricted Line Forcing There is a second solution to the vertical control problem available to the integrated monopolist, restricted line forcing. This form of integration differs from full -line forcing in that the profitability of vertical integration can be obtained through the pricing of a single intermediate good. The solution assumes that the monopolist has knowledge of the optimal downstream input-output ratios. For simplicity, it is assumed that production of the final good requires only two inputs, x-| and x^. As noted above, for each level of output produced by the integrated firm, a unique input combination will be employed. Furthermore, the presence of constant returns to scale implies that this condition is met for expansions and contractions in output when the quantity of both inputs are increased or decreased in direct pro35 portion to these output changes. Stated alternatively, the input ratio for any level of production will be the same for all levels of production. The equations in (3) implicitly define this unique tional reduction in output and all inputs. There will be no incentive to substitute between inputs in the downstream productive process since relative prices remain fixed. 34 This case is also discussed in the trade union literature, see for example, Bronfenbrenner (1950). 35 The production input expansion path is linear. 3F For a given set of input prices the expansion path is uniquely defined.
input ratio, thus, let 3 represent it, where 3 X H / X 2r For the vertically divisionalized monopolist, integrated profitability can be achieved when the production division is required to employ 3 units of the controlled input, x-j for each unit of 37 employed. Under this vertical control, stipulating the precise input employment ratios, one condition that will be satisfied by the production division is When (16) is satisfied, there exists an infinite combination of OO transfer prices capable of achieving integrated profitability. This conclusion is explained briefly. Downstream equilibrium requires that (16) be satisfied and that total revenues equal total expenditures pq = p ] x 1 + p 2 x 2 (17) Substituting from (16) into (17) and eliminating q, the single requirement on the transfer prices, p-j and p 2 is met when P = BP-, + P 2 (18) 37 Since the efficient quantity of both inputs employed is proportional to the level of production, the additional simplifying assumption that the input-output ratio for the non controlled input is unity is maintained. Also, the previous fixed input ratio case 3 was set to one, but for the present, 3 will remain for expository purposes. 38 Technically and contractually imposed fixed proportions are distinct. The former is due to the physical nature of the production process, while the latter is an agreement regarding specifications on production, independent of the technology, to be adopted.
23 The weighted average of the input prices equals the integrated product price, where the weights are the respective input-output ratios. By setting pÂ£ at some arbitrary proportion of final price, for example, p^ = (l-s)p, then p-| satisfies p-j = sp/6, since s is arbitrary, an infinite set of transfer prices is available that yields integrated 3d profitability. The case of interest arises when the upstream division consists solely of the original input one monopolist. For this case, producers are permitted to procure all other inputs, here XÂ£, in the competitive intermediate good market, but they are required to employ the inputs in the stipulated ratio, B(thus, pÂ£ = CÂ£). When final good demand is expressed in direct form, p = h(q), and from (18), the inverse input demand function may be written as where (16), the equilibrium condition was used. Alternatively, employing the inverse final good demand function, q = H(p), from (16), the direct form of the input demand function may be expressed as where (18), the product price equals average cost equilibrium condition is used. Input one profit maximization, where = (p^-c^)x^, requires that (19) x-j 3H( 6p -j "i C 2 ) ? ( 20 ) 39 The possibilities of s > 1 and s < 0 need not be ruled out.
24 dn -i x, Â•j Â— = p,(l + Â— L dx, H v p-| V 1 and from (20) dp, dp, d^p) C 1 0From (,9) -3^ -h 1 6 2 5 dx! dp may employed to yield (21) -6 H, but since H' = 1/h', either result may 40 !<Â’ -spr>* Again, this method of vertical control does not yield surprising results. By contractually stipulating rigid input ratios, the solution is equivalent to that obtained when the production function is 41 characterized by technologically fixed input-output ratios. The nature of the vertical control was straightforward; eliminate factor substitution possibilities. 42 Lump-Sum Pricing Integrated profitability may be obtained through a system of per period lump-sum fees. The fee must accompany the requirement that a fixed quantity (no more and no less) of the formerly monopolized input be employed. To indicate the nature of this form of vertical inte^In (21), p| denotes the fixed proportions profit maximizing price for input one, p^ = p^ c^. 4 *k-jn=eii, for the fixed proportions case (a=0), for further discussion of this case, see Bronfrenbrenner (1961). 42 Lump-sum pricing takes the form of all-or-none bargains in the trade union literature. See Bronfrenbrenner (1951), Simler (1962), and Wei nstein ( 1 960)
25 gration, the production process is again assumed to be linearly homogeneous, and once again only the two input case is discussed. The upstream division may require the production division to be multiplant, in which case the number of plants is denoted by m. Introducing the lump-sum fee in the form of a total expenditure for a fixed quantity of the controlled intermediage good, the upstream 43 division alters the nature of each plant's cost structure. In the previous forms of vertical control, downstream average and marginal production cost remained constant for each type of control. Now, in the lump-fee case, each producer has both a fixed and variable cost, consequently, the plant average and marginal cost functions will have 44 falling, constant and rising portions as the plant output is expanded. This case is revealed diagramatical ly in Figure 1.2 which is a magnification of Figure 1.1. Final good demand and marginal revenue are given by ar and mr respectively, and integrated average production cost and final output are given by ACj and q^ respectively. 45 For the integrated firm, product price is given by Pj = p^ + c^. 43 The intermediate monopolized factor must enter the downstream production process. 44 As long as the upstream firm selects the number of plants so that combined plant fixed costs (total lump-fees collected) precisely equals integrated total profit, combined plant production will equal the integrated output level. That is, each plant operator is induced to produce where plant average cost is minimum, which in turn was previously equated to postintegration monopoly price. 45 ... It is assumed that the postintegration input expansion path is identical to input expansion path for the previous fixed proportions case, x-| j/qj = 1
26 Associated with this price is integrated final output = x^, and, for m plants, each will incur the per-period fixed expenditure, F^, for X-, units of input one, of p*tX 1t x 1t 46 ,m t_Ui = p* v = F where x _J1. m K 1 1m M lm m Plant production costs are then given by TC m = c^x^ + F^, where average production costs are ac = avc + afc and where avc = c 0 x 0 /q and m m m m 2 2 mi 47 afc^ = F^/q^. The plant operator will select the quantity of the competitive input to be employed, or the quantity of final food, q to be produced in the plant, m Under the present control, each plant will produce where q m = q^/ m. That is m-plant output equals integrated final output. This is seen by supposing each plant did not produce this level. If combined m-plant output is less than q ^ q m < q^/m, product price will rise above Pj = minimum ac marginal revenue exceeds marginal cost in some or all plants, and in these plants production will expand. Alternatively, the m plants expand output beyond q^/m, product price will fall, and in some or all plants marginal revenue will be exceeded by marginal cost and production will decline towards q^/m in those plants. The solution is depicted in Figure 1.2 where a representative pi ant cost structure is superimposed on the expansion of Figure 1.1. The area of the shaded p*x region rii m F f<1 = (p C 2 )q m > equals the size of the lump-fee for the plant. 46 See n. 17, and n. 20. 47 The multi pi ant firm has been analyzed within the context of cartel theory by Patinkin (1947).
Price Quantity Figure 1 2
28 48 Product Royalty Still another variation of vertical integration is obtained by requiring product royalty payments, which is like a privately imposed unit tax upon producers. If all downstream producers are required to pay a per unit royalty or r, where r = Pj/rij, the result is simply an upward shift in downstream marginal production costs to the product monopoly price level. Summary Depending upon the context within which it is examined, the ubiquity of vertical integration yields to greater specificity, and in the present case, various forms of it were examined in the context of unilateral monopoly. For ease of discussion the equivalence of the various forms was demonstrated by considering the integrated yet vertically divisionalized firm, and transaction and potential enforcement costs were abstracted from. The various forms of vertical integration are summarized in Figure 1.3, which diagrams the industry isoquant map. Depicted is the two input case, where the price of the competitively supplied input, is set equal to one (c^ =1). Three isoquants are present: q^ represents the output level for the vertically disintegrated case absent fixed input-output ratios; q^ v represents the postintegration output level with variable proportions; and q Jf represents the pre postinte40 gration output level for the fixed proportions case. Warren-Boul ton (1 977) analyzed the comparative statics of this case, where, again, both production and product demand are in constant elasticity form. 49 The minimum profitability to integration discussed above is
29 *2 Figure 1 .3
30 For the fixed proportions case, integrated profitability is obtained when input one's relative price is given by the negative of the slope of line Rjl, = p ^ which is then the industry isocost line. For this isocost line, producers purchase the input combination indicated by point I, for a total expense of Rp Since expenditures for the competitive input, c^Xp remain the same, input monopoly profit is R I c r Full -line forcing is represented by isocost line Cjl, which has incorporated the proportionally higher prices for both inputs, while relative input prices remain at the post integration level. Restricted line forcing yields contractually (as opposed to technologically) fixed input-output ratios. In this case downstream production expands along line Oil', and the relative transfer price obtained in the text, (p^)is reflected in downstream isocost line R^I. The lump-sum fee requires that the entire industry purchase x-p at a total price of Rj 02 2 \ which, again, yields integrated profi tabi 1 i ty Finally, product royalties are represented by a parallel and downward shift in an isocost line through Rp to the point where it intersects Cj. Since relative input prices remain unaffected, this control yields the isocost line through Cjl, and, again, integrated profit R i c r obtained through input substitution from point D to point I'. As Vernon and Graham (1971) indicated, this is the substitution effect due to integration and is independent of monopolization effects, where the latter is indicated by output and factor quantity reductions, a movement from point I' to I. The postintegration isocost line is given by the line C T I where C, is postintegration total production cost. Post integration total revenues are given by Rj hence integrated profitability is given by Rj Cp
CHAPTER II METER PRICING AND PRICE DISCRIMINATION Introduction Meter pricing is a vertical pricing arrangement, between a seller and a buyer, where the items exchanged between the parties are embodied services of durable or capital goods. The implementation of meter pricing results in the receipt of service payments by the seller in accordance with the quantity of services utilized by the buyer. One difference between simple service meter pricing and a lease requiring rental payments based solely upon the time of capital good possession, is that the former may result in variable per-period payments. Meter pricing requires that buyers, the purchasers of embodied services, make per-period payments that are directly related to the perperiod quantity of services utilized, or alternatively, payments that are directly related to intensity of durable good use. Common examples of meter pricing are made available by several cases passed upon by the Supreme Court. Typically, a producer of a patented durable obtains payment for services by charging a higher price for a second commodity, one used in conjunction with the services, in lieu of pricing the services directly. Of course, the buyer must be required to purchase the second commodity from the seller. In this 31
32 fashion, the receipts for embodied services utilized are obtained through the higher price levied for the jointly purchased second commodity. The classic example of meter pricing is provided by IBM's former method of obtaining card processing payments for all cards processed in IBM card processors. IBM sold the cards to the machine users at above market prices, and machine users were required to meet their card requirements with cards purchased from, or through, IBM. As a testimony to the apparent frequency with which private practitioners find meter pricing desirable, several other examples of it may be found in the Supreme Court case literature.^ Fortunately, a review of these cases is provided in several contributions by economists 2 and scholars and is, therefore, eschewed here. The practice of meter pricing, subsumed under the rubric of "tying arrangements," has been declared illegal per se by the Supreme Court, which has advanced a diversified rationale to underpin this rule. These rationales are, however, generally spared any sentiment from economists writing on the subject. A review of the literature indicates these authors conclude that meter pricing is price discriminatory, but Typical examples provided by a history of Supreme Court decisions involve the leasing of machinery where the meter rates were obtained through pricing of a second intermediate good which required a unit of machine service to be processed. Common examples of machine and meter goods are: card processing machines and cards processed, shoe-button fastening machines and buttons fastened, salt processing machines and salt processed, riveting machines and rivets used, etc. 2 The legal tying arrangement literature is extensive; for selected references see Bowman (1957), Hilton (1958) and Dam (1969).
otherwise its impact upon economic efficiency may be regarded as 3 ancillary and innocuous. Recently, the Supreme Court has demonstrated a recognition of these developments in the economic literature, and in so doing, the Court has accorded recognition to the unchallenged 4 conclusion that meter pricing is discriminatory. Obviously, the Court must also have been made aware that there is no economic basis for the remaining several arguments previously advanced in defense of the per se ban on meter pricing arrangements. In this Chapter, the discussion is centered upon challenging and refuting the conventional wisdom that meter pricing is discriminatory. This conclusion has been advanced constantly by several influential scholars and it is, therefore, of some interest that it receive close 5 and careful scrutiny. In addition, a successful refutation of this conclusion shedsserious doubt upon the necessity of the existing per se ban on meter pricing. The discussion is divided into three parts. The first is concerned with an overview of the conventional wisdom that meter pricing is discriminatory. The second section probes more deeply into this view, and demonstrates more rigorously, the inadequacy of it. The Chapter concludes with a few brief remarks. This view assumes that the purpose of antitrust policy is economic efficiency, see Posner (1974). 4 The Court was unanimous in its opinion; United States Steel Corp v. Fortner Enterprises Inc ., 853, U.S. 861 (1977) 5 This conclusion has been supported by economists for twenty-seven years, and no refutation of it has been found in the literature.
34 Price Discrimination and Meter Pricing: An Overview Prel iminaries Economists recognize that the fundamental commodities demanded by durable users are their embodied services. This is made self-evident g in the traditional analysis of producer or consumer durables. Indeed, while often masked by other considerations, the traditional analysis of durables centers upon the problem of marketing their embodied services. It is perhaps due to focus upon these other considerations that little recognition is given to the fact that the resulting rental arrangements obtained in that literature are meter pricing arrangements. Underlying most analyses of the economics of durable goods, an initial assumption fixing the physical relation between durable goods, their per-period service capacity, durable user service requirements, and units of time is typically invoked. Thus, in the remarks preparatory to the discussion of the durables, one encounters the "onehoss shay," the "constant efficiency," or durable "evaporation" type assumption.^ This assumption permits considerable analytical inquiry, yet leaves something to be desired when certain durable good problems are actually confronted For example, a successful service sales policy requres a method of detecting or monitoring the utilization of the services embodied in r Consider Swan's (1970) approach where the capitalized price for the durable good is derived from the market level per-period service demand function. ^These assumptions are employed when the focus of the analysis is upon market structure and product durability, Swan (1970), and the problem of leasing durables. Miller and Upton (1976). Lutz and Lutz (1951) also employ this type of assumption in their classic analysis of investment decisions.
35 O the durables. This problem does not typically arise when a perishable commodity exchanged is physically visible, since use and physical exchange go hand-to-hand. The case of embodied services can differ in that the amount of them withdrawn from the durable may differ at different times. Consequently, the marketing of embodied services must go hand-in-hand with a policy of monitoring utilization. It is an interesting feature of the traditional durable good economics that this monitoring problem never arises, yet the embodied services are successfully marketed. To understand how the traditional approach circumscribes the monitoring problem, and thus clarifying the nature of meter price arrangements, the intial one-hoss shay type of assumption is reconstructed by parts. First, it must be realized that the assumption requires the service flow capacity and units of time to be coincidental. The coincidence of time and service flow capacity alone, however, is insufficient to resolve the monitoring problem. There is no assurance that utilization will be constant over succeeding time periods, and there is no assurance that service capacity is fully utilized during durable good possession time (it is unlikely, for example, that two perfectly identical airplanes when leased, will be used in equal intensity over similar time periods) O Services are jointly supplied from durable goods, thereby raising the familiar problem of excluding nonpayers.
To obtain the assumption characterizing the durable good economics, intermittent durable good utilization must be assumed away. Thus, for example, leased airplanes must be visualized as being utilized throughout succeeding time periods. Eliminating intermittent durable utilization, which may be achieved when the durables and various service customers are constantly brought together over successive time periods, eliminates one aspect of the utilization monitoring problem. The durable producer is now assured that each durable, and hence some amount of the service flow capacity is used in every time period for the life of the durable. The constant efficiency type assumption is finally realized by invoking the requirement that each durable used in the succeeding time periods is utilized to full capacity (in terms of airplanes, each is then viewed as being utilized at full intensity for its life). The full utilization assumption eliminates the final source of actual service flow variability, differing yet simultaneous utilization rates. The monitoring problem is now obviously resolved. The traditional economic approach to durable goods invokes the convention that service units utilized, service capacity, and units of time are all one and the same thing, and therefore, the monitoring problem is absent. All resulting service sale and purchase arrangements are resolved by sale and purchase of the perfect service unit proxy, time units. The monitoring of durable good service utilization is reduced to observing the amount of time for which the various durables are in the possession of the users. Alternatively, a metering
37 function is performed by time. It should be noted, however, that the service metering function is still being performed, and the resulting time rental lease is indeed a meter pricing arrangement. The traditional approach to the marketing of embodied services implicitly resolves what might otherwise be difficulties resulting from different intensities of durable good use by different purchasers of embodied services. The solution requires that the various users make service payments depending upon durable good possession time, which is to say that users make service payments in accordance with the quantity of time units purchased. Again, under the time rental arrangement, durable users are required to make variable payments according to intensity of durable use, where payment variability is directly related to the quantity of time units, and hence service units, purchased by the various users. In effect, the seller is charging above market prices for the jointly purchased second commodity, time units, and it is in this fashion that the producer obtains the receipts for services utilized. This solution does not yield variability in the per-period payments made by various users of the durables. Thus, using the benchmark of time, all users are paying identically the same price (for the time units). However, it remains correct that all users are making payments based upon intensity of use. Indeed, under the traditional rental solution, the seller may price the service units directly, i.e., employ service meter pricing, with the sum of the resulting per-period user payments equaling, precisely, the per-period fee that is otherwise set.
38 In short, the traditional time meter pricing method and the service meter pricing method may be viewed as conceptually similar in that durable users are required to make service payments for services utilized. However, the two cases do differ, not due to the method of marketing services, but rather, their difference is attributable to differences in the physical nature of the durables; in the former, services and time are directly proportional, and in the latter, the two are generally unrel ated. It is now evident, independent of time, that efficient marketing of the services of specific capital goods requires that durable users incur rental payments according to the quantity of services utilized. By positing the existence of a metering commodity, one that serves as an exact proxy for service units, and where the utilization of the former is detectible (e.g., by exchange from hand-to-hand), above market prices for the former can be charged in lieu of service prices and the efficient marketing of embodied services may then be achieved. The result is that durable users make payments directly reflected in the intensity of durable good utilization. The Price Discrimination Conclusion In the case where services used and possession time are not coincident, variability of durable user time payments occurs. For this case, the use of a simple meter pricing results in different per-period payments Q according to intensity of durable utilization. The existence of 9 In this Chapter, simple meter pricing occurs when all service customers are charged the same service unit price, and no other charge is levied. Note that this is a contractual process, it requires using
39 different per-period prices to different users has been recognized by Director and Levi (1956), where these authors have summarized that the observed instances of meter pricing "... can be explained best as methods of charging different prices to different customers. ..." (p. 289). These authors refrain, however, from asserting that meter ... ... 10 pricing is discriminatory. It is within the subsequent contributions to the tying arrangement literature that the price discrimination conclusion is articulated. An early expression is found in Bowman's (1957) work. In referring to the metering device as the second commodity, and the durable as the first, Bowman acknowledges that different users may purchase different amounts of the former, with a use of the latter; Bowman (1957) then adds: "If the first commodity is worth more to the intensive users than to the less intensive users in economic terms, if the former's demand is less elastic tying the second commodity to the first can in effect achieve the goal of discriminatory pricing for the first" (p. 23). Apparently, the more intensive users are viewed as attaching greater value to the durable because their demands are posited to be less elastic and thus, a meter lease permits expoliting this posited relation. markets, and may, indeed, require the use of economic resources. These costs, as well as other transaction costs which may arise when other forms of vertical integration are sought, may differ, and as well, may be of primary importance in the choice of contractual form. In the present Chapter, however, the focus is upon the economics of meter pricing, not upon the vagaries of transaction costs. For an early discussion of the latter, see Coase (1937). ^The implementation of simple meter pricing is not correctly viewed as an additional restriction, beyond that of monopoly, when it is realized that the profits thereby obtained are nothing more than the original service monopoly profits.
HU Hilton's (1958) contribution yields a similar sort of analysis. Recognizing that a seller may discriminate among the durable users, Hilton (1958) writes: "If among Â£ purchasers, there are separate demand functions, the elasticities of which are inversely proportional to the rate of use of the machine, then a monopolist should seek to extract the monopoly gain in direct proportion to its use" (p. 269). In adopting the same sort of construction of meter pricing advanced by Bowman, Hilton appears to conclude that it permits the monopolist to reach the quoted objective. There are other sources available that, in essence, support this approach to the economics of meter pricing. The conclusion obtained has survived half a generation of economists, and is exemplified in Posner's (1974) recent statement that "Tying does, however, enable the monopolist to practice price discrimination. By providing the computer at cost and selling each card at a monopoly price, the computer monopolist can vary the charge for computing according to the amount, and thus presumably the value, of each purchaser's use"^ (p. 508). Of course, meter pricing results in different total charges for services rendered according to the amount of each customer's use. This is so regardless of whether the correct meter is time, miles or cards Summari zi ng, the theory in support of the price discrimination conclusion is understood as follows: Under non-time meter pricing ^In a footnote Posner (1974, p. 509, n.5) conveys the opinion of Ronald Coase that this construction of meter pricing is doubtful.
41 arrangements, when service customers pruchase different quantities of services from different duarbles in the same time period, the total per-period service payments made by the various users will differ according to per-period intensity of durable good utilization. Thus, in effect, different per-period prices for the same good (the durable) are being charged. Assuming the users that pay more, at the same service price, have lower demand elasticities, price discrimination is being practiced. This is a fair enough representation of the theory supporting the conclusion that price discrimination characteri zes the meter pricing arrangement. In general, there appear to exist two routes over which this conclusion has been attained: (1) through the assumption that intensity of use and demand elasticity are inversely related, and (2) through the view that the resulting per-period prices are, in effect, durable good prices. Each of these are now examined. The Assumption of an Inverse Relation Between Elasticity and Intensity of Use It is a well known result that under the market segmentation form of price discrimination, each buyer's marginal revenue is equated to the marginal cost of combined output, and the inverse relation between 1 2 the market prices and demand elasticities is present. Applying this to the case of simple meter pricing, it would appear therefore, that meter pricing is certainly price di scrimi natory because it is assumed to be price discriminatory. When the inverseality relation is invoked, the conclusion is assumed. 12 Successful price discrimination requires preventing arbitrage between separated buyers whose demand elasticities differ, see Stigler (1972, pp. 209-214).
42 Obviously, supposing the inverse relation to hold, the idea is to justify the conclusion, but a rather interesting case emerges by invoking the equally acceptable assumption that intensity of use and demand elasticity are directly related. In this case, while the relatively more intensive users make the relatively larger per-period service payments, their demand is also more elastic. What is observed under typical meter pricing is that more intensive users pay more per unit of time. Demand elasticities have no bearing on this result, and the assumption that they do should be abandoned. The "In Effect" Hypothesis By allowing the not too unreasonable assumption that the initial captial outlays required to produce the durables is the same for all similar durables, the adoption of the in effect approach will generate the price discrimination conclusion. One example of this approach is provided by Bowman (1973). Bowman (1973) writes: Although each user of a patented button-fastening machine pays the same rate per pair of shoes manufactured, use of the tying device or of a meter has the effect of a different sales price for the machine according to intensity of use. This is discrimination if the large user pays a higher price relative to cost than small users, (p. 104, n. 29). The critical point of confusion engendered by this approach is that it treats the commodities purchased under a meter pricing arrangement, for all users, as being identical to the commodities that are purchased under a durable good sales policy. What is paid under non-time denominated meter pricing is different total service payments by different users for different per-period quantities of productive services utilized. Under a meter
43 pricing arrangement different users purchase different quantities of embodied services and any comparisons of the resulting different total prices, for the different total quantities purchased, cannot be meaningfully employed to support the price discrimination conclusion. The effective prices paid by the various users, under the simple meter price arrangmeent, may be viewed as prices paid for differently 13 sized units of durable service capacity, but not the entire capacity. There is no basis for presuming that the per-period service payments received under a meter pricing arrangement should equlaize across various per-period uses of the durable goods. The presence of the variable per-period payments, when time units are employed as the price benchmark, should not, therefore, be regarded as evidence that price discrimination is being practiced. The successful implementation of price discrimination requires that customers paying different prices be prevented from reselling their purchases, or purchase rights. Without the elimination of these arbitrage possibilities, customers having access to the lower priced goods can resell them to those who must otherwise pay higher prices. Under simple meter pricing there are no such gains to be realized from arbi tragi ng efforts. When all 13 It would appear that meter pricing, or alternatively direct service pricing when feasible, permits the producer of the durable to, in effect, sell portions of the durable. That is during any time period, since the durable good is simple a service stock or capacity, or a bundle of productive services, through a meter lease, this stock, capacity, or service bundle, is broken down into the units of basic components: productive services. For a single use or location of the durable, the size of the durable becomes variable, where size is now delineated in service units or equivalently, units of capacity. For a particular service price and resulting minimum utilization rate, durable good size becomes con-
44 durable users face similar service or meter commodity prices, the customers remain indifferent between uses of alternate durable goods. Under simple meter pricing, service customers cannot resell their purchased services nor their access to additional services, to other users of durables at prices that are more favorable than those currently levied on the latter users. The price discrimination conclusion, therefore, fails a simple arbitrage test. To this point, it is now obvious that there are fundamental difficulties with the widely accepted conclusion, and underlying theory, that meter pricing is a durable good pricing policy implemented to achieve maximal, price discriminating, monopoly profit. The above refutation of this theory may be sufficient for some readers, however it cannot serve the more rigorously inclined. To satisfy the latter, the following discussion approaches, analytically, the theory that the purpose of meter pricing is price discrimination. Price Discrimination and Meter Pricing: A Second View It is not enough to refute a casual claim with a casual counterclaim. The conventional view of meter pricing characterizes the former, while the discussion up to this point, may be said to characterize the latter. What is needed to dispel the accepted theory are two things. First, the accepted theory must be more rigorously crystalized so that it can be subjected to critical scrutiny, without this, there exists tinuously variable, ranging from the lower threshold level to the upper per-period durable service capacity level. Simple meter pricing then permits a more complete supply of the basic commodity demanded by buyers, productive services.
45 only a body of doctrinal thought, and while the latter (when all are similarly indoctrinated) may be a comfort, it is hardly a substitute for more careful reflection. Second, a competing theory must be advanced, one that is capable of displacing the existing one. The first of these is satisfied in the present Chapter and the second is the task of Chapters III. One might suppose, given the number of proponents of the price discrimination hypothesis, that there exists a rigorous formulation of it. A review of the literature, however, yields, other than scattered 14 supportive opinions, no such model. The Assumptions First, there is little doubt that the conventional view of meter pricing implicitly assumes that the various, yet similar, durable goods, through which the services are marketed, are simultaneously underutilized in their respective uses (see Bowman, 1957). This assumption is, therefore, adopted here. Once adopted, however, further complexities are introduced into the economics of meter pricing. These complexities are dealt with here, as in the conventional view, by invoking more assumptions. Two of these are now explicitly recognized. A rationalization of the simultaneous underutilization condition may be obtained by invoking conditions that render infeasible any efforts by the durable monopolist to eliminate it(clearly, the monopolist can 4 This review includes the familiar two-part tariff literature, where, upon careful reading, one is left empty handed, despite slippery illusions to meter pricing arrangements. For selected literature on two-part tariffs see Murphy (1977) and Oi (1971).
4b reduce capital outlays by reducing underutilization, and therefore, where possible, the monopolist will seek to require that users of the durables combine to achieve the fuller utilization). The rationale for this condition may be sought on the basis of spatial separation of users, or, perhpas, on the basis of excessive transaction costs incurred in efforts by users to combine. However the condition is rationalized, there is the distinct possibility that each of the resulting uses for the durables takes on the appearance of a separate market. In turn, there is then, several demand functions for the services of the durables, one for each market, and moreover, there may exist some monopoly power in each of the various durable uses. The simultaneous underutilization condition, therefore, admits the possibility of bilateral, and/or successive monopoly. It is these additional complexities, not entirely insurmountable, that are assumed away both in the conventional view, as well as here. A second assumption implicit in the conventional theory suppresses important considerations of intertemporally related cost effects. Simultaneous underutilization implies that the durables may be used at various rates of intensity in any time period, and they may also be characterized by a greater deterioration in the rate at which services may be extracted from them during any future period, when they are very intensivley employed in previous periods. For example, the market value of two machines whose age in years may be identical, may differ substantially according to the rate at which they have been historically utilized. One may rightly expect that, of the two machines, for the one previously used more intensively, the amount of per-period services it
47 is capable of providing to be relatively less. These noted effects are dealt with here, as in the conventional theory, by assuming they do not exist. In the following discussion, therefore, simultaneous underutilization is assumed, it is also assumed that bilateral and successive monopoly are not present, and finally, it is assumed that costs, introduced by intertemporal effects, are absent. Conventional Meter Pricing Economics At the outset it is expedient to recognize the view (see Bowman, 1957) and Hilton (1958)) that, conceptually, simple meter pricing, where all monopoly service revenues are recovered through the above market level, meter price, and no other fee is levied on durable users, can exemplify the discriminatory meter pricing case. This case is explicitly addressed below, while the alternate case, where two prices are charged, is briefly considered in the final remarks. The assumption is, that for every potential productive service employment stream for which the discounted value of service revenues (at the monopolistically set meter rate) is no less than capital outlays, a durable good is installed. The Case of a Singe! Use for the Durable Good Consider first the case where there is but one use for the durable good, that is, there is only one intensity of use for it. The demand for the services obtainable from a unit of the good are derived from the demand for the processed good, the production of which relies upon the employment of the services. To obtain this demand function, the product market equilibrium conditions (in the present case, price equals marginal cost) are employed.
Initially, let the production of a unit of the final good, q, require the input of two service units, s, obtainable from the durable, and two units of a second unit, m, termed the "meter" input. Production efficiency requires that i.e., the production of a unit of the final good requires two units each of the meter and service inputs. Letting product price be denoted by p, and denoting the prices to be set on the meter and service inputs by p^ and p $ respectively, m C equating product price to marginal cost yields P = P m ^ + P s ^ anc by substituting from (1), the final good price equals marginal cost equilibrium condition is obtained; It should be noted that the input prices, p g and P are the prices to be set by the metering monopolist, and that the cost of otherwise obtaining the meter input, k, is taken to be constant. Product demand is assumed to be linear, and is given by ( 2 ) p = A Bq (3) where A = 2(a + K)+r, and B = 4gb, (a,b,g,k,r >0), and where the constants are chosen for ease of discussion. Substituting into the demand function for q from (1), and equating the result to (2), the respective derived demand functions for the meter and service inputs are:
49 p =a+k+Â£-p = -gbm (4) 'm 2 r s x and P s = a + k + | p m gbs. (5) The similarity of the two derived demand functions is attributable to the fixity of the production coefficients. Since the sum of the input prices set by the durable monopolist always equals the monopoly product price, the discussion can proceed by focusing solely upon the service input demand function (5). In that case, the price of the meter input is then set to its competitive level, k, yielding the derived service demand function p s = a + Â£ gbs. (6) Had the monopolist choose to focus upon the meter input demand function, p s is then set to zero, which, from a comparison of (4) and (6), reveals that the individually set profit maximizing service price, p* and the individually set monopoly meter rate, p^, are related as follows; p* = p* + k. (7) K m K s v When meter pricing is adopted, the optimal meter price will be set equal to the optimal service price that would be set in the absence of meter pricing, plus the unit meter input cost. Analytically, therefore, 1 5 one only needs to determine p*. The monopolist may then charge 1 5 Note that here, an "extra competi ti ve" price for the metering good is in fact the sum of an "extra competitive" price for service units, plus a competitive price for the meter input.
50 p* directly for services used, or, through meter pricing, indirectly price for the services used by adding this fee to the users cost of From (6) the maximization of service profit obtainable from a use of the good, p s s, yields the optimal service price and output levels; Product price and output levels are then obtained by substituting these values into (2) and (1) respectively. The results are straightforward. The durable monopolist simply maximizes the profit obtainable from marketing the embodied services. As a practical matter, however, observing the rate of service utilization may be costly. When this is not the case, in particular when an inexpensive service meter is available, the monopolist can recover service revenue as the services are utilized. Alternatively, these revenues may be collected ex post, based upon some cummulative meter measure. Of particular relevance is the selection of the second input as the metering device, whereby service revenues are recovered when these inputs are purchased. When this input is employed as the meter, specifically when the durable user is required to make all purchases of the meter input from the monopolist at the above market price, p* + k, a meter pricing tying arrangement exists. ^For this case, maximizing service profits is similar to maximizing the per-period quasi-rents obtainable from the machine. obtaining the meter good. 16 p s 2^ a + 2^Â’ ( 8 ) and ( 9 )
51 This case of a single use for the productive services is depicted in Figure 2.1. In the Figure, the vertical axis measures price, while the horizontal axis measures quantity. The product demand function is denoted by AR^, and product marginal revenue by MR^. To obtain the derived demand function for services, the product demand function is first netted for the average cost of purchasing the variably employed meter goods. The average cost, per unit product, of purchasing these inputs is constant at 2k, and the product average and marginal revenue are then netted, graphically, by visually shifting the price-quantity origin to the level 2k. Thus, in the Figure, the broken horizontal line through the origin, 0, is the relevant abscissa for discussions pertaining to the product market, while the relevant abscissa for the derived service demand functions is represented by the horizontal line through the shifted origin, 2k. There are now two remaining steps to obtain the derived (service) input demand function. Because the service intensity embodied in the product is given at two units of service per unit, the netted product demand function is first vertically halved, then horizontally doubled, yielding the perperiod derived input demand function. The vertical division of the netted product demand function indicates the per-period price for half the services required to produce a unit of the final good. This function, denoted by the the dashed line MR S is horizontally doubled to obtain the per-period derived (service) demand function, AR s> In sum, the derived demand function is given by AR $ and the schedule of prices marginal to AR g is given by MR $
52 Price Figure 2.1
53 As in the previous discussion, to simplify matters, it is assumed that the marginal cost of providing a unit of service is zero. In Figure 2.1, this marginal cost of service production is then given by the service quantity abscissa, 2k. The service monopolist equates service marginal revenue, MR g to service marginal cost (which here, is zero at 2k), and this determines the optimal service price p*, output level, s*, and service monopoly profit, p*s*. Taking account of the service origin, 2k, this optimal service price is given in Figure 2.1 by p* + 2k. Final good average production cost, and hence price, now equals 2(p* + k). The resulting level of final good production is then q* = s*/2. It is of partial interest to recognize that this solution for the single use case is identically the same as that which would arise had the durable monopolist fully integrated into final good production. To see this, return to the final good market, and, recognizing that integrated final good marginal production cost is 2k, equating final good marginal revenue to marginal cost yields the same level of output, q*, a product monopoly price of 2(p* + k), and profits of 2p* per unit of the product (or profits of p* per unit of service employed) To implement the meter pricing method of recovering service revenues, the durable monopolist must require the user of the durable to purchase all meter input requirements from him, at the above market price p* + k = p*. K K s K m
54 The Case of Two Service Employments First, assume that the prevention of meter good arbitrage between different durable good users is prhoi bi tively expensive to enforce. There are now two products and the production of each requires the employment of services and the meter inputs. These products, denoted by q-| and q^, differ in that the production of a unit of the former requires one unit of the meter and service inputs, while the production of a unit of the latter requires, as before, two units each of the respective inputs (the latter product is the more service intensive of the two). The q-| and q^ production efficiency conditions q-, = m 1 = s 1 (10) n m 2 s 2 (11) q 2 2 2 Â’ where the subscripts identify the particular employments for the respectively designated inputs (note that a separate durable is employed by each user). Identifying the respective product prices by p-j and p^, and by following the approach outlined above, the respective product market equilibrium conditions are P 1 p sl + p ml Â’ (12) and P 2 = 2 ^ P s2 + P m2^ Â• (13) From these relations, it is evident that, when both users of the durables face identical input prices, the price for the more service intensive product, q 2 > is twice the price of the less service intensive are then; and product, q-j
55 The respective product demand functions are now given by p-j = A* B*q.| (A* = a + k + r, B* = b) (14) and P 2 = A Bq^. (15) Proceeding as before, the respective input demand functions are now p s = a + r bs,. (16) and r 1 7 P s 2 ~ ~2 bgsÂ£. (17) The horizontal sum of these service demand functions is the per-period service market demand function P s = A Bs, (18) where s = s-j + s^, A = a+r(l+2g)/2(g+l ) and B = bg/(g+l). The maximization fo service monopoly profit, n s = p s s, yields the optimal market level service price p* = A/2, and the market level of I O services purchased is then s* = A/2B. A comparison of this market level price for services with the price formerly obtained in the single use case, (8), reveals that the price to the producers of the more The role of the constants is now clear. A positive a and r assures that both users are in the service market at monopolistically set service market prices. A positive r assures that, given a is positive, the different demands will have different price elasticities. Finally, varying the positive g permits one to alter the relative intensity of durable use by the qÂ£user. 1 8 Under uniform meter pricing the value of the service unit to the durable good user is not being assessed. Value of service pricing requires that each service rendered be priced with explicit recognition of the demand for the product from which the demand for the services of a unit of the durable is derived.
56 service intensive product, q^, has increased. This reflects the impact, at the market level, of the addition to the market of the less elastic demand for services which is derived from the demand for the less service intensive prodict, q-| Barring costs of implementation, it should be apparent that the profits obtainable from direct service pricing (given it is feasible to do so) are identical to the profits obtained through meter pricing. The service monopolist may, therefore, be viewed as integrating into the direct provision of productive services, charging the service price p*. Or, alternatively, the monopolist may be viewed as installing the durables at the alternate user locations, while indirectly pricing for services utilized by setting above market prices for the meter inputs, p* = p* k. The nondi scrimi natory meter pricing solution is depicted in Figure 2.2. In the Figure, the respectively derived service demand functions are denoted by ar-| and ar^, with their associated marginal revenue functions, mr-j and m^. Figure 2.2 is similar to that of Figure 2.1, where the service origin is now explicitly set to zero. The market level service demand function, AR s is the horizontal sum of the individual user demands ar-j and a^, and the schedule of prices marginal to it is denoted by MR s> Equating marginal revenue to marginal cost, the resulting monopoly solution is at price p* and output level s*. The resulting service quantities employed in the product 1 9 industries are given by s| and sÂ£. 1 9 Note that in general there may not be equivalence between meter pricing and market level service monopoly. In the latter case.
57 Price Figure 2.2
58 One obvious feature of this treatment of meter pricing is that intensity of durable use is directly related to durable user perperiod service payments, but nothing more is present. Users requiring greater per-period quantities of productive services incur greater total per-period service expenditures for their greater service employment needs. Furthermore, it is evident that the different durable users are purchasing different amounts of the same commodities, the services of capital goods, but the respective durable users do purchase these commodities at identical prices. It is now possible to examine further the price discrimination theory. From the demand functions given by (16) and (17), by varying g(>0), either durable user may be characterized as the intensive user (increasing g rotates a^ clockwise around its price intercept). For example, as depicted in Figure 2.2, the more intensive user, the q^ producer, also has the more elastic demand function. The presence of the different demand elasticities prevailing at the single market price, indicates that there are potential gains if market segmenting price discrimination can be successfully implemented. The necessary requirement for successful meter price discrimination is, therefore, that the various users of the durables be prevented from reselling, to each other, the differentially priced meter input (durable if the quantity of services demanded at the service market monopoly price is satisfied, it may be that among the various users of the durables, when individual utilization rates are not observable, some may be forcing employment of durables at rates insufficient to recover the capital outlays for them. When meter pricing is adopted, capital outlays are reduced by not satisfying these service demands. In this case, fewer durables are produced, and unless these potential users can share with other actual users, the quantity of services marketed through the meter pricing arrangement will decline relative to the former market level. The effect on the resulting net meter or service price of removing this service demanders will ultimately depend upon the demand elasticities for each of the particular excluded users.
59 users must, therefore, be prevented from arbitraging away the resulting meter input price differential). Once this latter requirement is satisfied, additional profit from meter price discrimination may be real i zed. The familiar solution to this form of price discrimination requires that the price of services employed in the market with the relatively less elastic demand is raised, while the price in the remaining market is lowered. In the above example, the profit maximizing meter price is raised for services employed in the less service intensive product industry, and that the price charged to the more service intensive product user is lowered. These additional gains from discriminatory meter pricing are revealed in Figure 2.2 by the shaded regions. There are different methods by which the nonarbitrage condition may be realized. Obviously, the most economical among those available will be chosen. In any case it is a familiar result that the discriminatory profits obtained by the input monopolist are identically the same as those obtainable through vertical merger. Alternately, the effect of vertical merger by the input monopolist is indistinguishable from price discrimination without the merger. More generally, the price discrimination and vertical merger profit maximizing solutions are simply different forms of vertical integration into the production of the relevant final goods.
60 Price Discrimination and Meter Pricing: A Final View The above presentation obtained by modeling the conventional economics of meter pricing, was confined to the case of simple meter pricing. Most authors on the subject recognize that this is not the case typically encountered; however, it was presented to permit a clear focus upon the existing discrimination theory. For this case, it is evident that simple meter pricing cannot be viewed as purposefully price discriminatory. This is so despite claims to the contrary. All users of the durables pay the same price for services units utilized, there is no incentive for arbitrage, and demand elasticity is entirely irrelevant. As noted, however, meter pricing can be purposely implemented to achieve gains from price discrimination, and, in that case, there is a necessary finding of different meter prices being set for different users of identical meter service inputs (given identical unit costs for each). As a final point, when extreme meter pricing is modified to incorporate a per-period fee, in addition to a price charged for the meter input, it can be claimed that price di scrimiantion is, implicitly, present. The resulting price discrimination that emerges, however, is not in the direction asserted to exist by those supporting the conventional view. That view claims that the two-part meter pricing arrangement discriminates against the heavy users of the durable, and this is simply incorrect in the broader two-part meter pricing case. For example, suppose as it is often suggested in the tying literature, that the durable monopolist sets a time rental fee that equals
61 the per-period opportunity cost incurred in providing the durable good. Evidently, this time rental fee should be set so that the capital cost incurred by the monopolist is fully recovered by it. Now, to implement the broader meter pricing arrangement, an additional service charge is levied on each user (for services utilized), via the meter input. It is self-evident that when this is to be regarded as a case of discrimination, the less intensive user is being discriminated against. The heavier user is implicitly i ncurri ng a lower pri ce for each service unit employed as the fixed charge is spread over more units of service. There is then implicit price discrimination against the less intensive users. This Chapter focused on refuting the existing theory and conclusion that the meter pricing form of tying arrangement is purposely price discriminatory. This theory has been rejected on many counts: (1) the view that intensity of use, demand elasticity and price discrimination are somehow connected has been falsified, (2) the claim that the per-period prices paid for the use of similar units of the durable may be viewed as, in effect, different prices for the same good has been shown to be generally inadmissible, and, (3) having adopted the implicit assumptions of the conventional view, it was shown that it cannot withstand even slight critical inquiry. It was revealed that the case of simple meter pricing results in all users paying identically the same price for services, and, at those prices, durable users do not have any incentives to arbitrage. It was then suggested that this extreme case is more appropriately viewed as an allocatively neutral, short-run, quasi-rent problem. When the
62 extreme case was modified to that of two-part meter pricing, it was further revealed that implicit price discrimination can be inferred, however the direction of that discrimination was revealed to be exactly the opposite of that advanced by the conventional theory, i.e., it was revealed that the discrimination worked in favor of the more intensive 20 users, and against the less intensive users. on To obtain these results it was necessary to sidestep difficulties that implicitly underlie the conventional theory. Abstracted from are the complexities inherent in the phenomenon of simultaneous underutilization of durable goods, and the additional difficulties that are thereby generated (e.g., potential bilateral and successive monopoly). Alos abstracted from are potential costs generaged by intensity of use. (Increased depreciation on the potential per-period service flow obtainable from them is an example). These considerations alone, score heavily against the existing economics of meter pricing.
CHAPTER III VARIABLE SERVICE FLOW DURABLES AND TWO-PART RENTAL ARRANGEMENTS Introduction Durable goods play a central role in many areas of economic inquiry. They are encountered in the peak-load pricing literauter (Hirschleifer, 1958; and Steiner, 1957), the second-hand markets literature (Swan, 1972), the leasing literature (Fama and Miller, 1972; and Miller and Upton, 1976), as well as the literature addressing the impact of market structure on durability (Roberts, 1978). In this Chapter, many of the complications faced in that wider literature addressing durables are set aside. The focus here is upon the pricing of leased durables that may be used at variable rates of intensity. To further simplify this inquiry, durable good production considerations are suppressed, or alternatively, considered posterior to the resolution of the pricing problem considered here. The presentation is also greatly simplified by not addressing the possibility that the durables may be employed at various rates of intensity over some cylical time period. This aspect of using the durables at various rates over time can be treated within the model presented below, but analysis of it is deferred to future inquiry. In the model presented, to highlight the basic pricing problem, the con63
64 ditions are such that a unique optimal rate of utilization exists, where this is assured by assuming product demand invariance with respect to time. The discussion is divided into two sections. The first focuses upon the specification of producer durables that may be utilized at various rates of intensity, and upon methods of marketing the services embodied within them. Among the results obtained is that the durable goods considered cannot be leased, in the traditional manner, and still yield the profitability obtainable from alternate marketing strategies. The second section of the Chapter then examines a two-part rental pricing policy, where this policy is shown to be a viable marketing alternative. In the final section it is shown that this two-part rental policy, whether monopolistically or competitively implemented, is not inherently price discriminatory. Variable Service Flow Producer Durables Assumptions and Preparatory Remarks A simple two-stage production process is postulated where the perperiod production of the final good, Q, requires the employment of a volume of services, s, obtained from the hired durable good stock, k, and the stock of a third input that is identified as labor, 1. The rate of utilization of the hired durable stock is given by the ratio of the per-period volume of services utilized to the existing stock of the good. Referring to this as the intensity of utilization per unit of the durable, this intensity is denoted by a, where a = s/k.
bb Units of the durable are assumed to decay at an exponential rate, d, where this rate of depreciation is dependent upon a "builtin" rate of deterioration, y, and, as well, the intensity with which a unit of the good is utilized, d = d(y, a) and 3d/8a=d' > 0. A unit of the good used at some intensity a for t years, therefore, provides e ^ units of service. The cost of a unit of the durable is assumed constant at C. Denoting the rental or opportunity cost incurred in optimally utilizing a unit of the good by p, the capitalized value of this rental cost over the infinite life of a unit of the good is 06 f pe(r+d)t dt = Â— where r is the rate of discount. Alternatively, the full rental cost incurred in utilizing a unit of the good, for some a, is equal to p = (r + d)C, where p' = d'C 0, and p" = d"cJ The per-period service stock of the durable defines the upper bound to the per-period volume of services obtainable from it. For any stock of the good, k, there is then, a capacity limit upon the total volume of services available for actual utilization. In the present discussion, this capacity is assumed to be equal to that stock, and thus, if it is utilized to full capacity, a = 1 the volume of per2 period services employed equals precisely this stock. The analysis is in the steady state, and, therefore, what is sought is the optimal utilization rate, hence the equilibrium depreciation rate, and thus the optimal rental cost, p. Because it is a steady solution, once p is determined, it shall remain constant over time. 2 In the production of the final good, Q, where constant returns are assumed, the presence of the durable utilization capacity constraint places
66 Production of the product is assumed to be linearly homogenous, and when, as in the case examined here, the durable stock is not used to capacity, the production function is given by Q = f(l, s, k), a < 1, f(0, k) = 0, where subscripts on f denote the usual derivatives (e.g., f $ > 0 and f^ > 0, denote the marginal products of s and k respectively). Finally, the labor wage is assumed to be constant at w, while product demand P = H(Q) is assumed to be invariant with respect to time, and where P is product price, and q = -H/H'Q is product demand elasticity. Service Marketing Alternatives Vertical integration (merger) Consider first the case where the durable producer(s) is vertically integrated into the production of the final good. The maximization of per-period profit, it = PQ-wl-pk, requires that the familiar first-order conditions be satisfied. Choosing 1, s, and k, to maximize profit, these conditions are met when mrf-| = w, (la) mrf s = p' (lb) mrf k = p-otp' (lc) where mr = P(l1) is marginal revenue. These conditions, (1), may be bounds upon the substitution possibilities between the volume of services utilized, and stock of the durable hired. In a neoclassical framework, when the stock is utilized to capacity, there is a fixed proportions nature in final good production between services employed and durable stock hired (see Marino, 1978). When, however, there is less intensive utilization of the existing durable stock, final good production may be characterized by variable proportions between these inputs. Generally then, the presence of durability constrains the feasible choices for the volume of services employed.
expressed alternately as the socially optimal input employment costminimizing conditions, which require equivalence between the rate of input substitution and input cost ratios; 67 and M-, = Â— Â— r lk p-ap M = sk p-ap (2a) (2b) (2c) where M. = f./f. (i, j = 1, s, k, and i f j) is the rate of input substitution. The first point to recognize is that these first-order conditions, (2), will be satisfied in the integrated production of the product regardless of market structure. That is, whether there is monopolisitc or competitive (n =0 ) production of the product, the socially optimal cost-minimizing conditions, (2), are identically obtained and, therefore, intensity of durable utilization is independent of the structural conditions in the industry requiring their employment. The general interpretation of the profit maximizing conditions, (1), differ, in the familiar manner, according to the structure of the product industry. Generally, the input stocks will be employed up to the level where their respective marginal revenue products equal the respective marginal cost of their employment. For the case of a competitively structured product industry, these marginal revenue products also equal the value of the respective marginal products (i.e., in the competitive case, n = Q0 and mr = P). From (la), the stock of labor employed is increased to the level where its marginal revenue product equals its wage. The interpretation
68 of (lb) is slightly less apparent, but with it, the interpretation of (1c) is straightforward. As indicated in the above profit function, the explicit production cost incurred does not include a payment for the volume of utilized services, yet, as indicated in (lb), there is an opportunity cost incurred in their employment. The utilized services are jointly employed with the hired durable stock, and their cost is, likewise, jointly and implictly realized in the full rental cost of the hired durable stock. When the durable stock, k, is held idle, the per-period opportunity cost incurred, in perpetuity, is [r + d(y,0)]Ck, capital cost plus losses due to built in deterioration of the stock. As services are withdrawn from the stock, i.e., as intensity of utilization is increased to a, the full opportunity cost of utilizing the existing stock increases by ([d(y, a) d(y, 0) ] Ck ) and, for an existing stock, this increase is given by p 1 the additional depreciation cost from more intensive utilization of the given durable stock. Thus, from (lb), the volume of employed services is increased up to the level where the marginal contribution to the firm's total receipts is just offset by the marginal increment to the opportunity cost of the hired durable stock. Turning to (lc), as the durable stock is utilized more intensively the rate of deterioration in that stock raises the opportunity (depreciation) costs incurred for all services, less than capacity, not utilized. These increased per-period losses are reflected in an increase in the rental cost of hiring units of the durable. A proportion of the rental cost incurred, as noted, is attributable to the per-period
69 volume of services withdrawn from the stock, and, in one sense, these costs, per unit of the durable employed, are deducted from the marginal opportunity cost of employing units of the durable. The total perperiod service charges incurred are spÂ‘, which, for a unit of the durable stock are then sp'/k = ap', and this per unit user cost is deducted from the full rental cost of hiring a unit of the durable, p. The incremental cost incurred in hiring a unit of the durable may then be viewed in this way, and it equals p ap' the right hand side of (lc). In sum, units of the durable are added to the hired stock up to the level where their marginal revenue product equals their incremental cost. This completes the discussion of the marketing of productive services through vertical merger. It was straightforward, and its primary usefulness is in serving as a reference solution to the alternative policies of durable good sale and rental, as well as the subsequent discussion. Vertical disintegration: durable good sale and traditional rental Suppose first, that the durable good industry is competitively structured. When sold, units of the durable are then marketed at the price of C. In this case, producers of Q will employ them efficiently, regardless of product market structure. The resulting solution is that discussed above. Durable sale is then, an alternative to the vertical merger solution, where neither is less profitable than the other.
7 0 A durable good rental policy, however, when implemented in the O traditional manner, is inferior to either of the above alternatives. To see that the rental policy is inferior to sale or merger, suppose that units of the durable are leased on a time-rental basis of R per-period. Profit maximizing producers, where now Tr=PQ-wl-Rk, maximize profit when mrf-j = w, (3a) mrf = 0, s (3b) and mrf ^ = R. (3c) Comparing (3) and (1), (or the rates of substitution between the inputs), reveals that units of the good and the remaining inputs, will be employed in a socially inefficient manner under this leasing policy. In particular, units of the good will be utilized more intensively than if, for example, they were owned by their employers (the rate of factor substitution between services and units of the durable is now zero, M s k = 0/R). The rate of utilization of the durable stock will be increased as users drive the utilization rate up to the level where the marginal product of services is zero. While this leasing arrangement yields pecuniary rewards to lessees, units of lessor's durables are being utilized in an inefficient manner, and it is for this reason that the lessors will opt for a durable sales policy, or, they may market the services through vertical merger. The source of this difficulty with 3 In the consumer durable case presented by Epple and Zelenitz (1977), precisely the same conclusion is obtained.
71 renting durables characterized by the variable service flow is evidently in the failure of the traditional, single price, time rental policy.^ In the case of monopolistic provision of the specific capital services, both the durable sale and the traditional rental policy are inferior to the vertical merger alternative. This conclusion follows from the familiar result that an intermediate good monopolist, when variable proportions are present, has a profit incentive to achieve 5 vertical integration. To see it, suppose the monopolist considers selling units of the durable at some price, T, for which there is the equivalent alternative of leasing a unit at an implicit rental rate R*, where R* = (r + d)T It is again apparent that lessees, and as well, purchasers, will employ units of the durables in a socially inefficient manner. Durable purchasers, while taking into account the costs of increased intensity of use, will be induced to combine the labor uti 1 i zed, service and unit of durable inputs in a socially inefficient manner. Through vertical merger the monopolist can, therefore, obtain, at minimum, the additional gains from eliminating this social waste. Durable lessees, while also induced to combine the inputs in an inefficient manner, have the additional Epple and Zelenitz (1977) conclude that the rental policy is inferior. Actually, these authors, by not considering the two-part lease, attempted to lease the durables in a financially inefficient manner, i.e., they only examined a traditional, one-price rental policy. 5 The presence of variable proportions permits substitution from the monopolized product, and, in turn, inefficient production of the final good. Vertical integration enhances profitability by insuring efficient production.
n incentive to employ the inputs in such a way that the marginal product of the employed service volume is zero. Thus, as in the competitive rental solution, the lessees increase the level of intensity of durable use beyond the socially efficient, vertically integrated level. For the monopolistic supplier of producer durables, therefore, the durable sale and traditional lease policy alternatives are economically inferior and will be abandoned in favor of vertical merger, ceteris paribus. Two-Part Leasing In this section it will be shown that a viable durable rental policy exists, and that its implementation permits competitive lessors to achieve the vertically integrated solution, and, in one class of cases, this also holds true for monopolistic supply of the durables. The lease is a two-price rental arrangement where one primary purpose served by it is to induce lessees to take the costs attributable to intensity of use directly into account. 6 The effect of the lease, then, is to induce durable users to employ them efficiently. The two-part lease is, in general, a variable time rental arrangement. The per-period payments required of lessees depend upon the intensity with which units of the durable stock are employed. However, in the 0 Two-part leasing, as discussed here, is distinguished from the familiar two-part tariffs. Two-part tariffs are typically associated with indifference analysis where, aside from distributional aspects, their purpose is to price discriminate, and they have served, analytically, to extract consumer surplus (see for example, Gabor, 1955). Oi (1971) and Murphy (1977) have applied two-part tariffs, verbally, to the case of producer durables, but neither author offers any theory of durable goods in the process. The two-part rental arrangement, on the other hand, is not designed as a discriminatory pricing practice in the traditional sense. The
73 steady state, as here, these payments stabilize. Under this lease, the full per-period durable utilization fee is split into a user fee, p and a time payment, p^.. When the durable good industry is competitively structured, the user rental fee for a unit of the durable stock hired is set to satisfy P u P s (4) where p $ is the effective price for the employed service stock, per unit of the hired durable. The time fee is then set to recover the remaining per-period opportunity costs incurred, P t = p P s a (5) To insure efficient utilization of each unit of the good, the user and time fees must be further related by condition, (2c), P A = P (6) P t P otp' Solving (4), (5), and (6) the rental fees are and p t = p-ap'. The decomposition of the implicit rental is into the user fee, p which recovers the cost of providing the employed service volume, and the time fee, p^, that recovers the remaining opportunity costs incurred in propurpose of a two-part rental policy, under both competitive and monopolistic implementation, is to insure efficient utilization of the durable goods marketed thereby.
74 viding a unit of the good. Lessees facing this rental schedule have the obvious incentive to employ units of the durable efficiently (a typical lessee' s total cost is now given by wl + p g s + p^k = wl + pk, and the relative input price ratio is given by (6)). One way in which the time fee may be further illuminated is to look at a discretized case. The idle rental cost for a unit of the good is Pq = [r + d(y, 0)]C, and the rental cost incurred for intensity of use a, is ^ = [r + d(y, a)]C. The increase in the rental cost for utilizing a unit of the good is then Ap^ = p a -PQ = [ot)-d(y,0)]C, and the time rental fee, p^ = p^ aAp^, may then be written as P t = rC + d(y, a)(l a)C + d(y, 0)aC. The time rental fee may be viewed as being composed of three parts, a capital fee, rC, plus a premium for depreciation on nonutilized services, d(y, a)(l a)C, and a second depreciation premium for utilized services. The first depreciation premium equals the losses incurred, at the higher depreciation rate (both "built-in," and intensity depreciation), on the proportion of the initial outlays, for the unit of good, not utilized. The remaining depreciation charge is on the proportion of utilized capital services, where the rate of depreciation is the "built-in" depreciation rate, and this is incurred despite intensity of use. Thus, when the time fee, p^, is summed with the user fee, p u = [d(y, a) d(y, 0)]aC, the full opportunity cost of leasing the unit of the good, p^, is recovered. When the durable good industry is monopolized the two-part lease will not, alone, permit the monopolist to reach the vertically integrated
75 solution. Under the present model, there remains variability in the proportions with which potential lessees can combine the labor input with units of the durable and utilized services. As long as this variable proportions remains out of the control of the monopolist, vertical merger is the most profitable alternative. 7 There is, however, one class of cases within which a monopolist, as well as competitive producers, will find that a viable two-part lease yields results equivalent to vertical merger. Consider now the case where the final good is a processed input. This input, termed the "meter" good, is processed by the utilized services formerly embodied in the durable service stock. The product, q, is produced with the linearly homogeneous production, q = F(m, s, k), where now the meter input, hired units of the durable, and utilized services are combined to produce the product. The significance of the meter input is that units of it are processed by units of the employed service volume. Thus q is produced with fixed proprotions between the meter good and utilized services, while there remains variable input proportions between the volume of meter inputs employed, and hired units of the durable. The unit cost of obtaining the meter input, c, is assumed constant, while product demand is P = h(q) and demand elasticity is n = -h/h'q. When the service and meter inputs are combined in the fixed ratio, producers of the durables, independent of market structure, can Another alternative is full-line forcing discussed in Chapter I. For an early discussion of this case see Burstein (1960). The full-line forcing solution, for the present case, is noted in n. 9.
76 efficiently market their embodied services through two-part rental contracts. This assumption of fixed proportions, while restrictive, may not be as severe a limitation as it appears. It is particularly relevant in those cases where the vertical merger alternative is not available to the monopolist, in which case, units of the durable may be O leased on a service metering basis. First consider the integrated solution. The maximization of integrated profit, tt = Pqcm pk, yields the first-order conditions mrf b = (c+p 1 ), (7a) and mrf k = (p-ap'), (7b) where a=s/k=m/k is used, and where mr denotes marginal revenue, mr = P(1 Â— Â— ). The interpretation of these conditions differs only slightly from those in (1). Because units of the service and meter inputs are employed in unit bundles, their combined price is equated to their joint marginal revenue product. The firm will then employ the servicelabor input up to the level where its marginal revenue product, mrf b (where f b is the marginal product of the input bundle), equals the incremental cost of its employment, c+p'. That cost, as noted, is the sum of the meter cost plus the opportunity cost incurred in employing the services from the hired durable stock. The interpretation of (7b) is the same as before; units of the good are employed up to the level u There is, then, vertical integration into the provision of the product processed by the durable. For a discussion of the feasibility of the fixed proportions assumption see McGee and Bassett (1977).
77 where their incremental cost is just recovered from their marginal additions to the firm's revenues. These conditions, (7), are applicable to both monopolistic and competitive (n =0 ) supply of the product, and the usual interpretations apply. Moving now to the disintegrated case, it is apparent, for the same reasons given above, that the traditional rental policy is inferior. The two-part leasing policy however, is now a vialbe rental arrangement for both competitive and monopolistic supply of the durables. The competitive case yields a rental schedule, obtained as before, where the efficiency condition P t P-ap' Â’ now replaces (6) For the case of monopolistic supply, the profit maximizing user fee, p um = P sm a> and time fee, p tm are obtained by first recognizing that competitive users of the durables will employ them so as to attain the cost-minimizing conditions p I f b = p sm + c (8a) and p I f k = p tmÂ’ (8b) where Pj is the integrated product monopoly price and P gm is the effective service unit price. To achieve integrated profitability, as given by (7), the monopolist must set the two fees so that the integrated monopoly price, p^ (with related demand elasticity, nj).
78 results, i.e., so that mr = p T (l Â— ) Recognizing this, the i n I Q correct rental fees are obtained by solving (7) and (8) to yield and sm < -^ 4 > c, tm 1 i(9a) (9b) These prices, the service price of p $m (yielding the per-period user payment of p um =ap per unit of the durable) and the time fee of P tm result in the attainment of integrated profitability at the disintegrated position. The monopolistically set rates are proportionally larger than the competitive rates (when n.j = the competitive fees are obtained), and they are set so that producer-users employ the inputs up to that level where the respective value of their marginal products (evaluated at Pj) equals their respective, and monopolistically set, prices. In short, the monopolist is earning integrated profitability (2), the full. and the case of variable forcing solution, set prices be set on the II Q_ w 1 1 p I 5 P = MTIS p' 1 Â— n I 5 P ap' p tm i 1 ^m full jrtions between all inputs, in Chapter I, would require Â•line of inputs. To implement this pricing method, the lessee must be required to purchase all inputs from the lessor, at these extracompetitive prices. Since all input prices are raised proportionally, no input distortions are introduced by them.
79 on the inputs which equals, precisely, the difference between the average and marginal revenue contributions of the input in the integrated position, times the quantity of the respective inputs employed. Moreover, these prices induce optimal intensity of durable utilization. The lessees will equate the rate of input substitution to the new input prices, M fak = (c + p')/(p ap 1 ). Price Discrimination Regardless of the form which the two-part lease may take, e.g., payment as services are used or payment ex post, it is not inherently price discriminatory. This is so regardless of market structure. There is, of course, the possibility that a monopolist can set discriminatory prices, but the conditions required are the familiar ones, and remain independent of the two-part rental arrangement. It might be thought, however, that because two different prices are set, that a two-part tariff is in operation and, therefore, price discrimination is present. For the general case of competitive two-part leasing discussed above, there is no price discrimination. All durable users are required to make per-period payments that fully recover the per-period opportunity costs of serving them. For example, suppose there are distinctly different uses for units of the durable which are manifested in different yet simultaneous rates of utilization intensity. Thus, in the production of the different products, q^ and q ^ there are the corresponding intensities of durable utilization, and a j and the corresponding two-part rental fee schedules p p and p ., p ., CS 1 Ctl CS J C Lj where the respective marginal costs of serving each of the distinct
80 uses are and p^. Now, the economic definition of price discrimination is that the ratio of price to marginal cost of serving any particular customer is different than the corresponding ratio for serving another customer. But here, in the competitive two-part rental arrangement, these ratios are identical across all possible uses of the durables; (p^.c^. + P cti )/Pj = (P cs j + P ct j)/PjConsequently, there is no price discrimination in this case of two-part leasing arrangements, despite the presence of different full per-period rental rates. Each user is required to make per-period payments that are directly related to intensity of use, and which equal the opportunity costs of being served. The ratios of the various potential total perperiod prices to opportunity costs are identical across all users and, as well, the discounted value of the different payment streams are identically equal to the same thing, notably C, the cost of producing units of the durable. The mere observation that different users incur correspondingly different per-period full rental payments is not a sufficient indicator that price discrimination is present. Here, for the competitive case, the costs of serving the different uses are distinctly different, and, when they are explicitly taken into account, the different prices for the different uses are clearly nondi scriminatory. The same reasoning applies to the second case of two-part pricing, where the fixed proportions assumption was invoked. Moreover, when simple or uniform two-part leasing is employed, the resulting two-part rental arrangement is non-discriminatory, regardless of market structure. When monopoloistical ly set, the per-period price to opportunity cost ratio does however, depart from unity, just as it does for the nondurable good monopoly case.
81 When the conditions are such that the monopolist can segment his potential lessees into distinctly different markets, and when this condition is augmented by the inability of the segmented lessees to undertake arbi tragi ng activity, the monopolist may implement two-part rentals that are price discriminatory. Suppose, for example, there is one product industry requiring the use of the durables. Suppose further, if the monopolist were to merge into the production of the final good, that final buyers may be separated into two or more markets, and that the product may be priced differently in the separated markets. The presence of these conditions, when fixed proportions are present, imply that a disintegrated single pricing monopolist can achieve additional profits through integration into the production of the output of all but one of the separate product markets. It is equally well recognized that the same profitability may be achieved through the implementation of discriminatory intermediate good prices. To be successful this method of achieving integrated profitability must be accompanied by the nonarbitrage requirement at the intermediate market level. Supposing this requirement to be satisifed, the durable monopolist may then set a discriminatory schedule of two-part rental prices. In terms of the above notation, given i separable product markets, from (9), the optimal discriminatory service and time fees are set at (10a) and (10b)
82 where is the demand elasticity in the i'th product market. The implementation of these two-part prices achieves integrated profitability. In setting these prices, the quantity of the inputs employed in the separate product markets is identically the same as that which would arise under the vertical merger alternative. These quantities, determined from the integraged optimality conditions, the respective input marginal revenue products equaling the respective marginal factor costs, are then marketed to the separate product markets at prices equaling the respective value of the marginal product for these input quantities. This discriminatory two-part rental arrangement permits examination of another aspect of these durable good pricing solutions. Recalling that in all of the rental fee schedule solutions presented above, the solutions obtained required explicit use of the socially optimal costminimizing conditions, the rental fee schedules obtained, when implemented, induce an optimal intensity of durable good utilization. Indeed, if these rental fees did not yield this result, the rental arrangement would prove to be inferior to alternate marketing policies. From the discriminatory prices, (10), downstream producers are induced to employ the inputs optimally. The costminimizing conditions impl ied in (7) require that durable users equate the rate of substitution between the service-meter input, and the hired capital stock, to the respective factor price ratio. From (7) this implies that = pÂ— Now ^ rom (10) the induced factor price r 4n 1 ratio, in product market i, is and, obviously, the same r p ap intensity of durable utilization occurs in each and every product
83 market discriminated against. In short, there is no relation existing between intensity of durable good utilization and discriminatory two-part rental arrangements.^ The conclusions obtained in this section of the Chapter may be briefly summarized as follows: (1) a viable durable good rental policy, given that the durables are characterized by a variable service flow, does exist in the form of a two-part rental arrangement. Abstracting from the vagaries of transaction costs, this rental solution, in the more general case, may be adopted by competitive firms as an alternative to a durable sales policy as well as a vertical merger policy. (2) When the services of the durables are employed in fixed proportions with a second good, or, alternately, when the policy for marketing the services is the leasing of durables on a service metering basis, twopart rental arrangements provide, again, a viable method of marketing the embodied services. This conclusion is independent of the structure of the durable good industry. (3) Two-part rental arrangements are not inherently discrimi natory. When, however, a monopolist can set discriminatory prices, the two-part price arrangement can be di scriminatorial ly set. In any case, there is no relation to be found between intensity of durable utilization and the discriminatory prices. Some authors have supported the conventional wisdom that there is a relation between these magnitudes. See for example, Bowman (1973) and Posner (1974), as well as the discussion in Chapter II.
CHAPTER IV TYING ARRANGEMENTS AND ANTITRUST POLICY ISSUES Introduction Among the "exclusionary" business practices subject to the policy of the law are those subsumed in the term "tying arrangements." Tying arrangements, or perhaps more aptly, "conditional sales," may be defined as selling one item conditional upon the simultaneous purchase, or agreement to purchase, another item. In establishing the tests for the legality (or illegality) of a "tying arrangement," the initial approach to the problem by the Supreme Court was the recognition that two separate products must be involved: the "tying" good and the "tied" good. The sale of the former is conditioned upon the sale of the latter. According to the Supreme Court, tying arrangements have anticompetitive effects whenever there is a presence of some power over the "tying" product, and/or, whenever the value of sales of the "tied" product policy exceeds $200,000. ^ The requisite power over the tying product may be inferred from the 2 power to set price, or the presence of entry barriers. The argument is. Following the finding that, when patents are present, tying arrangements are illegal per se ( International Salt Co. v. U.S. 332 U.S. 392, 1947), the Court established the two product test for tying arrangements in TimesPicayune Publishing Co., v. U.S. 345 U.S. 594 (1953). Some twenty-five years later, the $200,000 "foreclosure" standard was established in Fortner Enterprises, Inc, v. United States Steel Corp. 394 U.S. 495 (1969) ( Fortner I ). 2 The standards for tying illegality are still emerging. In previous tying cases, where, as Dam (1970) clearly points out, distinguishable 84
essentially, that the creation of a tying arrangement may create barriers to entry, thereby introducing anticompetitive effects for potential entrants. The power may also be inferred bacause there is "leverage" involved in tying arrangements where the leverage results in the extens ^ on .f existing monopoly.^ In addition to these standards, the Supreme Court, citing scholarly contributions on the subject, recently acknowledged' the conclusion advanced by some economists that metering tying arrangements are price discriminatory, and evidently, meter pricing may be banned upon evidence of the latter. 4 That the illegality of tying arrangements may be inferred from tied good sales receipts of $200,000 or more is based upon the "foreclosure" doctrine. Basically, as a result of the tying arrangement, there is business practices were grouped together, the Court entertained far-reaching concepts from which the requisite power over the tying good could be inferred. Among these are: (1) copyrights on the "tying" good (United -S tates v. Lo ew s Inc. 371 U.S. 38, 1962, a block-booking case), ( 2 ) the tying product's desirability to consumers (again in Loew's, but see also United States v. Jerrold Electronics Corp. 365 U.S. 567, 1961, a metering oriented case, where it is asserted that this desirability confers everage to persuade customers, and that this buyer's leverage constitutes a sufficient economic power to invoke the per se doctrine), (3) the uniqueness in the tying good attributes (again, Loew's), where, in Ml e d States Steel Corp. v. Fortner Enterprises, Inc. 97 S.Ct. 861, ( Fortner II ), after noting that this uniqueness may be manifested in the power to raise prices, or other burdensome terms, the Court appears to have recognized that uniqueness may properly be considered as a seller's cost advantage, and (4) there is the appreciable restraints test ( Fortner I ). 3 The leverage test was established in Times-Picayune op cit, n.2. 4 In the Fortner II opinion, Justice Stevens noted that "If, as some economists have suggested, the purpose of a tie-in is often to facilitate price discrimination, such evidence would imply the existence of power that a free market would not tolerateÂ” (p. 831).
ob foreclosure in part or all of the sales in the tied good market, and this c is anticompetitive when this sum exceeds $200,000. The presence of any of these anticompetitive effects; power over price, barriers, leverage, price discrimination or foreclosure, establishes the illegality of tying arrangements. Moreover, when the tying arrangement is of the metering variety, it is illegal per se ( International Salt ),, but with the general attenuation of the power tests, and the wateringdown of the foreclosure standard, the various business practices subsumed under the tying rubric are almost automatically a violation of one or r more antitrust statutes. The scholarly debate on this subject can hardly be regarded as being as resolute as the Court in finding anticompetitive effects from tying arrangements. This is particularly the case where meter tying is involved, which, with few if any exceptions, brings a legal patent monopoly within the ambit of antitrust law. Bowman (1957) and Posner (1974) have advanced the view that, while meter tying arrangements may be characterized as price discriminatory, they do not involve leverage. Moreover, Posner (1974) has noted that any exclusionary effect encountered in meter ties may be regarded as a trivial adjunct to the tying product ..." (p. 508). 5 This standard was set in Fortner I Typically, economists caste the foreclosure theory in percent of market sales, see for example Comanor (1967), Bork (1969), Peltzman (1969), and Mueller (1969). ^In Times-Picayune where a unit-contract was at issue, the Court established that a Section 3 Clayton Act violation was established if either market power or foreclosure were found to exist; a Section 1 Sherman Act violation was established if both of these effects were found to exist; and that a Section 5 FTC Act violation occurred in either event.
87 It was noted in Chapter II that the theory supporting the conventional view, that meter tying is inherently price discriminatory, is incorrect. This theory gives insufficient account to the obvious presence of producer durable goods in observed meter tying arrangements. Moreover, in Chapter III, where the economic theory of durable goods is accounted for, it was shown that the existence of meter pricing (the two-part lease) is not inconsistent with conditions of competition, and that, from this theory, it cannot be inferred, a priori, that meter pricing is discriminatory. In this Chapter, these last two points are again emphasized through discussion of two examples, examples obtained from the two-part leasing model developed in Chapter III. The general thrust of the subsequent discussion is that, among the types of tying arrangements considered, all may be viewed as forms, and degrees, of vertical integration, and that the vertical integration effect of meter tying may be distinguished from the effect of package tying arrangements. Through consideration of these integrating effects of tying arrangements, further clarification of their leveraging nature is obtained. What emerges from the discussion is that the price discrimination thesis must, indeed, rely upon the traditional definition of price discrimination, and not the sweeping conventional conclusion that meter pricing is, necessarily, discriminatory. Moreover, it is argued that the leveraging nature of tying arrangements is not so easily obtained as implied by Posner (1974). The first section of the Chapter defines selected methods of vertical control, including the meter tie. These definitions initially serve to distinguish metering from the other forms of tying, where the latter are
identified as package tying arrangements. The second section of the Chapter distinguishes, by example, the vertical integrating effect of meter and package ties, where the former is cast within a leasing framework. Implications for existing the tying policy debate are reviewed in the last section of the Chapter. It should be noted that the examples used in the subsequent discussion are selected solely to highlight the leverage, price discrimination, and vertical aspects of tying arrangements. A more general treatment of vertical control requires recognition of the various incentives to vertical integration (see for example Blair and Kaserman, 1978b; Burstein, 1960b; Coase, 1937; Frank, 1925; Gould, 1977; Machlup and Taber, 1960; J. Robinson, 1933, appendix) as well as the relationship of contractual vertical controls to outright vertical merger (see for example Bork, 1954; Coase, 1937; Comment, 1952; Kaserman, 1978; and Kessler and Stern, 1959). Tying Arrangements : Definitions and Selected Vertical Controls Implicit or Explicit Package Tying Arrangements Full -line forcing Full-line forcing is a vertical control that, in pure form, is manifested by an input supplier requiring that producers purchasing his intermediate product, also purchase their entire line of inputs from or through him.^ When this contractual requirement is met, all producers It has been suggested by Bowman (1957), among others, that an example of full -line forcing may be found in United States v. United Shoe Mach. Co. 247 U.S. 32 (1918). Whether or not this is so, as noted in the text, would depend upon whether or not United was engaged in pricing other than the pure metering type.
89 subject to it may be induced to undertake production and employment precisely as the supplier deems it desirable (this assumes, of course, that these purchasers are not able to obtain all their input requirements at lower prices offered elsewhere). This inducement is achieved by supplier set prices upon all inputs utilized by producers, that is, by setting all imput prices, the economic incentives of producers are direct by the supplier. In particular, when optimally instituted, fullline forcing directs producers to behave as would a downstream production division in an integrated firm, where overall management decisions are made at the input supplier level. In this way, the supplier reaches forward to the product market, and the vertical integration effect of optimally instituted full line forcing is then achieved. Restricted line forcing Restricted line forcing may be viewed as a variant of full-line forcing, whereby the supplier contractually specifies the technique of producing the final good. Restricted line forcing, optimally instituted, fixes proportions in which producers may employ their inputs, an expli8 cit type of packaging. By fixing the input proportions, the supplier may then achieve full integrated profit by pricing but one component of the specified input bundle. Obviously, when all other inputs contractually bundled with suppliers input are available at given market prices, g One example may be offered in F.T.C. v. A. and B. Gratz, et al I.F.T.C. 249 (1918). Here, Gratz marketed the cotton bailing materials, steel ties and square yards of burlap bagging, in the fixed ratio of six of the former to six of the latter.
in setting the price on his own product the supplier sets the entire price for the input bundle. Like full-line forcing, restricted line forcing induces producers to employ the various inputs in a specified manner, and both controls fix the costs of production (and perhaps price) for the final good. Lump-sum pricing Lump-sum pricing behaves like a lump-sum tax on producers, impacting therefore upon the producer's fixed or overhead cost.^ To avoid the possibility that particular producers may seek to expand their level of production beyond that desired by a supplier (and they may seek to do this to spread out the overhead charge), the supplier may institute supplemental control that (implicitly or explicitly) fixes the scale of each producer's production facilities. The optimally instituted lump-fee control again induces producers to select a particular employment combination, one previously deemed desirable by the instituting supplier. Producers are then induced to behave as would a production division in an integrated firm, where management is again located at the supplier stage. Another familiar form of tying contract is block-booking, where movies of different grades are marketed as a block. As an example, suppose grade A and B movies will fetch the following net revenues when shown in movie houses I and II; movie/house I II A $50 $60 B 70 30 Sum 120 90 Four pricing arrangements for these movies, with associated distributions of the returns, are:
91 Product royalties Product royalties, an obvious form of vertical control, subjects producers to an internally imposed ad valorem tax on output. The supplier then collects integrated revenues on each unit of product sold. Meter pricing Meter pricing invariably arises when intermediate suppliers are marketing services embodied in capital goods, typically machines, but other capital goods need not be excluded.^ Pure meter pricing requires levying two prices, a price for units of service utilized, and a per-period time fee that assures a per-period rental rate sufficient to recover the cost (plus an additional sum when monopolistically implemented) of serving the particular user. prices prof i ts (package) movie house option A B A+B distributor I II i $50 $30 or $80 $160 $40 $10 i i 50 70 or 120 170 0 10 i i i N/A N/A 90 180 30 0 i v Vertical integration 210 0 0 Option i and ii are types of single pricing for the movies, option iii is block-booking, and iv includes alternate methods of obtaining integrated profit. In Loew' s, it was argued that options like i or ii should be used for the pricing of the movies. Thus, for this type of pricing arrangement, the distributor will choose ii, earning $170, while movie B is not viewed in movie house II. For a general discussion of block-booking, see Stiqler (1963). ^The capital good may be of many sorts, such as movies. Consider the block booking example presented in n.9. If movie tickets, net of movie house normal returns, are optimally priced at $1.00 each, and the same net revenues in that example are generated, these capital goods may be marketed on a metering basis (all tickets used must be purchased from distributor at $1.00 each), all quasi-rents are then collected by the distributor. For an analytical example of the quasi-rent case, see n.17. Examples of meter pricing abound in the antitrust case literature. For one discussion of them, see Hilton (1958). The most frequently cited
As the term implies, this type of pricing is on a metering basis, where users of the durables make payments for services withdrawn from them according to their meter utilization. When the services are marketed through a leasing arrangement, payment for services utilized may be recovered ex post, where the sum recovered is determined by the amount of services withdrawn as registered on a meter. Alternatively, the service revenues may be recovered directly as services are withdrawn, through, for example, a coin receptical. In the case of meter tying, the service revenues are recovered through the pricing of a second good, where a unit of the latter is employed in conjunction with a unit of service, and the price of their combination equals the sum of the service price plus the price of the second good. Tying Arrangements: Two Examples, Metering and Packaging As the discussion in Chapters II and III made clear, when producers seek to market embodied capital services, a successful marketing policy requires a two-part leasing arrangement when the durables may be employed at various rates of intensity. It was noted that is, when the lessors adopt a traditional time rental arrangement, the leased durable stock will not, generally, be employed in a socially efficient manner, lessees are induced to employ it too intensively. Fundamentally, the underlying need for the two-part lease is generated by the existence of costs of utilizing the capital stock, operating costs borne by lessors that cannot be precisely example is IBM's former practice of charging a machine rental fee, and also charging users an operating fee, where the latter was collected by premiums levied upon the price of cards sold to users through IBM, see International Business Machines Corp. v. U.S ., 298 U.S. 131 (1936).
93 covered without recourse to a pricing method which assures that lessees bear these costs as they utilize the services embodied in that stock. One overriding purpose of the two-part lease is to insure that lessees bear the full opportunity costs incurred by lessors in serving them, thereby permitting efficient utilization and optimal recovery of lessors' capital outlays. In the following two examples, one such cost is introduced, lessors' losses due to depreciation of the durable good's per-period service stock ("wear and tear"). Introducing this particular cost is sufficient to highlight the distinctions sought, and to make the exposition most clear, a particular form of the depreciation function is employed. For a particular period, given the hired durable good service stock k, and the per-period quantity of the embodied services employed, s, the per-period intensity with which the durable stock is utilized may be measured by a = s/k, the quantity of services utilized to service stock ratio. The depreciation rate of the stock is then given by d = y + ga, where y is the "built-in" rate of deterioration in the service stock, and g is the incremental increase in the depreciation rate resulting from the employment of one or more service units from the existing stock. With this depreciation rate, the full per-period rental or opportunity cost, p, of utilizing a unit of the stock is p = (r +y )C + gaC, (1) where r is the interest rate and C is the constant cost of obtaining a unit of the good. The opportunity of cost of using a unit of the good, is the sum of the two interest premiums; an "idle rate" premium, and a user "depreciation" premium. The former is the sum that must be paid regardless of whether or not it is used, and equals the interest paid on
*4 the initial cost of the unit of the good plus losses due to built in depreciation. The user depreciation premium is a payment that just recovers the opportunity cost attributable to actual use per unit of the durable (i.e., the cost attributable to withdrawing capital services). "Pure 11 Meter Pricing Here, the two-part lease results in the receipt of the revenue that would be obtained when durable lessors integrated forward into the direct supply of the processed good, and not into the production and sale of any subsequent output the production of which requires the use of these goods. This may be seen more precisely by considering a product q, whose production function (assumed linearly homogeneous) is given by q = f(s, m, k) where the hired stock, utilized services, and the stock of a third input, m, the "meter" good, are the inputs employed (subscripts on f denote the relevant derivatives). The meter good is assumed available at a constant cost of c per unit, and, to perform an accurate metering function, it is defined so that q is produced with fixed proportions between it and services utilized, s = m, while the proportion in which services may be employed with the hired stock is variable. Given the product demand function, P = h(q) (where q = -h/hq is product demand elasticity), profit obtained in the production of q, n = Pq cm pk, is maximized when mrf b = c + gC (2a) and mrf k = (r + y)C, (2b)
95 where mr = P(1 f b is the marginal product of a unit of the servicemeter input, and f k is the marginal product of a unit of the hired stock. 11 These conditions implicitly define an optimal intensity of durable utilization that is independent of product market structure. This is seen by (3), the cost-minimizing condition, where the rate of factor substitution, Mbk = f b / f kÂ’ 1S ec 1 ua ted to relative input costs H bk ( 3 ) From (2), it is evident that the firm simultaneously employs units of the service-meter input, and the durable, up to the level where their respective marginal revenue products equal their respective marginal factor costs. For the service-meter input, this cost is the sum of the unit cost of the meter good plus the marginal depreciation cost incurred in using the embodied capital services, c + gC. The unit cost of hiring the stock is the opportunity cost of durable utilization, p = (r + y)C + gaC, less the per-period user cost gaC, yielding the incremental capital cost plus losses due to built-in deterioration, (r + y)C. The interpretation of equations (2) is easily modified for the alternate product market structures, monopoly (n < ) and competition (n = ) where for the latter, the marginal revenue products equal the value of the respective marginal products (mr = P, conditions (2) also describe product market equilibrium). 11 It is assumed, throughout, that there is an efficient rate of durable utilization, less than maximal capacity.
96 Now, consider the two-part leasing arrangement, where intermediate durable good producers market the embodied capital services to competitive firms in the product market through a two-part rental policy (meter pricing). For the case of direct service pricing, the twopart lease requires setting a unit fee for services utilized, p s as well as a time fee, p^, per unit of the leased stock. As shown in Chapter III, these fees are optimally set when and sm c + ngC n 1 Â’ tm = n(r+y) C n 1 (4a) (4b) The fee schedule given by (4) is applicable to monopolistic supply (these prices are subscripted by m), while the competitive fee schedule (subscripted by c), (5), is obtained by setting n =0 > p sc = 9 C Â’ (5a) and P tc = (r+Y)C. (5b) Clearly, under either competitive or monopolistic two-part leasing arrangements, durable lessees are induced to utilize the stock efficiently = (C+P )/p = (c+gC)/(r+y)C, when required to make payments for services as they are withdrawn from it. Moreover, it is not difficult to establish that, independent of durable good market structure, when the lessors employ the metering input as a device to recover payments for utilized services, in lieu of direct service pricing, an optimal two-part lease results. This is, of course, the meter tying arrangement case.
y/ In the case of pure meter tying, the combined service-meter input price, p^, is set where IL(_ c+ .9.C), = c + d bm r)~l ^smÂ’ (4 1 a ) be = c+ 9 C = c + PscÂ’ (5'a) where p bm is the optimal monopolistically set price for the input, and P bc is the corresponding competitive price (g=). From the right-hand side of ( 4 1 a ) and (5'a), it is evident that the optimal price for the service-meter input is the sum of the prices for the two inputs when they are priced individually. This is the only substantive observation to be made for the case of meter tying. Essentially, through adding the service price on top of the meter good price, the service revenues are collected. A few features of this example of pure metering form of tying are noteworthy. First, it is plainly evident that pure meter tying cannot be characterized, a priori, as a monopolistic pricing practice. The implied purpose of meter pricing, independent of meter selection, is to assure recovery of the full value of durable good utilization, and this is so regardless of whether that value is competitively or monopolistically 12 determined. Normally, competitive firms can market the services in one of three ways; sell the durable, lease the durable, or enter into the sale of the thing processed by the embodied services of it. There is no necessary reason to expect that, among the competitive suppliers, some firms would sell the durables, some may lease them, while others may integrate forward. One would expect however, that all firms would earn the same normal return, regardless of the method in which the services are marketed. Moreover, there would be competitively determined prices for units of the stock, there would be competitive prices for
98 Second, there is no distinction between the substantive economic effect of pure meter pricing tying arrangements and the direct supply of the goods processed by the metered durables, identically the same allocation results in either case. Granted, these are two different arrangements for marketing the embodied services, but in the present context, where the alternate marketing costs are assumed to play an insignificant role, the substantive equivalence of the effect of either marketing policy is established, independent of durable good market structure. Third, some caution should be exercised in characterizing the tying input price, p bm or p bc as extracompetitive. When meter pricing is effectuated through ex ante recovery of user charges, through a service fee levied directly on top of the metering input price, there may be a temptation to conclude that an extracompetitive price for the latter good is being levied. Once it is realized that this price is a price for both the meter and service input, however, it does not follow, a priori, that this price is extracompetitive. Whether or not this input price is extracompetitive depends upon whether price exceeds marginal cost. When there is durable good monopoly, it should be further recognized that the additional fee levied through the pricing of the metering good is still a charge for capital services utilized, and not an extracompetitive fee for the meter good. the processed goods, and there would be competitive prices for processing those goods. If, asthe services are taken from the durables, costs of wear and tear are introduced, owners of the durables will consider these costs when utilizing them, and lessees, the users of the durables, will bear these opportunity costs if a rental marketing policy is to remain viable. In short, lessees will incur a rental rate that includes an "idle rate premium as well as a "depreciation" premium, where the latter varies according to the amount of services extracted.
99 Metering and "Packaging To combine full line forcing with meter tying, suppose that a final good, Q, is produced with the linearly homogeneous production function Q = F ( 1 s, m, k), where labor services, 1, are simultaneously employed with units of the durable, utilized services, and the metering input. Labor's wage, w, is assumed to be constant.^ Given the product demand function, P = H(Q) product profit, II = PQ wl cm pk, is maximized when the following optimality contitions are satisfied mrF.| = w, mrF b = c+gC, and mrF^ = (r+y)C, where mr = P(l-^-), the F.. are the respective marginal products of the inputs (i = 1, b, k), and where b again denotes the meter-service input. Employing the results obtained in Chapter I, when there is monopoly in the durable good industry, the full line forcing solution obtains when the firm sets transfer prices for each of the three inputs, p p, and W D P t at the following levels gw n-l Â’ (6a) n(c+gC) n-l Â’ (6b) n(r+y)C n-l Â• (6c) In contrasting packaging with metering tying arrangements, only the full-line forcing package tie is examined. It is, analytically, the most tractable. But because of the previously noted similarity among all package ties, the results obtained apply equally well for all previously selected forms of package ties.
I 00 When there is competitive supply of the durables, rp 00 and the fullline forcing prices reduce to 'wc w Â’ (7a) 'be = c+gC (7b) 'tc = (r+Y)C (7c) In the light of the previously discussed pure metering case, it is evident from (7) that competitive durable producers would not transfer the labor unit input at an extracompeti tive wage. There remains, however, the need for competitive two-part pricing to recover payments for services utilized, i.e., to meter price. When competitive lessors require that lessees purchase their labor input from them, it is evident from (7) that the transferred labor would be priced at the going market wage. This result provides one basis for distinguishing whether packaging is a feature of a competitive tying arrangements. If competitive lessors sought to make an additional return on the services of the labor transferred, lessees would then simply contract with other lessors, perhaps those offering pure meter tying arrangements. When the tie is monopolistically implemented, however, lessees would not have this latter option.^ 14 There are recognized circumstances where packaging vertical controls exist, yet may be accounted for by legitimate considerations. One may be a maintenance requirement, where suppliers require lessees to purchase their maintenance requirements from them. Thus, there is an appearance of full -line forcing, yet it can easily be legitimized by realizing that it may not be in lessees' interest to perform maintenance on leased machinery in the most efficient way. See, for example, United States v. Jerrold Electronics Corp. 365 U.S. 567 (1961).
101 The vertical integration effect of meter tying is, then, distinguished from the integrating effect of package ties. When the vertical control is used to induce producers to select a particular and pre-specified entire method of production and employment, the effect is vertical integration into the production of the supplier's product. Pure meter tying, however, has the effect of integrating into the production of the thing processed by units of the durable, and that is all. Tying Arrangements: The Policy Issues When Is Meter Pricing Discriminatory? Definitionally, price discrimination will manifest itself in the presence of unit price to marginal cost ratios that differ among buyers 1 5 of the product. In terms of the present discussion, these ratios may be measured in either per-period values, or in present values (they come to the same thing). To further clarify the necessity of applying this test to determine the presence or absence of discriminatory meter pricing, three examples, where pricing variability is present, are di scussed. Suppose that a durable monopolist sets the two-part fees, through a meter pricing tying arrangement, where the fees are given by (4'a) and (4b). Suppose further that, in each period, units of the durable are identically employed in the production of the same final good, but that in two succeeding time periods, the demand in the latter 1 5 Marginal cost is interpreted as inclusive of all unit costs incurred in serving a particular user (e.g., transport costs, etc.).
expands, while product demand elasticity stays identically the same. Taking the change in product demand as a short run, temporary change, so short that the service stock is the same in both time periods, the intensity of durable utilization will temporarily increase in the high demand, or peak, period. Thus, there is a different a for the succeeding time periods ( keeping the service stock fixed), say a-j and ap (a-| < c^). Becuase, by assumption, demand elasticity has not changed over the two periods, the monopolist will charge the same service-meter unit price in both periods, p, = n -'c + bm n 1 Given these conditions, it is apparent that the monopolist will obtain receipts in the two successive periods that differ according to intensity of use. The full per-period monopoly price for durable use in period i, p .. (i = i, 2), equals p mi p bm a i + p tÂ’ which from (4 'a) and 4b) may be written as P mi n-1 me ( 8 ) where mc^ = ca^ + (r+y+ga^)C. Now, from (8), it is clearly evident that p m _j/mc.j = p^j/mCj = n/n-1 and, therefore, the existence of different per-period durable user payments does not provide sufficient information to conclude that there is price discrimination. Note further that there may well be different per-period durable user payments, regardless of durable good market structure (in (8), let n = 00 for the competitive case, and observe that me. f me. when a. f a.). J 0
103 A second case may arise when the unit cost of the meter input, c, is different for two different uses for units of the service stock. For this case, the meter-service unit price is now D = n( c 1 + gC) ^bmi n 1 where i now denotes a particular use whose meter unit cost is c^. Once again the per-period fees for the different use differ, where these differences are now manifested in different service-meter input prices, and attributable to different costs of the meter input. The full per-period fee in use i is again given by (8), where now me. = c^a. + (r+y+ga. )C. Once again, p ./me. = p ./me. = n/n-1 and it cannot be ^ J J concluded, a priori, from observed differences between prices for the meter-service input, that meter pricing is discriminatory. Moreover, observed differences in these prices are insufficient indicators of whether or not there is monopoly in the durable good industry (again, let r\ = a>, and observe that (8) still holds, i.e., me. f me., if c Â• f c-). J J Consider now, a third case, one of price discrimination. Suppose the product market can be segmented into i markets, where if the monopolist integrated into all but one of these markets, different monopoly product prices, p^ would be set (and, as well, a different demand elasticity, > arises in each product market) Equations (4'a) and (4b) are then replaced by (9). 1 6 For example, it may cost t. to ship a unit of the meter good to user i's location. Then c. = c + t..
104 (9a) and ( r+y) C a n, 1 (9b) where these are the two-part rental fees set for durable users in product market i. Now, if the durable good monopolist can prevent arbitraging activity among users of the durables facing different fees, however collected, the full per-period receipts for use i of the durable is then where me ca + (r+y+ag)C. Clearly, p^/mc f p m j/mc, and price discrimination is present.^ These examples make clear that price variability in the meter tying case is not a sufficient indicator of price discrimination. The latter is present when there is divergence between the price to cost ratios for different customers. An alternative formulation of the metering case, one perhaps of monopoly, would be to suppose that units of the durable have separate and isolated uses, while no bilateral or successive monopoly is present. Abstracting from the depreciation charge, let there be rigid meter or service input to processed output ratios for i separate uses, them m. = s i ~ ^i^i 1S serv i ce quantity employed in the ith market for processed product q i (the p. are constants, i=l, ., I). Given the ith product market demand function q^ = H ( ) where P. is the price of the i'th product, it is then assumed that price will equal marginal cost, P.j = 3 1 -(c+p sl ), where p is the service unit price charged in use i. Now, for brevity, assume that in all uses, the present value of the returns from each of the service revenue streams are no less than capital outlays. The service market demand function is simply, S E8.jH.j [3.j (c+P s1 ) ] where the product market clearing condition was used (price equals marginal cost). S = ZB i q i or
105 When Does Meter Pricing Involve Leverage Ward Bowman (1957) distinguishes the optimal pure meter pricing tie (his counting case) by noting that unlike other types of tying arrangements, leverage is not one of its characteristics. Leverage describes the creation of a new or second monopoly, and when, as a result of the tying arrangement, there is a reduction in the output of the tied good, leverage is present. Bowman's test for leverage, the impact upon the output in the tied market, is a correct test when it is assumed that alternative means of meter pricing are available to the durable monopolist, or, that the durable monopolist has the option of entering into the supply of processed goods. 19 When this is the case. Bowman's test would reveal the presence of leverage only if a packaging type of control were used. Bowman is, therefore, When setting a uniform service unit price, p service monopoly profits, n=p s S, are maximized when price is set s so I P sm = c /( Z kjP-j-l), where q. is the resulting product demand elasticity in market i, and k^= s^/S. When the services are priced through the pricing of the service-meter input, the uniform price for this input is then E k n n Â• P bm = c ^zk. r -l ) Â• Here, in the pure quasi-rent case, different revenues are earned from different units of the durables, but it is the solution to a quasi-rent problem, and, generally, is unrelated to deliberate price discrimination. 1 8 This is Bowman's (1957) suggested test for determining whether or not leverage is present. 1 9 Posner (1974) apparently supports this view. With the pure meter tie evidently in mind, Posner writes: People used to regard tying as a method by which a firm having monopoly in one market (for example computers) could obtain
implicitly arguing that a patent confers the right to market the embodied services through sale, lease, or a "do-it-yourself" policy. When this is indeed the state of affairs, his distinction is quite useful When a durable monopolist can meter price through tying or an alternative method (or is permitted to integrate into the sale of the goods processed by the durables), there is no leverage: the quantity of the meter good utilized is the same in either case. When the durable monopolist also contractually adopts a package form of vertical control, the pricing of the other inputs by the monopolist will affect the quantity of the latter employed, and, from this perspective, the usefulness of Bowman's distinction emerges. No leverage may be attributed to the meter tie, but leverage is present in the package tie. From the standpoint of the vertical integration effects distinguished earlier, it is now evident that whether or not there is leverage, depends more fundamentally upon the degree of vertical integration rights granted to the input monopolist, and not upon the conceptual availability of a meter alternative. When an input supplier has the option to achieve any desired level of vertical integration, Bowman's test for the presence of leverage reveals that no leverage is present when the supplier adopts either a meter or package tie. a monopoly of a second product (such as computer cards) by requiring all purchasers of the first product also to buy the second from it. We now know that this "leverage" theory is incorrect, (p. 508).
107 Thus, when a patentor of an intermediate durable good is entitled to market the services embodied in it, either by sale, rental, or a "do it yourself" policy, meter pricing tying arrangements cannot be objected to on the basis of the leverage theory. Similarly, if a franchisor is entitled to the returns from the finished goods protected by the franchise, the use of any of the selected tying arrangements cannot be objected to on the basis of this theory. When, however, a durable good supplier has the option of vertically integrating into the supply of the processed goods, but no further, the application of Bowman's test does reveal that leverage is present for package vertical controls, and not for meter tying. It is evident, therefore, that whether or not leverage is present depends solely upon the rights to vertical integration. Summary The illegality of tying arrangements may be inferred from the presence of power over price, entry barriers, leverage, price discrimination, or foreclosure. In the scholarly debate on this subject, however, it is concluded that the practice of meter tying may be distinguished in that it is only characterizable as price discriminatory. This Chapter has argued that meter tying cannot, a priori, be regarded as discriminatory. To conclude that meter pricing is discriminatory, requires a finding that the ratios of price to marginal cost for different customers differ. Moreover, it has been shown that meter pricing may not be characterized by leverage when patentors of durables have the option to market the goods processed by units of them.
108 What emerges from these results is the proposition that the per se ban on meter tying arrangements, established in International Salt may lack a supportive economic rationalization. This conclusion, for the patent tie-in case is implicitly supported in the works of Bowman (1973) and Posner (1974). These authors have offered, however, that a basis for prohibition of meter tying, by a "good" monopoly, may rely upon the conclusion that the practice is discriminatory. The results of this Chapter (as well as the results obtained in Chapter II and III), clearly demonstrate that there is a priori, no economic basis for this price discrimination conclusion. Thus, barring unforeseen refutation of the above mentioned results, the per se ban on meter tying arrangements cannot be adequately supported purely on the basis of allocative economics. This conclusion, that the per se rule is insufficiently supported by purely economic consideration, suggests that a rule of reason approach be adopted when antitrust statutes are brought to bear on meter tying arrangement cases. Through this policy approach, with potentially higher enforcement costs, more accurate attention may be brought to bear upon vertical aspects of tying arrangements, discrimination aspects of these practices, and, indeed, upon a more thorough understanding of the competitive impact of them.
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BIOGRAPHICAL SKETCH The author was born in Hanover, New Hampshire, on October 16, 1947. Since that time he moved with his family of six children to New York, then on to Florida. In 1965, high school education was completed at P. K. Yonge High School in Gainesville. The author spent the following year working and playing semiprofessional basebal 1 The author spent three years in the United States Army, serving the last two as an Infantry Officer. The author received the Bachelor of Arts degree in Education in 1973, at the University of Florida. On August of that year, the author married Ms. Nora Ruth Kenny, a former lifelong resident of Miami, Florida. From 1973 to the present, the author was a graduate student in the Department of Economics at the University of Florida. During that time, on October 12, 1976, Nora gave birth to Rebecca Ruth Hansen. 114
I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Roger D. Blair, Chairman Professor of Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Sanford^V. Berg Associate Professor of Economics
I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. This dissertation was submitted to the Graduate Faculty of the Department of Economics in the College of Business Administration and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 1978 Associate Professor of Management Dean, Graduate School