Journal of Regulatory Economics; 22:1 85±95, 2002 # 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.

Rent Extraction by an Unregulated Essential Facility* FRANCËOIS BOLDRON

University of Toulouse (Gremaq)

21 alleÂes de Brienne, F-31000 Toulouse, France E-mail: [email protected]

CYRIL HARITON{

University of Toulouse (Gremaq)

21 alleÂes de Brienne, F-31000 Toulouse, France E-mail: [email protected]

Abstract This paper shows that consumers may bene®t when a regulator chooses not to regulate a ®nal product in an industry characterized by an unregulated essential facility sold through non-linear tariffs. Two main reasons drive this result. First, the regulator maximizes social welfare and values the ®nal good production more than the producer itself. Second, the regulator has access to an extra source of ®nancing with the public funds. Therefore, the essential facility seller can ask more of the regulator than of the ®nal good producer.

1. Introduction Should a regulator regulate a downstream industry which purchases an input from an unregulated upstream essential facility? We show that when the essential facility uses nonlinear tariffs and has bargaining power, the regulator should not regulate the downstream industry. There are many important settings where an upstream monopolist employs non-linear tariffs to sell an essential input to a regulated ®rm. For example, in the pharmaceutical industry, laboratories that develop new medications protect themselves with patents in order to maintain a temporary legal monopoly on the use of these molecules in the * We thank Claudes Crampes, feu Johannes Jaspers, GwenaeÈl Piaser, John Turtle, Helmuth Cremer, an anonymous referee, the editor and all the participants of the EARIE congress (Lausanne, September 2000), the EEA congress (Bolzano, September 2000), the JourneÂes de Micro-EÂconomie AppliqueÂe (QueÂbec, June 2000) as well as those of the Jamboree 2000 (University College London, January 2000) for their helpful comments. We are largely indebted to Jacques CreÂmer for its encouragement. All remaining errors are ours. { Corresponding author.

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Figure 1. The industry vertical structure: without regulation or with regulation.

development of drugs. Production of these molecules typically takes one of two forms: (1) the laboratories produce these drugs themselves for all the geographical markets they serve, or (2) the laboratories delegate the production for some local markets to other ®rms which buy a licence. But the sale of drugs to consumers is often regulated by the country in which these are sold. Therefore, the local ®rms are regulated and must purchase an inputÐ the licenceÐfrom a ®rm that has monopoly power. In our model, a foreign monopoly uses non-linear tariffs to sell an essential input to a local ®rm regulated by a domestic agency. The domestic regulator maximizes national social welfare, and faces a shadow cost of public funds caused by distorting taxation.1 We show that the upstream ®rm bene®ts from the downstream benevolent regulation because it can always extract more rent from consumers when there is regulation. More importantly, domestic consumers are hurt by the presence of the regulator. The intuition behind this result is simple. As described by ®gure 1, the industry structure can take two simple forms. Either the downstream ®rm is not regulated (case on the left) and ®rms contract directly, or the regulator chooses the ®nal output (case on the right) and the upstream ®rm contracts with the regulator. Without regulation, the upstream ®rm extracts, with a simple two-part tariff, a pro®t equal to the maximum pro®t of the structure made of both the upstream and the downstream ®rms. Under regulation, it can extract not only this pro®t but all the increase in social welfare from the product. Therefore, the regulator will, if possible, not regulate the downstream ®rm. Section 2 describes the formal model. Section 3 deals with some benchmark cases and section 4 analyzes the equilibrium when the regulator is given two choices: to regulate or to shut down the downstream ®rm. Section 5 completes the formal study with the introduction of a third choice: not to regulate the downstream ®rm. Finally, section 5 summarizes the results, discusses further extensions and concludes. All the proofs are detailed in the appendix.

1 More insights about the background of this framework can be found in the introductory chapter of Laffont and Tirole (1993).

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2. Model An upstream monopoly, ®rm U, sells an essential input to a regulated downstream monopoly, ®rm D. These two ®rms are located in two different countries. In order to produce q1 units of good 1, ®rm D must purchase q1 units of good 0 from ®rm U. The national economy consists of ®rm D, the consumers of good 1 and the national regulator (hereafter, the regulator) who maximizes national social welfare. Firm U is a foreign ®rm, is not regulated and its pro®t is not included in national social welfare. Moreover, ®rm U is assumed to have all the bargaining power in any negotiation. Firm U sells q0 units of good 0 for a cost2 CU …q0 † ˆ FU ‡ cU q0 , with a two-part tariff T U …q0 † ˆ H0 ‡ p0 q0 . Its pro®t function is then pU … q 0 † ˆ H 0 ‡ p 0 q 0

FU

c U q0 :

…1†

The cost of ®rm D, exclusive of the two-part tariff T U , is CD …q1 † with a constant ®xed cost FD which is assumed not to be sunk.3 When ®rm D is regulated, there is no loss of generality to assume that the cost CD and the tariff T U are paid by the regulator which also receives all the revenues from the sale of good 1. Then, ®rm D receives a net transfer t and its pro®t function is pD ˆ t:

…2†

The consumers' gross surplus is S1 …q1 † with S1q …q1 † ˆ p1 …q1 † the inverse demand function and S1qq < 0. The regulator maximizes national social welfare SW ˆ ‰S1 …q1 †

 …1 ‡ l† t ‡ CD …q1 † ‡ T U …q1 †   lpD …1 ‡ l† CD …q1 † ‡ T U …q1 † ;

p1 …q1 †q1 Š ‡ ‰tŠ

ˆ S1 …q1 † ‡ lp1 …q1 †q1

 p1 …q1 †q1 ;

…3†

where l > 0 is the shadow cost of public funds. All information is common knowledge. Before detailing the timing of the game, two benchmark cases are studied for comparison convenience.

3. Benchmark Cases 3.1. The Vertically Integrated Firm Let us call ®rm V the vertically integrated ®rm, that is the hypothetical ®rm created by the merger of ®rms U and D. Its cost function is CD …q1 † ‡ CU …q1 †. 2 In general, superscripts are used to distinguish between ®rms (U and D) or situations (vi for vertically integrated, R for regulated) and subscripts denote markets (1 and 2) or derivatives …q†. 3 This eases the description of the arbitrage that occurs in the model, but does not modify the intuition behind the results.

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FRANC Ë OIS BOLDRON AND CYRIL HARITON

Without regulation, ®rm V would produce qvi 1 such that it maximizes its pro®ts  qvi 1 ˆ arg max p1 …q1 †q1 q1

 ‰CD …q1 † ‡ CU …q1 †Š :

The associated pro®t is noted pvi . With regulation of ®rm V, social welfare would become, omitting the arguments, SW ˆ S1 ‡ lp1 q1

lt

  …1 ‡ l† CD ‡ CU :

Maximizing social welfare under the participation constraint that ®rm V's pro®t should be positive, t  0, yields this constraint to be binding and production4 to be qviR 1 , solution of the following ®rst order condition p1 …q1 †

CD q …q1 †

CU q …q1 † ‡

l p …q †q ˆ 0: 1 ‡ l 1q 1 1

It is assumed that second order conditions are satis®ed and that these equations have unique solutions. 3.2. Regulation of Both Firms Regulating both ®rms is equivalent to regulating ®rm V. This yields an outcome qviR 1 which is socially ef®cient. It generates the highest total social welfare level possible in this setting, noted SWviR . 3.3. No Regulation at All Without regulation, ®rm U, which has all the bargaining power, can extract the same pro®t that ®rm V could have. Lemma 1: Without regulation, the optimal two-part tariff for ®rm U is vi T U …q1 † ˆ pvi ‡ FU ‡ cU q1 . The quantity produced is qvi 1 . Firm U's pro®t is p and the vi vi vi social welfare level is S1 …q1 † p1 …q1 †q1 . Firm D gets zero pro®t. This is the tariff, so called no-regulation tariff, the upstream ®rm U proposes if there is no regulation of the downstream ®rm D.

4. Socially Harmful Regulation We now examine the game in which the regulator regulates ®rm D. In order to model the bargaining power of U, we use the following game: ®rst, ®rm U makes a take-it-or-leave-it offer to the regulator, which consists in a two-part tariff T U …q1 † ˆ H0 ‡ p0 q1 ; second, 4 Superscript viR stands for ``vertically integrated and regulated.''

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the regulator decides whether to accept the tariff and computes the optimal contract for ®rm D. 4.1. Strategy of the Regulator In the second stage, if the regulator has accepted the tariff T U , it faces the following problem  max S1 ‡ lp1 q1 q1 ;t

lpD

…1 ‡ l†…CD ‡ H0 ‡ p0 q1 †



subject to the participation constraint of ®rm D: pD  0. Standard results obtain 8 < p …q † CD …q † q 1 1 1 : D p ˆ 0:

p0 ‡

l p …q †q ˆ 0; 1 ‡ l 1q 1 1

We assume that the second order conditions are satis®ed and that the ®rst order condition has a unique solution q1 …p0 † for any proposed p0 . Notice from the above system that q1 depends on p0 but is independent of H0 . If there is no production, the social welfare is S1 …0†. Thus, the regulator accepts T U as long as social welfare with production is greater than S1 …0†. 4.2. Strategy of Firm U Suppose ®rm U proposes the no-regulation tariff T U …q1 † ˆ pvi ‡ FU ‡ cU q1 . Lemma 2: The regulator always accepts the no-regulation tariff if the upstream ®rm U proposes it. In that case, the regulation of ®rm D is not costly for ®rm U, but neither is it bene®cial. Firm U can extract from the regulator what it could obtain directly from ®rm D in the absence of regulation. But is it the best strategy for ®rm U? With linear prices in the downstream sector, the consumers save some surplus that the downstream ®rm is not able to extract. Therefore, when contracting with ®rm D, the upstream ®rm can not gain more than the maximum pro®t of the vertically integrated ®rm (what ®rm U gets with its no-regulation tariff ) and the consumers keep this net surplus.5 But, here, the upstream ®rm contracts with the regulator. For the latter, consumer surplus is part of its social welfare objective function and it has a strictly positive value. To abandon the production is therefore 5 Other tools than non-linear prices may also be used in the downstream sector to extract consumer surplus. For instance, in another regulatory context, Segal (1998) uses the soft budget constraint to show that a monopoly can extract part of the social surplus in the form of a state subsidy.

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FRANC Ë OIS BOLDRON AND CYRIL HARITON

more costly for the regulator than for ®rm D. Moreover, the regulator has access to an extra source of ®nancing, its public funds. To sum up, the regulator has a higher value for production and more money to pay for the essential facility.6 Therefore, if ®rm U acts optimally, it should ask the regulator to pay at least for part of this consumer net surplus. Proposition 1: Firm U can always obtain a greater pro®t when the downstream ®rm D is regulated. Moreover, the optimal two-part tariff for ®rm U is T U …q1 † ˆ

1 ‰SWviR 1‡l

S1 …0†Š ‡ FU ‡ cU q1 ;

which yields a pro®t of pU ˆ

1 ‰SWviR 1‡l

S1 …0†Š

and a ®nal production qviR 1 . The level of social welfare is S1 …0† and corresponds to the zero production one. Firm D gets zero pro®t. The pro®t of ®rm U can be rewritten  viR pU ˆ pviR 1 q1

CU qviR 1




CD qviR 1




‡

1  viR S 1‡l 1

S1 …0†

 viR pviR 1 q1 :

The ®rst term corresponds to the vertically integrated ®rm's pro®ts when producing the quantity qviR 1 . The regulation of ®rm D allows ®rm U to indirectly collect part of the consumer net surplus on top of the regulated vertically integrated monopoly pro®t. Because consumers do not pay directly ®rm U, the real cost for the regulator of an additional e asked by ®rm U is …1 ‡ l†e, which explains the multiplicative factor in front of the net consumer surplus in the tariff. There are three interesting points about this result. First, when ®rm U maximizes its pro®ts, its objective function becomes qualitatively identical to the one of the regulator when this latter regulates a vertically integrated monopoly. Second, there is a separation in the role of p0 and H0 . The ®rst instrument p0 is used to generate the highest social welfare, that is, induces socially ef®cient production, whereas H0 is chosen to extract all this social welfare just short of causing rejection of the tariff. Finally, the social welfare is equal to S1 …0† and all the bene®ts derived from the production of good 1 are taken by ®rm U. 6 In other words, the upstream ®rm U can consider the regulator as a ®rm whose objective function is the sum of social welfare, consumer surplus and the cost of public funds. By using its non-linear tariff, ®rm U is able to extract all the surplus from this new downstream ®rm.

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91

As the rent extracted by the upstream ®rm is decreasing in l,7 the essential facility seller is better off when dealing with countries characterized by low shadow cost of public funds (for the same kind of consumers). In particular, this shadow cost is estimated8 at around 30% in Western European countries, whereas it is often suggested to be up to 100% or more in some developing ones. In these countries, the upstream ®rm's pro®t is therefore a priori limited by the high cost to the regulator of raising money.

5. Endogenous Decision to Regulate The previous section shows that with regulation national social welfare is as low as if there were no production, despite the fact that the level of production is ®rst-best optimal. The natural question raised by this result is whether regulation is worthwhile. To handle this question, we assume that, in a ®rst period, the regulator decides whether or not to regulate ®rm D. In a second period, ®rm U proposes a two-part tariff to the regulator if there is regulation, to ®rm D otherwise. In a third period, the tariff is accepted or rejected by the regulator if there is regulation, by ®rm D otherwise. If, in the ®rst period, the regulator decides to regulate ®rm D, social welfare will be equal to S1 …0†, as shown in section 4. On the other hand, in the absence of regulation, the vi social welfare will be S1 …qvi p1 …qvi 1† 1 †q1 , as shown in section 3. Social welfare is higher without regulation, and this proves the following proposition. Proposition 2: The regulator never chooses to regulate ®rm D. Firm U extracts only pvi, the ®nal production is qvi 1 and ®rm D gets zero pro®t. Thus, the viR consumers are better off when there is no regulation even if they consume less …qvi 1 < q1 †. Nevertheless, this equilibrium is not Pareto optimal. Indeed, faced with the optimal two-part tariff described by lemma 1, the regulator would prefer to regulate ®rm D and this would not change ®rm U's pro®t. Therefore, there is place in our model to introduce other bargaining procedures in order to reach a better ®nal equilibrium for both agents.

6. Concluding Remarks This paper shows that consumers do bene®t when a regulator does not regulate an industry where an unregulated essential facility has monopoly power. From a regulatory policy point of view, the usual scrutiny of which ®nal good market to regulate (subadditivity of cost, universal service obligations) has to be reviewed in the sense of a deeper analysis of 7 The proof is detailed in the appendix. 8 Please refer to Laffont and Tirole (1993, p. 38) and Ballard et al. (1985) for insights on the methodology of the computation of the values of the parameter l.

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FRANC Ë OIS BOLDRON AND CYRIL HARITON

the upstream context of these industries. In a sense, ®rm U should be the most fervent supporter of regulation and, for instance, should lobby for it. The results are driven mainly by two assumptions. First, we have made an extreme assumption as far as the bargaining power is concerned, assuming that ®rm U can make a take-it-or-leave-it offer to either the regulator or ®rm D. It can be shown that the argument of the basic result remains true as long as ®rm U has some bargaining power.9 Second, the upstream ®rm must use a non-linear tariff for the sell of the intermediate good. We derive our result with the simplest form on non-linear tariffs, the two-part one, for expositional convenience. Moreover, the analysis is robust to changes in some assumptions. For example, one could suspect that asymmetries of information would modify our results. When the upstream ®rm and the regulator have the same information on the cost of the downstream ®rm, Boldron and Hariton (2000) show that our main result does not change: the regulator prefers not to regulate the downstream ®rm. The only differences are that: (1) the upstream ®rm extracts less rent, and (2) the ef®cient downstream ®rm D gets a higher informational rent when it is not regulated. Indeed, asymmetry of information limits the ability of the regulator to increase social welfare and, consequently, it limits the amount that the upstream ®rm can ask the regulator for its product. However, this does not change the way the rent is extracted. Another case of interest is the one where there is a difference in the asymmetry of information between the regulator and the upstream ®rm. This is the topic of our current research.10 Moreover, the assumption of a foreign ®rm U is not needed for the result. What is required is that the regulator, for any reason, has no regulatory power over the upstream ®rm. The rent extraction phenomenon worsens when the regulator takes into account the pro®ts of the upstream ®rm in its objective function. Indeed, the value of production of the ®nal good for the regulator is increased by the value of the pro®ts of the upstream ®rm. Taking this for granted, ®rm U can extract more rent from its production. Finally, this result is robust to a change in the regulatory framework. In a RamseyBoõÃteux model, with n downstream industries (among which the one requiring the essential facility) regulated under the same budget constraint and with some limited monetary transfers, the same kind of results occurs. One of the striking features of this model lies in the equilibrium where the regulator, which is supposed to regulate, decides to slack because it is not socially optimal to regulate. Therefore, introducing a government (which decides whether or not to regulate) separated from the regulator (which sets how much to regulate) may help to understand better when a government should introduce a regulator.

9 Please refer to Hariton (2002) for details. 10 This has been motivated by a remark of a referee.

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Appendix Proof of Lemma 1: This proof follows the same line as standard textbooks such as Tirole (1988, p. 176). At the second step, when the tariff is set, ®rm D decides whether or not to accept the tariff T U . It accepts T U if it can at least break even while maximizing its pro®t with the extra cost of T U , that is, if there exists q~1 such that   q~1 ˆ arg max p1 …q1 †q1 CD …q1 † H0 p0 q1 q1

and p1 …q~1 †~ q1

CD …q~1 †

H0

p0 q~1  0:

If it exists, then it is characterized by the ®rst order condition which yields a solution noted q1 …p0 †. The second order condition is assumed to be satis®ed. At the ®rst step, ®rm U maximizes its pro®t subject to the constraint that ®rm D is maximizing its own pro®t under its participation constraint 

max H0 ‡ p0 q1 p0 ;H0

U

C …q1 †



( s:t:

q1 ˆ q1 …p0 †; p1 …q1 †q1

CD …q1 †

H0

p0 q1  0:

Because leaving pro®ts to ®rm D is costly to ®rm U, the participation constraint of ®rm D is binding at the optimum, pD ˆ 0. This yields, omitting the arguments,  max p1 …q1 †q1

CD …q1 †

p0

 CU …q1 † :

This program is the same as that of ®rm V, the vertically integrated ®rm and attains its U maximum for the value q1 ˆ qvi 1 . Therefore, the optimal tariff for ®rm U to set is p0 ˆ c .  U vi This yields q1 …c † ˆ q1 which is the argument that maximizes the objective function of ®rm U. Finally, the ®xed part is given by the participation constraint. Firm U gets pU ˆ pvi , vi while social welfare is S1 …qvi p1 …qvi & 1† 1 †q1 . Proof of Lemma 2: When it faces T U …q1 † ˆ pvi ‡ FU ‡ cU q1 , the regulator maximizes social welfare under the constraint pD  0. This constraint is binding and social welfare becomes S1 ‡ lp1 q1

…1 ‡ l†…CD ‡ T U † ˆ S1

vi With q1 ˆ qvi 1 , social welfare is S1 …q1 † tariff.

p1 q1 ‡ …1 ‡ l†…p1 q1

CD

CU

pvi †:

vi p1 …qvi 1 †q1 > S1 …0† and the regulator accepts the &

vi Proof of Proposition 1: Lemma 2 sets that S1 …qvi p1 …qvi 1† 1 †q1 > S1 …0†. Therefore, one can ®nd some e > 0 such that the left hand side minus e remains greater than S1 …0†. This

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FRANC Ë OIS BOLDRON AND CYRIL HARITON

means that, when it faces the no-regulation tariff with e=…1 ‡ l† more in the ®xed part, the regulator gets more than the acceptation threshold S1 …0† when it makes ®rm D produce qvi 1. Thus, the regulator still accepts this two-part tariff thanks to which ®rm U obtains pvi ‡ e=…1 ‡ l† > pvi . Given T U , the regulator solves the following program  max S1 ‡ lp1 q1 q1 ;t

lpD

…1 ‡ l†…CD ‡ T U †



under the participation constraint of ®rm D: pD ˆ t  0. Because leaving rents to ®rm D is costly, pD ˆ 0. This yields the standard ®rst order equation inducing an outcome noted q1 …p0 †. The acceptance condition is S1 …q1 † ‡ lp1 …q1 †q1

…1 ‡ l†‰CD …q1 † ‡ H0 ‡ p0 q1 Š  S1 …0†:

Firm U maximizes its pro®t with respect to p0 and H0 , subject to the acceptance condition and the reaction of the regulator. For a given p0 , the acceptance condition de®nes an upper limit to the value of H0 . As ®rm U's pro®t is strictly increasing in H0 , the constraint is binding at the equilibrium and the objective function of ®rm U becomes max p0

1 ‰S 1‡l 1

S1 …0† ‡ lp1 q1





…1 ‡ l†…CD ‡ CU †Š: 1

Except for the constant S1 …0†, this objective function is …1 ‡ l† times the objective function of a regulator who would be surpervising the vertically integrated ®rm. Therefore, the optimal price is p0 ˆ cU . Finally, the value of H0 is given by the individual participation constraint which can be written in two different ways:  1  SWviR S1 …0† ‡ FU 1‡l  viR viR

 CD qviR ‡ ˆ p1 q1 CU qviR 1 1

H0 ˆ

1  viR S 1‡l 1

S1 …0†

 viR ‡ FU : pviR 1 q1

From the acceptance condition, the social welfare level is S1 …0† and the ®nal outcome is vi qviR & 1 . The beginning of the proof ensures that U's ®nal pro®t is higher than p . Proof that the upstream ®rm's rent is a decreasing funtion of k: Recalling section 3, SWviR stands for the highest social welfare in a situation where both ®rms are vertically integrated. By Proposition 1, the rent of the upstream ®rm is pU ˆ

1  SWviR 1‡l

 S1 …0† :

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Then, with a slight abuse of notation on SWviR , one can get dpU 1 dSWviR dq1 ˆ 1 ‡ l dq1 q1 ˆ qviR dl q1 ˆ qviR dl 1

1



1 …1 ‡ l†

2

SWviR

 S1 …0† :

The last term is clearly negative. Moreover, SWviR , as a function q1 , is maximized for viR the production level qviR with respect to q1 in q1 ˆ qviR 1 . Therefore, the derivative of SW 1 is equal to zero and the rent of ®rm U is decreasing in l. &

References Ballard, C., J. Shoven, and J. Whalley. 1985. ``General Equilibrium Computations of the Marginal Welfare Costs of Taxes in the United States.'' American Economic Review 75(1): 128±138. Boldron, F., and C. Hariton. 2000. ``Rent Extraction by an Unregulated Essential Facility.'' Working paper 20.07.538, University of Toulouse (Gremaq). Hariton, C. 2002. ``Gestion et ReÂglementation des Infrastructures'', PhD Dissertation, University of Toulouse (Gremaq). Laffont, J.-J., and J. Tirole. 1993. A Theory of Incentives in Procurement and Regulation. Cambridge, MA: Massachussets Institute of Technology Press. Segal, I. R. 1998. ``Monopoly and Soft Budget Constraint.'' Rand Journal of Economics 29(3): 596±609. Tirole, J. 1988. The Theory of Industrial Organization. Cambridge, MA: Massachussets Institute of Technology Press.