Legal vs Ownership Unbundling in Network Industries

Transcription

1 Lega vs Ownership Unbunding in Network Industries Hemuth Cremer, Jacques Crémer, Phiippe De Donder University of Tououse (IDEI and GREMAQ) 1 Aée de Brienne Tououse Juy 3, 006

2 Abstract This paper studies the impact of ega unbunding vs ownership unbunding on the incentives of a network operator to invest and maintain its assets. We consider an industry where the upstream rm rst chooses the size of a network, whie severa downstream rms then compete in seing goods and services that use this network as a necessary input. We contrast the (sociay) optima aocation with severa equiibrium situations, depending on whether the upstream rm owns zero, one or two downstream rms. The rst situation corresponds to ownership unbunding between upstream and downstream parts of the market. As for the other two cases, we equate ega unbunding with the foowing two assumptions. First, each downstream rm maximizes its own pro t, without taking into account any impact on the upstream rm s pro t. Second, the upstream rm is not aowed to discriminate between downstream rms by charging di erent access charges for the use of its network. On the other hand, we assume that the upstream rm chooses its network size in order to maximize its tota pro t, incuding the pro t of its downstream subsidiaries. Our main resuts are as foows. Because the investment in the network is not protected, at the time at which it is made, by a contract, the upstream rm wi not take into account the interests of its cients when choosing its size. This e ect can be mitigated by aowing it to own part of the downstream industry. In other words, ownership separation is more detrimenta to wefare than ega unbunding. We aso obtain that these resuts are robust to the introduction of asymmetry in network needs across downstream rms, imperfect downstream competition and downstream investments.

3 1 Introduction This paper studies the impact of ega unbunding vs ownership unbunding on the incentives of a network operator to invest and maintain its assets. We consider an industry where the upstream rm invests in and maintains a network, whie severa downstream rms compete in seing goods and services that use this network as a necessary input (i.e., no bypass technoogy is avaiabe, at east at an economicay reevant price). Many network industries t this description (teecommunications, raiways, eectricity, etc.) but we have in mind particuary the natura gas industry. There are many papers in the reguation, industria economics and economics of organizations iterature that study the impact of various ownership structures in network industries. The simpest such structure is one in which an upstream rm ( rm U) provides an input to a downstream rm ( rm D). These papers often compare the behavior of a verticay integrated rm with the equiibrium situation where the upstream and downstream activities are undertaken by separate rms (i.e., rms whose ownership di er from one another). There are two types of considerations that might induce rm D and U to merge. First, they might want to use the combined weight of the two rms for strategic purposes. For instance, when the upstream rm has market power in the suppy of the input, but the downstream rm faces competition, the merger can be a way to prevent a form of tricking up e ect of competition. We wi ca this view the antitrust perspective, as it is the fear of this type of consequences that prompts competition authorities to disaow some mergers. Second, there might be some e ciency gains to running the two rms as a singe unit, and the aim of the merger is to take advantage of these e ciency gains. This type of merger can arise in a competitive market, whereas the rst type coud not. To stress the fact that authors who write on this topic are interested in the interna functioning of the rm, we wi abe this branch of the iterature the manageria perspective In this paper, we wi be considering a situation where rm U is reguated, and 1

4 where severa downstream rms compete with each other. Reguatory practice has typicay anayzed the ownership of a downstream rm by the upstream rm in the antitrust perspective and with suspicion: this ownership is seen as an open door to anticompetitive discrimination; we think that it is fair to say that reguators have often accepted vertica integration as a poitica compromise. The aim of this paper is to begin exporing what the manageria perspective can bring to the debate. >From the manageria perspective, this paper mainy draws on the insights inked to the notions of incompete contracts and speci c capita. In many circumstances, upstream and downstream rms must make investments in order to improve the bene ts they derive from their reationships. For instance, they need to conduct some research and deveopment. This investment is speci c if it is productive excusivey within the context of this reationship. 1 Because of the incompeteness of contracts, the two rms, if they are not integrated, wi choose suboptima eves of investment. Vertica integration wi incite them to take into account the interests of their partner, and wi therefore mitigate the resuting ine ciency. What the manageria perspective cas vertica disintegration corresponds to the ownership unbunding scenario that we study in the current paper. On the other hand, the intermediate situation of ega unbunding has, to the best of our knowedge, not been studied previousy in the iterature. By ega unbunding, we mean the situation where the upstream and one or many downstream rms beong to the same owners and where these owners, athough they are the residua caimants over the nancia returns generated by the rms assets (i.e., they keep the rms s pro ts), do not have the fu contro rights over the rms decisions. 1 There are degrees of speci city depending on the usefuness of the investment outside of the reationship with the other rm. For simpicity, we assume that the investment is ony usefu in the framework of the reationship that we are considering. The notion of incompete contract is introduced in the economic iterature by Simon (1951). Among the cassica eary references on vertica integration one can cite Kein, Crawford & Achian (1978), Wiiamson (1985) and Grossman & Hart (1986) (which is criticized by Riordan (1990)). For accessibe surveys see Crémer (1995) and Tiroe (1995).

5 More precisey, in our context ega unbunding between upstream and downstream woud mean that the upstream rm does not contro its downstream subsidiaries actions, such as their pricing or investment decisions. That this intermediate (between integration and fu divestiture) situation has not been studied before is a the more surprising that it is at the heart of most European directives on network industries. For instance, the 003/55 European Directive on natura gas states In order to ensure e cient and non-discriminatory network access it is appropriate that the transmission and distribution systems are operated through egay separate entities where verticay integrated undertakings exist. It is important however to distinguish between such ega separation and ownership unbunding. Lega separation impies neither a change of ownership of assets [... ]. However, a non-discriminatory decision-making process shoud be ensured through organizationa measures regarding the independence of the decision-makers responsibe. The way we mode ega unbunding is as foows. We consider a sequentia game where the upstream rm rst chooses the size of its network, and where two downstream rms then compete by seing goods that use this network as an essentia input. We contrast the (sociay) optima aocation with severa equiibrium situations, depending on the ownership structure in the industry. More precisey, we consider the market equiibria when the upstream rm owns zero, one or two downstream rms. The rst situation corresponds to ownership unbunding between upstream and downstream parts of the market. As for the other two cases, we equate ega unbunding with the foowing two assumptions. First, each downstream rm maximizes its own pro t, without taking into account any impact on the upstream rm s pro t. Second, the upstream rm is not aowed to discriminate between downstream rms by charging di erent access charges for the use of its network. On the other hand, we assume that the upstream rm chooses its network size in order to maximize its tota pro t, incuding the pro t of its downstream subsidiaries. In other words, the reguator is unabe to prevent the network operator from choosing the dimension of its network that maximizes the tota pro t of its owner. 3

6 We show that the same concerns as those raised by the manageria perspective on vertica integration are at pay here. Because the investment in the network is not protected by a contract at the time it is made, the upstream rm wi not take into account the interests of its cients when choosing its size. This e ect can be mitigated by aowing it to own part of the downstream industry. In order to show this, we present four di erent modes. After introducing our genera framework in section, in section 3 we expore the strategies of the rms when the two downstream rms face the same cost functions, use the network with the same intensity and are price takers on the market for the na output (on which they se their production). Section 4 revisits the same mode assuming that the rms have the same non-network cost function, but have di erent network utiization requirements. In section 5, we reax the assumption that the downstream market is competitive. Section 6 assumes that the downstream rms can make some investments that reduce their use of the network at given output. In a these cases, we obtain the same resuts: disaowing joint ownership of network and downstream faciities reduces the investment in the network. The concusion, section 7, discusses the imits of our work and the extensions that woud be necessary for a more compete comparison of ega and ownership unbunding. The mode Consider an industry where one rm (referred to as upstream, indexed by U) is in charge of buiding and maintaining a network, whie two rms ( downstream, indexed by i = 1; ) se goods or services that use the network. One prominent exampe of such an industry is the natura gas sector, where the upstream rm buids the pipeine network whie the downstream rms se natura gas to househods and industria customers. In order to bring gas to their customers, downstream rms need to transport this gas from the pace where it is injected into the upstream rm s network to the consumption node. The upstream rm chooses the size of the network it buids and maintains. 4

7 The (constant) per-unit cost of the network is denoted by k, so that its tota cost is K = k. Downstream rm i ses x i units of its product at price p i. Production technoogy is such that each unit of good i uses one unit of network: there is no bypass technoogy avaiabe at an economicay reevant cost, so that the network is an essentia faciity. In addition to network costs, rm i incurs downstream costs of C i (x i ). In the natura gas sector, these downstream costs are the costs of buying the gas and a other costs not reated to transport, such as the distribution or marketing costs. We assume that the downstream technoogy shows decreasing returns to scae, so that C 0 i(x i ) > 0 and C 00 i (x i ) > 0. 3 To ensure concavity of the pro t functions, we wi aso often assume that C 000 i (x) is positive. As for the network costs, downstream rms pay to the upstream rm a constant access charge a (that is endogenous in our mode) for each unit of the network that they use. The products sod by both downstream rms are perfect substitutes. 4 This appears to be a sensibe assumption in the natura gas market, since natura gas is a homogenous product. 5 Let X denote the tota quantity in the downstream market, so that X = x 1 + x. We denote by X(p) the aggregate demand for the downstream product, and by p(x) the aggregate inverse demand. that the revenue functions px(p) and Xp(X) are concave. We assume We mode the foowing sequentia game: rst, the upstream rm chooses the size of the network and then the downstream rms choose their price. This timing is natura given the nature of the decisions invoved. We sove this game for various scenarios concerning the downstream competitive conditions and the symmetry between downstream rms. In Sections 3 and 4, we assume that the downstream 3 This assumption is crucia in the rst part of the paper, since it guarantees that competitive downstream rms earn a positive pro t. However, it is not important for our argument per se. To show this, the assumption is reaxed in section 5 where we introduce imperfect downstream competition. 4 This assumption is not crucia: our resuts woud carry through if the downstream goods were sod on totay separate, unreated markets or if they were imperfect substitutes. 5 However, note that the services that are sod together with the gas moecues can be di erentiated, for instance by adding interruptibiity causes. We abstract from these considerations for the time being. 5

8 rms are perfecty competitive (price takers). Consequenty, they choose their output eve to equate margina cost and market price. Section 3 is concerned with the case where both downstream rms are symmetrica: they share the same downstream cost function and have the same needs in terms of network usage. Section 4 considers the case where the network is more adapted to one of the downstream rms than to the other, whie the non network reated cost functions of the two downstream rms are the same. This aows us to have a rst go at understanding the impact of the abiity for the upstream rm to discriminate between downstream rms. Section 5 then studies the situation where downstream rms have market power and pay a Cournot game. Finay, section 6 anayzes the impact of aowing downstream rms to make investments that woud aow them to decrease their need of network usage for any given output eve. We proceed simiary in Sections 3 to 6. We rst study the surpus-maximizing aocation. We then sove for the downstream equiibrium, to obtain prices and quantities as a function of the network size. We then study successivey the equiibrium aocation when the upstream rm owns both downstream rms, when it owns none of them and when it owns one but not the other. As mentioned above, we impose ega unbunding for the two cases where the upstream rm owns at east one downstream rm. Our objective is to assess how ega and ownership unbunding a ect the equiibrium network size. 3 Symmetric Equiibria >From this point on, we assume that both downstream rms have the same (non network reated) cost function C i and drop the subscript i. We begin by studying the outputs that woud be chosen by a wefare maximizing panner before turning to the anaysis of the game between the rms. 6

9 3.1 Socia Optimum The socia optimum is the aocation that maximizes tota surpus S in the economy. Assuming quasi-inear preferences for consumers of the downstream products, tota surpus is equa to consumers gross surpus minus upstream and downstream costs. The socia panner chooses a network size that soves Z max S = p(s)ds 0 C Denote the optima eve of variabes by a. The soution is given by x 1 = x = X = where X = is de ned by X p(x ) = C 0 + k = C 0 (x i ) + k: This condition is easy to interpret; it requires margina cost to equa margina wiingness to pay for the na good. The margina cost is equa to the sum of margina upstream and downstream costs. Further, observe that, at the optimum, the margina cost is the same for both rms. 6 the voume of goods sod at this optima price. 3. Equiibrium in the downstream market k: The optima network size equas In the remainder of this section, we sha study di erent ownership structures. For a of them, once the size of the network has been chosen, the downstream rms act as price-takers; in this subsection, we study the prices which wi prevai given a choice of a network size. Because the downstream rms are price-takers, they consider both the market price p of their output and the network access a to as given. Consequenty, they choose their output in order to equaize their margina cost with the market price p: p = C 0 (x i ) + a: (1) 6 This wi hod true aso when we introduce an asymmetry between the downstream rms. In other words, productive e ciency is necessary for socia optimaity. 7

10 Their tota production wi be X(p), which is equa to their tota demand for the services of the network since equiibrium on the network input market requires X(p) = : () Given a size chosen for the network in the rst stage of the game, equations (1) and () simutaneousy determine the access charge a and the downstream price p (and therefore aso the quantity sod X) as functions of ; we denote these functions by ~a() and 7 function of the choice of. ~p() = p(): they denote the prices that wi prevai as a We now turn to the equiibrium when the upstream rm owns both downstream rms. 3.3 Equiibrium when U owns both downstream rms If U owns both downstream rms, it chooses so as to maximize the sum of its pro ts, U = ea() and those of the two downstream rms, 1 and, where xi (ep()) i = x i (ep()) [ep() ea()] C ; i = 1; : This sum is equa to U = ea() k + X (ep()) [ep() ea()] X(ep()) C ; where ~a() and ~p() are the soutions to equations (1) and (). Observe that rm U has some market power, since it anticipates the equiibrium downstream prices (access charge a and na price p) induced by its choice of. Further, the assumption that C 00 (x) > 0 means that downstream rms make k; a positive pro t even when they act as price takers. 7 Notice the di erence: p() represents the price at which consumers wi choose to consume units of the na good whereas ~p() represents the price which wi prevai if units of network services are provided. In the mode of this section, they are equa; with other technoogy of productions they need not be. 8

11 This scenario of ega unbunding di ers from the cassica vertica integration case because the upstream rm U does not contro the pricing poicy of the two downstream rms. In other words, the managers of the downstream rms maximize their pro t given the market price. We reorganize this optimization probem to obtain X(p) max U = a k + X(p) (p a) C ; ;a;p X(p) s. t. p = C 0 + a; X(p) = : Simpifying and using the inverse demand function yied U = p () C k: (3) Maximizing this expression with respect to gives the foowing rst-order condition: p + p 0 = C 0 + k: (4) Equation (4) is the same condition that we woud obtain if we assumed that the three rms acted as an integrated pro t maximizing monopoist and maximized p() C(=) k. Tota margina cost is the sum of the downstream margina cost C 0 and of the upstream margina cost k, rather than the access charge paid by the downstream rm: when setting its network size, the upstream rm understands that the access charge is a pure transfer between its subsidiary and itsef. Using the superscript e to index the equiibrium eves of the di erent variabes, we obtain e < and p e > p : In words, the equiibrium network size is ower than optima whie the equiibrium retai price is arger than optima. Intuitivey, the upstream rm chooses a owerthan-optima network size in order to reduce the downstream output eve and to 9

12 increase downstream pro ts. This resut hods even with ega unbunding between downstream and upstream rms i.e., even when managers of the downstream rms do not take into account the pro ts of the upstream rm when they set their pro t-maximizing prices. We now turn to the situation where downstream and upstream ownerships are separated. 3.4 Equiibrium with ownership unbunding When the upstream rm owns neither of the downstream rms, it sets the network size in order to maximize its own pro ts, U = ~a() k: Using equations (1) and () together with the symmetry between the downstream rms, this optimization program can be rewritten as max ;a;p U = a k s.t. p = C 0 X(p) X(p) = : + a; The two constraints impy a = p() C 0 which we substitute in U to obtain U = p () C 0 k; (5) = p () C k C 0 C : (6) Observe that the rst term in the right hand side of (6) corresponds to U as de ned in (3). Because the two downstream rms are price takers, their downstream prices re ect their margina costs: per unit of output, they each 10

13 charge C 0 (=) to their customers to re ect their costs. The second bracketed term represents the di erence between the resuting revenue and their true cost. These are pro ts that the network must abandon to the downstream rms. From (6), we obtain d U d = e = e C00 e < 0: Denote by e0 the equiibrium eves of variabes in the ownership unbunding scenario. If the function U is concave, which it wi be if the revenue function is concave and if C 000 0, 8 this impies e0 < e < : In words, the fact that the upstream rm does not share in the downstream pro ts induces it to further decrease and X, compared to the ega unbunding situation. Ownership unbunding is thus more detrimenta to wefare than ega unbunding in our setting. The intuition for this resut is as foows. With ownership unbunding, the upstream rm s ony source of pro t is the seing of access to its network. Tota revenue of the upstream rm is given by ax i = (px i x i C 0 ); with x i = =. This is ower than downstream pro t, which equas (px i because decreasing returns to scae impy that x i C 0 > C. The gap between upstream revenue and downstream pro t increases with the di erence between x i C 0 and C, which is itsef increasing 9 with x i and. This expains why the upstream rm has an incentive to further decrease its network s size when it does not own any downstream rm. We now ook at the intermediate situation where the upstream rm owns ony one of the two downstream rms. We continue to assume ega unbunding 8 Let R(x) = p(x)x be the revenue function. From (5), the second derivative of U with respect to is R 00 () C 00 1 C000 : It is negative if R is concave and both C 00 and C 000 are positive. 9 The derivative of x i C 0 (x i ) C(x i ) with respect to x i is x i C 00 (x i ), which is positive by convexity of C. 11 C);

14 e1, one shows 10 e0 < e1 < e < : between the upstream and the downstream rm it owns. 3.5 Equiibrium when the upstream rm owns one of the downstream rms To study the situation where the upstream rm owns ony one downstream rm, one can proceed as in the previous section to obtain that U + i = p () C k C 0 C ; i = 1; : (7) Di erentiating this equation, and denoting equiibrium eves by the superscript Another way to proceed wi prove easier and more genera. Note that the objective function of U in this section, given by (7) is a convex combination of the objectives in the previous two sections, which are given by (3) and (6): U + i = 1 ( U ) + 1 U; i = 1; : This in turn gives the same ranking of equiibrium and optima network sizes, provided that the objective functions are concave. In words, incentives for the proper determination of the network size increase with the number of downstream rms that the upstream rm owns. The intuition for this resut is as expained at the end of the previous subsection: because of decreasing returns to scae, the di erence between the access revenues of the upstream rm and the downstream pro t increases with output. If the upstream rm does not share in this downstream pro t, it is induced to under-invest in its network. As the upstream rm acquires more downstream rms, its incentives to invest in the network increase, and the equiibrium network size increases toward the optima eve. Observe that we have assumed throughout the anaysis 10 This requires to prove that the reevant objective functions, ( U, U + i and U + i + j ) are concave. This is a straightforward consequence of the concavity of the revenue function, and of the convexity of C and xc 0 (whose second derivative is C 00 + C 000 ). 1

15 that ega unbunding prevais in the absence of ownership unbunding. We have aso obtained that, with ega unbunding, the equiibrium network size when the upstream rm owns both downstream rms fas short of the optima network size. 4 Downstream rms asymmetry and discrimination Let us now introduce some asymmetry between downstream rms, in the form of di erent needs in terms of network access. We assume that the investments made in the network by the upstream rm bene t more one rm than the other. In the natura gas sector, this situation coud arise because of the ocaization of the investments (new pipeines buit in a region where one downstream rm has a arger share of its customers portfoio than the other rm) or their type (investing in LNG rather than pipeines for instance). The objective in this section is to understand how the existence of discrimination a ects the optima and equiibrium size of the network, and how it reates with ega and ownership unbunding. We mode asymmetry in network needs as foows. We assume that downstream rm 1 bene ts more than downstream rm from investments in the network: rm 1 needs ony (1 ) unit of network for each unit of na good that it ses. On the other hand, downstream rm needs one unit of network use for each unit of na good sod, as previousy. The parameter [0; 1[ measures the intensity of the additiona bene t that rm 1 gets from the network. We assume that this parameter is set exogenousy (given by the technoogy, for instance). An extension to our anaysis woud be to endogenize the setting of this parameter by etting the upstream rm choose its pro t-maximizing eve. Except for the introduction of the parameter, we maintain a the assumptions made in the previous section. We proceed as in the previous section by ooking rst at the optima aocation before turning to the equiibrium aocations in the various unbunding scenarios. 13

16 4.1 Socia Optimum The socia panner s optimization program is max S = x 1 ;x Z x1 +x 0 yieding the foowing rst-order conditions p(s)ds C(x 1 ) C(x ) k[(1 )x 1 + x ]; p(x 1 + x ) = C 0 (x 1 ) + (1 )k; p(x 1 + x ) = C 0 (x ) + k: These are the usua conditions that price shoud equa margina costs. Together, they impy that C 0 (x 1) + (1 )k = C 0 (x ) + k; i.e., that we have productive e ciency at the optimum. The rst order conditions aow us to obtain the optima downstream quantities and network size, which we denote as previousy with a : x 1; x and = (1 )x 1 + x : 4. Equiibrium in the downstream market As in section 3, we need to compute the equiibrium of the game payed by the downstream rms as a function of. Competition in the downstream market generates the foowing equiibrium conditions, which repace (1) and (: p = C 0 (x 1 ) + a(1 ); (8) p = C 0 (x ) + a; (9) = (1 )x 1 + x ; (10) X(p) = x 1 + x : (11) The soution to these four simutaneousy equations, yieds the equiibrium eves of the access charge, retai price and downstream quantities as functions of the 14

17 network size and the parameter. Given that is treated as exogenous in this section, we denote these reationships by ea(); ex 1 (); ex () and ep() = p(ex 1 () + ex ()): (1) Observe that unike in the earier section we now have that ep() 6= p() since 6= x 1 + x : We now ook at the equiibrium where the upstream rm owns the two downstream rms, with ega unbunding between the upstream and downstream segments. 4.3 Equiibrium when U owns the two downstream rms We start by using the equiibrium quantities and price in the downstream markets in order to obtain the pro t eves of the three operators as a function of the network size: U = ea() k; 1 = ex 1 () [ep() (1 )ea()] C (ex 1 ()) ; = ex () [ep() ea()] C (ex ()) : The objective of the upstream rm is to nd the network size that maximizes the sum of the three operators pro ts: max U = [ex 1 () + ex ()]ep() C (ex 1 ()) C (ex ()) k: (13) The rst order soution of this program is given by ep()[ex 0 1() + ex 0 ()] + [ex 1 () + ex ()]ep 0 () To simpify this expression, we use (1) and C 0 (ex 1 ()) ex 0 1() C 0 (ex ()) ex 0 () k = 0: (14) ep 0 () = [ex 0 1() + ex 0 ()]p 0 (ex 1 () + ex ()); (15) (1 )ex 0 1() + ex 0 () = 1; (16) 15

18 where (15) and (16) are obtained by di erentiating, respectivey, (1) and (10). We substitute equations (1) to (16) in (14). Using the superscript e to denote the equiibrium eves of the variabes in this scenario, we obtain after simpi cations that p(x e 1 + x e ) + (x e 1 + x e )p 0 (x e 1 + x e ) = C 0 (x e 1 ) + (1 )k = C 0 (x e ) + k; i.e., the same conditions as if x 1 and x were directy controed by the upstream operator. Margina revenue is equa to margina cost for both downstream operators. Observe that productive e ciency is maintained by the combined rm, since margina costs are the same at equiibrium for the two downstream operators. Comparing these pro t-maximizing downstream quantities with their optima eves, we obtain that x e 1 < x 1 and x e < x ; which impies that e = (1 )x e 1 + x e < = (1 )x 1 + x : This is the same ranking of downstream quantities and network sizes as in the symmetric case. Athough the mechanism is made more compex by the existence of asymmetric network needs between downstream operators, the intuition for the resut is not a ected by this asymmetry: the upstream rm under-invests in the network, anticipating that ower downstream quantities wi generate arger pro ts for the two downstream rms that it owns. 4.4 Equiibrium with ownership unbunding One coud proceed as in the symmetric situation in order to sove for equiibrium quantities when ownership is unbunded between upstream and downstream segments. It wi prove easier to use the indirect method introduced in 3.5. The upstream rm maximizes its own pro t, which can be expressed as U = ( U ) ( 1 + ): (17) 16

19 We can aso rewrite the pro t functions of the two downstream rms as 1 = ex 1 () [ep() (1 )ea()] C (ex 1 ()) ; = ex 1 ()C 0 (ex 1 ()) C (ex 1 ()) ; = ex () [ep() ea()] C (ex ()) ; = ex ()C 0 (ex ()) C (ex ()) : Di erentiating pro ts with respect to network size, we then obtain 0 1 = ex 1 ()C 00 (ex 1 ()) ex 0 1() > 0; 0 = ex ()C 00 (ex ()) ex 0 () > 0: Using equation (17), we show 0 U( e ) = 0 U( e ) + 0 1( e ) + 0 ( e ) 0 1( e ) + 0 ( e ) ; = ( e ) + 0 ( e ) < 0; which by concavity of the function U impies e0 < e : This shows that the intuition obtained in section 3.4 carries over to the case of asymmetric downstream cost functions: with ownership unbunding, the upstream rm fais to take into account downstream pro ts, with the di erence between upstream and downstream pro t eves increasing with downstream voumes. The upstream rm has then an incentive to invest ess in its network than in the case where it owns the two downstream rms. 4.5 Equiibrium when the upstream rm owns one of the downstream rms We distinguish between the case where the upstream rm owns the downstream rm 1 (denoted by e11) and the case where U owns rm (denoted by e1). In the e11 scenario, the objective of the upstream operator is to maximize U = ( U ) ; (18) 17

20 which aows us to use the same argument as in the e0 scenario where ownership is totay unbunded between the upstream and downstream segments. More precisey, we evauate 0 U (e0 ) and 0 U (e ); with U given by equation (18), to show that (provided that U is concave in ) e0 < e11 < e : Simiary, one can show that e0 < e1 < e : The genera concusion that we draw from this section is that the reative ranking of the equiibrium network sizes is robust to the introduction of asymmetry between downstream rms. With such an asymmetry, ownership unbunding eads to more under-investment than ega unbunding: the more integrated the industry is, the coser the equiibrium network size comes to its optima eve. We now study the robustness of our resuts to the introduction of imperfect competition in the downstream market. 5 Imperfect competition in the downstream market In this section, we assume that both downstream rms compete à a Cournot on the na market. We maintain the assumption that the products they o er are perfect substitutes. We retain the assumption that they are totay symmetric: they have the same cost function and require the same use of the network. We further assume that the downstream cost function is inear, with C i (x i ) = cx i. Finay, we assume that the downstream rms act as price takers in their purchase of network services. 5.1 Socia Optimum The socia panner s objective is to max S = Z 0 p(s)ds c k: 18

21 The soution X = to this probem is de ned by p(x ) = c + k: This is the usua condition that margina wiingness to pay shoud equa margina cost. Since the (constant) margina cost is the same for both downstream rms, the sociay optima aocation is concerned with the tota downstream quantities and not with the individua quantities sod by each rm. 5. Equiibrium in the downstream market With Cournot competition, each downstream rm chooses its output eve x i in order to maximize i = x i p(x i + x j ) ax i cx i ; = x i [p(x i + x j ) a c] ; given the output eve x j suppied by its competitor j. The fact that rm i acts as a price taker in the market for network services impies that it takes the access charge a as given, and independent of its own demand for these services. The rst order condition for downstream pro t maximization is x i = p(x i + x j ) a c : (19) p 0 (x i + x j ) Equation (19) together with the condition X(p) = determine as previousy the access charge and retai price as a function of network size. These reationships are denoted by ~a() et ~p() = p(): The symmetry between the two rms, together with the equiibrium condition on the market for input impy that both rms choose the same output at equiibrium x 1 = x = =: This reationship aows us to simpify equation (19) to obtain ~p() = a + c 19 ~p0 ();

22 with ~p 0 () < 0: The intuition for this resut is that each rm ses its product at a price arger than its margina cost a + c, with the mark-up being inversey proportiona to (haf) the demand-price easticity of output. We now proceed to study equiibrium network size under various integration scenarios. 5.3 Equiibrium when U owns both downstream rms In its choice of network size, the upstream rm internaizes the downstream pro t and soves max ;a;p U = a k + X(p) [p a c] s.t. p = a + c X(p) = : ~p0 (); After simpi cation and using the inverse demand function, we obtain U = (~p() c k); (0) whose maximization with respect to gives the condition ~p + ~p 0 = c + k: (1) This condition is the usua pro t-maximization soution of a monopoy, equaizing margina revenue and margina cost. Observe that the second order condition for tota (downstream pus upstream) pro t maximization is given by We wi use this resut ater. ~p 0 + ~p 00 < 0: () As in the previous two sections, we obtain e < and p e > p. The intuition for this resut is aso the same as previousy: the upstream rm under-invests in 0

23 the network in order to decrease downstream quantities and increase downstream prices. The main di erence with the previous section ies in the fact the downstream rms make a pro t because of imperfect competition, not because returns to scae are decreasing. 5.4 Equiibrium with ownership unbunding If ownership is separated between upstream and downstream segments of the markets, the upstream rm chooses the network size that maximizes U = ~a() k: We can rewrite the optimization probem as max ;a;p U = a s.t. p = a + c X(p) = : k p0 (); We obtain after substitution that U = [p () c k] + p0 (): (3) The rst term in the right hand side of (3) is equa to the tota pro t U as speci ed by equation (0) when the upstream rm owns both downstream rms. This impies d U d = e = e p 0 ( e ) + e p00 e < 0; where the inequaity is a consequence of condition (). Therefore, by concavity of U, e0 < e < : Athough this ranking of network sizes is the same than under downstream perfect competition couped with decreasing returns to scae, the intuition di ers. Note rst that the upstream rm revenue is given by ax i = (px i 1 cx i + p 0 ()=4)

24 (with x i = =), which is ower than the downstream pro t (equa to px i cx i ) because of the mark-up posted downstream. Moreover, the second order condition for (tota) pro t maximization guarantees that the di erence between the two increases with x i and. In other words, the reason why the di erence between downstream pro t and upstream revenue increases with the network size varies with the downstream cost structure and competitive situation: under perfect competition, it is due to the (assumed) convexity of costs whie under imperfect competition, it is due to the increase in the downstream mark-up. 5.5 Equiibrium when the upstream rm owns one of the downstream rms If the upstream rm owns one of the downstream rms, one can repicate the argument mentioned in section 3.5: the constraints faced are the same in the cases where the upstream rm owns zero, one and two downstream rms, whie the objective in the case e1 is a convex combination of the objectives in the scenarios e0 and e: U + i = 1 ( U ) + 1 U ; i = 1; : We then obtain that, provided that the pro t functions are concave in, e0 < e1 < e < : We then concude from this section that the ranking of network sizes according to the number of downstream rms owned by the upstream rm is robust to the introduction of imperfect competition in the downstream market. 6 Investments by the downstream rms We now study the robustness of our resuts to the introduction of a second decision by the downstream rms, beyond the setting of their prices. This decision is how much to invest in an activity that, athough costy by itsef, aows the downstream

25 rm to economize on its network usage for any given eve of output. The kind of downstream investment we have in mind for the natura gas market consists in o ering to na cients interruptibe contracts or aternativey buying insurance to cover risks such as transport congestion due to a peak demand. These two types of contracts are obviousy costy for the downstream rm (in the rst case because they decrease its output price, in the second because of the direct outays they represent) but aow it to decrease its needs in terms of network usage for any eve of output sod to cients. We maintain the assumption of ega unbunding throughout the anaysis, so that the upstream rm cannot contro the investment decisions of its downstream subsidiaries. We mode this extension to downstream investments as foows. The pro t of downstream rm i is given by i = px i C(x i ) (y i )ax i y i x i ; where, as above, the non network cost function C is convex, with C 000 > Socia Optimum The socia panner chooses the network size and the downstream investment that sove the probem with X = =(y): Z X max S = p(s)ds ;y 0 C (y) y (y) Denoting the optima eve of variabes by a as previousy, the rst order condition with respect to network size is X p = p(x ) = C 0 + y + k(y) (4) i.e., margina wiingness to pay shoud equa socia margina cost. With constant margina costs, the socia optimum determines tota downstream output but not k; 3

26 how much is produced by rm 1 or rm. For ater use, we express condition (4) in terms of mark-up over the margina non network cost: X p C 0 = y + k(y) (5) The rst-order condition with respect to downstream investment is 0 (y )k = 1: (6) Both rms shoud invest the same per-unit of output amount, which equaizes margina bene t and margina cost per unit of output. 6. Equiibrium in the downstream market The two downstream rms, which are price takers both on the downstream market and on the market for the network input, simutaneousy choose their pro tmaximizing eves of investment, y i. Using the symmetry between downstream rms, the rst-order condition for y is 0 (y)a = 1; (7) which is very intuitive, since it cas for equaization of the monetary margina bene t from the investment with its margina cost. The price taking behavior of downstream rms impies X(p) p = C 0 + a(y) + y; (8) i.e., that the equiibrium price equas tota margina cost for the downstream rms. Equiibrium on the input market impies (y)x(p) = : (9) Equations (7) to (9) simutaneousy determine the access charge a, the downstream price p and the amount of downstream investment y (and thus aso X) as function of. We denote these functions by ~a(); ~y() and ~p(): Observe that, as in section 4, ~p() 6= p() because 6= X = x 1 + x : We now turn to the equiibrium when the upstream rm owns the two downstream rms. 4

27 6.3 Equiibrium when U owns both downstream rms When the upstream rm owns the two downstream rms, it maximizes the sum of its pro t, U and of pro ts of the two downstream rms, 1 and : U =ea() k + X (ep()) [ep() (~y()) ea()] X(ep()) C ~y()x (~p()) ; where ~a(); ~y() and ~p() are the soutions to equations(7) to (9). We reorganize this optimization probem to obtain X(p) max U = a k + X(p) (p (y)a) C ;a;p;y X(p) s. t. p = C 0 + a(y) + y; = (y)x(p); yx(p) 1 = 0 (y)a: After simpi cation, and using the inverse demand function, we obtain U = ~p () (y) C y k (y) (y) whose maximization with respect to gives the foowing rst order condition ~p() + ~p 0 () = C 0 + y + k(y); (30) (y) where y is determined by 0 (y)a = 1: This corresponds to the pro t-maximizing condition of a monopoy, where margina revenue equas tota margina cost. In order to compare with the sociay optima price, we denote as usua the equiibrium eves with the e superscript and reformuate (30) into p e C 0 e (y e ) = y e + k(y e ) e ~p 0 ( e ): (31) 5

28 We now compare the right hand sides of (5) and (31) term by term. The sum of the rst two terms is the (per unit of output) network cost, incuding the investment cost. Note that y + k(y ) < y e + k(y e ) if a 6= k, since y precisey minimizes y + k(y). This cas for a pro t maximizing price p e arger than its optima eve, because in the e scenario the downstream rms base their investment decision on the access charge rather than the margina socia cost k, and end up (when a 6= k) with a socia margina cost that is arger than its sociay optima eve. The third term in (31) pushes p e in the same direction since it represents the cassica impact of a pro t-maximizing rm concentrating on margina revenue rather than considering that its na price is exogenousy set. We then concude that the mark-up over the non network cost is arger when the upstream rm owns the downstream rms than its sociay optima eve. In section 3, the observation that the mark-up over non network margina cost C 0 was arger in the e scenario than its optima eve was enough to deduct that p e > p and > e. This is not su cient in the framework of this section, since such comparisons aso depend on the comparison between y e and the sociay optima downstream investment eve y. This comparison in turn hinges on whether the access charge a is arger or smaer than the network margina cost k. Observe that, with ega unbunding, the upstream rm cannot contro the pricing decisions of its downstream subsidiaries. In the absence of downstream investment, the upstream rm induces a positive mark-up on the downstream market by decreasing the size of its network and at the same time increasing the (market cearing) access charge a, so that a > k. Introducing downstream investment, we obtain that a further e ect of increasing a above k is to induce the downstream rm to invest more than woud be sociay optima: y < y e. This in turn impies that the downstream rm is abe to se more output for a given network size than with the optima downstream investment eve, which counteracts the e ect of a higher access charge a on p. We have not been abe to obtain anayticay unambiguous resuts with respect to the comparison between optima and e eves of a, y, and X. We surmise that 6

29 the new e ect mentioned above mitigates ony partiay the direct e ects described in section 3, so that the most ikey situation is the one where a e > k, y < y e, > e ; p e > p and X > X e i.e., where the reationships between prices and quantities obtained in section 3 carry through to the case where downstream rms make an investment. We show in section 6.6 that it is the case for the numerica exampe we deveop there. 6.4 Equiibrium with ownership unbunding We proceed as in section 4.4, noting that the objective of the upstream rm is to maximize its own pro t, which can be expressed as U = ( U ) ( 1 + ): We can aso rewrite the pro t functions of the two downstream rms as i = ex i () [ep() (~y()) ea() ~y()] C (ex i ()) ; = ex i ()C 0 (ex i ()) C (ex 1 ()) ; where ex i () = (~y()) : Di erentiating pro ts with respect to network size, we obtain 0 i = ex 1 ()C 00 (ex 1 ()) ex 0 1(); where ex 0 i() = (~y()) 0 (y) ~y 0 () 4 (~y()) is of an ambiguous sign since 0 (y) < 0 and ~y 0 () < 0: Observe that, if ex 0 i() > 0, then we can use the same reasoning as in section 4.4 to obtain, provided that the objective function U is concave, e0 < e : 7

30 In that case, we woud aso have e0 < e1 < e : Finay, it is easy to see that y e0 > y because, with ownership unbunding, the ony way for the upstream rm to make a pro t is to charge an access price arger than its margina cost, a > k. 6.5 Equiibrium when the upstream rm owns one of the downstream rms We can proceed as in sections 3.5 and 5.5, to show that the objective in the case e1 is a convex combination of the objectives in the scenarios e0 and e, with the same constraints in a three cases. Provided that the objective is concave, we then obtain that the e1 eves of the variabes p, y, and shoud be in between their equiibrium eves in scenarios e0 and e. 6.6 A numerica exampe The new e ects generated by the introduction of downstream investments have prevented use from reaching unambiguous anaytica concusions when comparing equiibrium and optima eves of prices, network size and output. We therefore present a numerica exampe where the comparison of the equiibrium eves in the various scenarios is the same as in the previous sections. We use the foowing functiona forms C(x) = x ; p y (y) = 1 10 ; X(p) = 100 5p: We rst study the case where y is set exogenousy equa to zero i.e., the case deveoped in section 3. This aows us to show graphicay the equiibrium and optima eves of the network size and of output price p as a function of the 8

31 margina network cost k. Figure 1 shows that e0 < e1 < e < whie gure iustrates that p e0 > p e1 > p e > p : [Insert Figures 1 and around here] We now turn to the case where y is chosen by the downstream rms. In Tabe 1, we compare the optimum and equiibrium vaues of y, X, p, and a when k is set equa to Tabe 1: Equiibrium eves when k = 5. Scenarios e e1 e0 y X p a Tabe 1 shows that we obtain the foowing reationship: k < a e < a e1 < a e0 : Intuitivey, as the number of downstream rms owned by the upstream rm decreases, the upstream rm reies more and more on the access charge to increase its pro t. At the imit, with ownership unbunding (case e0), the access charge is the ony way for the upstream rm to obtain revenues. In a scenarios, the equiibrium access charge is arger than its optima eve. It foows directy from this that we obtain y < y e < y e1 < y e0 i.e., the equiibrium eve of downstream investment is too arge and increases with ownership separation. The intuition is that downstream rms react to arge access charges by over-investing in activities whose objective is to imit their network usage. Tabe 1 aso shows that > e > e1 > e0 i.e., the main resut of the paper carries through to the case of downstream investments: the more ownership is unbunded, the arger is the incentive for the upstream rm to decrease its network size in order to raise its pro t. We aso obtain p < p e < p e1 < p e0 : 11 We obtain the same quaitative resuts for any vaue of k between 0 and 0. 9

32 prices increase with ownership unbunding. Finay, observe that, even though downstream investment increases with ownership unbunding, tota downstream quantity decreases with ownership unbunding: X > X e > X e1 > X e0 : In words, the main e ect at work when ownership is unbunded is the incentive for the upstream rm to decrease its network size. The impact on the downstream investment mitigates ony partiay the consequences of a smaer network size, so that tota quantity sod decreases with ownership unbunding. 7 Concusion In a the modes that we have deveoped in this paper, we nd that fu contro of the downstream industry by the upstream rm woud be sociay e cient. This is of course too strong a concusion, but we sti beieve that our anaysis highights important considerations for economic anaysis. In this concusion, we woud ike both to discuss these essons and expain how we beieve our mode shoud be expanded and/or modi ed. In a our modes, we assume that the reguator has a strong contro over the behavior in the downstream market. In particuar, it can competey prevent the network from favoring one of the downstream rms and, in the modes of sections 3 and 4 it can impose on the downstream rms that they behave competitivey. On the other hand, it has ess contro over the ong term decisions of the network, in our case new investment. We beieve that this is a fair, if caricatura, characterization of the powers of most reguators. Our mode stresses the fact that under these circumstances making the upstream rm internaize the pro ts of its cient can be a powerfu method for inducing it to invest more. Even if the upstream rm owns ony one of the two downstream rms, both rms bene t from this vertica integration. To anayze in more detais the tradeo s invoved, we woud need to modify the mode so that there is positive reasons why competition in the downstream market is bene cia. This woud invove introducing expicity some degree of asymmetric 30

33 information, whie preserving our emphasis on incompete contracts and speci c investment, and wi be the topic for future research. 31

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