RENT EXTRACTION by an UNREGULATED ESSENTIAL FACILITY∗ Fran¸cois Boldron Gremaq, Universit´e de Toulouse I 21 all´ees de Brienne, F-31000 Toulouse, France [email protected] Cyril Hariton† Gremaq, Universit´e de Toulouse I 21 all´ees de Brienne, F-31000 Toulouse, France [email protected]

Abstract This paper shows that consumers may benefit when a regulator chooses not to regulate a final 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 final good production more than the producer itself. Second, the regulator has access to an extra source of financing with the public funds. Therefore, the essential facility seller can ask more of the regulator than of the final good producer. Jel codes: D82, L12, L51 Keywords: Monopoly, Regulation, Two-part tariff, Vertical relation

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 firm. For example, in the pharmaceutical ∗

We thank Claudes Crampes, Johannes Jaspers, Gwena¨el 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 “Journ´ees de Micro-Economie Appliqu´ee” (Qu´ebec, 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 Cr´emer for its encouragement. All remaining errors are ours. † Corresponding author.

1

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 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 firms which buy a licence. But the sale of drugs to consumers is often regulated by the country in which there are sold. Therefore, the local firms are regulated and must purchase an input - the licence - from a firm that has monopoly power. In our model, a foreign monopoly uses non-linear tariffs to sell an essential input to a local firm 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 firm benefits 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 figure 1, the industry structure can take two simple forms. Either the downstream firm is not regulated (case on the left) and firms contract directly, or the regulator chooses the final output (case on the right) and the upstream firm contracts with the regulator. Without regulation, the upstream firm extracts, with a simple two-part tariff, a profit equal to the maximum profit of the structure made of both the upstream and the downstream firms. Under regulation, it can extract not only this profit but all the increase in social welfare from the product. Therefore, the regulator will, if possible, not regulate the downstream firm. 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 firm. Section 5 completes the formal study with the introduction of a third choice: not to regulate the downstream firm. Finally, section 6 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).

2

Firm U

Firm U Foreign Domestic

?



Regulator -



Public funds



?

Firm D  

?

Consumers



?

Firm D  

 

?

Consumers

 

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

2

Model

An upstream monopoly, firm U , sells an essential input to a regulated downstream monopoly, firm D. These two firms are located in two different countries. In order to produce q1 units of good 1, firm D must purchase q1 units of good 0 from firm U . The national economy consists of firm D, the consumers of good 1 and the national regulator (hereafter, the regulator) who maximizes national social welfare. Firm U is a foreign firm, is not regulated and its profit is not included in national social welfare. Moreover, firm U is assumed to have all the bargaining power in any negotiation. Firm U sells q0 units of good 0 for a cost2 C U (q0 ) = F U + cU q0 , with a two-part tariff T U (q0 ) = H0 + p0 q0 . Its profit function is then π U (q0 ) = H0 + p0 q0 − F U − cU q0 .

(1)

The cost of firm D, exclusive of the two-part tariff T U , is C D (q1 ) with a constant fixed cost F D which is assumed not to be sunk.3 When firm D is regulated, there is no loss of generality to assume that the cost C D and the tariff T U are paid by the regulator which also receives all the revenues from the sale of good 1. Then, firm D receives a net transfer t and its profit function is π D = t.

(2)

The consumers gross surplus is S1 (q1 ) with S1q (q1 ) = p1 (q1 ) the inverse demand 2 In general, superscripts are used to distinguish between firms (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.

3

function and S1qq < 0. The regulator maximizes national social welfare   SW = [S1 (q1 ) − p1 (q1 ) q1 ] + [t] − (1 + λ) t + C D (q1 ) + T U (q1 ) − p1 (q1 ) q1 ,  = S1 (q1 ) + λp1 (q1 ) q1 − λπ D − (1 + λ) C D (q1 ) + T U (q1 ) ,

(3)

where λ > 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

The vertically integrated firm.

Let us call firm V the vertically integrated firm, that

is the hypothetical firm created by the merger of firms U and D. Its cost function is C D (q1 ) + C U (q1 ). Without regulation, firm V would produce q1vi such that it maximizes its profits    q1vi = arg max p1 (q1 ) q1 − C D (q1 ) + C U (q1 ) . q1

The associated profit is noted π vi . With regulation of firm V , social welfare would become, omitting the arguments,   SW = S1 + λp1 q1 − λt − (1 + λ) C D + C U . Maximizing social welfare under the participation constraint that firm V ’s profit should be positive, t ≥ 0, yields this constraint to be binding and production4 to be q1viR , solution of the following first order condition p1 (q1 ) − CqD (q1 ) − CqU (q1 ) +

λ p1q (q1 ) q1 = 0. 1+λ

It is assumed that second order conditions are satisfied and that these equations have unique solutions. Regulation of both firms.

Regulating both firms is equivalent to regulating firm V .

This yields an outcome q1viR which is socially efficient. It generates the highest total social welfare level possible in this setting, noted SWviR . 4

Superscript viR stands for “vertically integrated and regulated”.

4

No regulation at all.

Without regulation, firm U, which has all the bargaining power,

can extract the same profit that firm V could have. Lemma 1 Without regulation, the optimal two-part tariff for firm U is T U (q1 ) = π vi + F U + cU q1 . The quantity produced is q1vi . Firm U ’s profit is π vi and the social welfare

level is S1 q1vi − p1 q1vi q1vi . Firm D gets zero profit. This is the tariff, so called no-regulation tariff, the upstream firm U proposes if there is no regulation of the downstream firm D.

4

Socially harmful regulation

We now examine the game in which the regulator regulates firm D. In order to model the bargaining power of U , we use the following game: first, firm U makes a take-it-or-leave-it offer to the regulator, which consists in a two-part tariff T U (q1 ) = H0 + p0 q1 ; second, the regulator decides whether to accept the tariff and computes the optimal contract for firm D. Strategy of the regulator.

In the second stage, if the regulator has accepted the tariff

T U , it faces the following problem 
 max S1 + λp1 q1 − λπ D − (1 + λ) C D + H0 + p0 q1 q1 ,t

subject to the participation constraint of firm D: π D > 0. Standard results obtain  λ p1 (q1∗ ) − CqD (q1∗ ) − p0 + 1+λ p1q (q1∗ ) q1∗ = 0, π D = 0. We assume that the second order conditions are satisfied and that the first 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). Strategy of firm U .

Suppose firm U proposes the no-regulation tariff T U (q1 ) = π vi

+ F U + cU q1 .

5

Lemma 2 The regulator always accepts the no-regulation tariff if the upstream firm U proposes it. In that case, the regulation of firm D is not costly for firm U , but neither is it beneficial. Firm U can extract from the regulator what it could obtain directly from firm D in the absence of regulation. But is it the best strategy for firm U ? With linear prices in the downstream sector, the consumers save some surplus that the downstream firm is not able to extract. Therefore, when contracting with firm D, the upstream firm can not gain more than the maximum profit of the vertically integrated firm (what firm U gets with its no-regulation tariff) and the consumers keep this net surplus.5 But, here, the upstream firm 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 more costly for the regulator than for firm D. Moreover, the regulator has access to an extra source of financing, 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 firm 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 profit when the downstream firm D is   1 regulated. Moreover, the optimal two-part tariff for firm U is T U (q1 ) = 1+λ SWviR −S1 (0)   1 + F U + cU q1 , which yields a profit of π U = 1+λ SWviR −S1 (0) and a final production q1viR . The level of social welfare is S1 (0) and corresponds to the zero production one. Firm D gets zero profit. The profit of firm U can be rewritten 

 viR π U = pviR − C U q1viR − C D q1viR + 1 q1

 1  viR viR S1 − S1 (0) − pviR . 1 q1 1+λ

The first term corresponds to the vertically integrated firm’s profits when producing the quantity q1viR . The regulation of firm D allows firm U to indirectly collect part of the consumer net surplus on top of the regulated vertically integrated monopoly profit. Because 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. 6 In other words, the upstream firm U can consider the regulator as a firm whose objective function is the sum of social welfare, consumer surplus and the cost of public funds. By using its non-linear tariff, firm U is able to extract all the surplus from this new downstream firm.

6

consumers do not pay directly firm U , the real cost for the regulator of an additional ε asked by firm U is (1 + λ)ε, 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 firm U maximizes its profits, 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 first instrument p0 is used to generate the highest social welfare, that is, induces socially efficient 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 benefits derived from the production of good 1 are taken by firm U . As the rent extracted by the upstream firm is decreasing in λ,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 firm’s profit 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 first-best optimal. The natural question raised by this result is whether regulation is worthwhile. To handle this question, we assume that, in a first period, the regulator decides whether or not to regulate firm D. In a second period, firm U proposes a two-part tariff to the regulator if there is regulation, to firm D otherwise. In a third period, the tariff is accepted or rejected by the regulator if there is regulation, by firm D otherwise. If, in the first period, the regulator decides to regulate firm D, social welfare will be equal to S1 (0), as shown in section 4. On the other hand, in the absence of regulation,

the social welfare will be S1 q1vi − p1 q1vi q1vi , as shown in section 3. Social welfare is higher without regulation, and this proves the following proposition. 7

The proof is detailed in the appendix. Please refer to Laffont and Tirole (1993, p. 38) and Ballard, Shoven and Whalley (1985) for insights on the methodology of the computation of the values of the parameter λ. 8

7

Proposition 2 The regulator never chooses to regulate firm D. Firm U extracts only π vi , the final production is q1vi and firm D gets zero profit. Thus, the consumers are better off when there is no regulation even if they consume less (q1vi < q1viR ). 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 firm D and this would not change firm U ’s profit. Therefore, there is place in our model to introduce other bargaining procedures in order to reach a better final equilibrium for both agents.

6

Concluding remarks

This paper shows that consumers do benefit 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 final good market to regulate (subadditivity of cost, universal service obligations) has to be reviewed in the sense of a deeper analysis of the upstream context of these industries. In a sense, firm 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 firm U can make a take-it-or-leave-it offer to either the regulator or firm D. Our intuition is that the argument of the basic result remains true as long as firm U has some bargaining power. Second, the upstream firm 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 firm and the regulator have the same information on the cost of the downstream firm, Boldron and Hariton (2000) show that our main result does not change: the regulator prefers not to regulate the downstream firm. The only differences are that: (1) the upstream firm extracts less rent; and (2) the efficient downstream firm D gets a higher informational rent when it is not regulated. Indeed, asymmetry of information 8

limits the ability of the regulator to increase social welfare and, consequently, it limits the amount that the upstream firm 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 firm. This is the topic of our current research.9 Moreover, the assumption of a foreign firm U is not needed for the result. What is required is that the regulator, for any reason, has no regulatory power over the upstream firm. The rent extraction phenomenon worsens when the regulator takes into account the profits of the upstream firm in its objective function. Indeed, the value of production of the final good for the regulator is increased by the value of the profits of the upstream firm. Taking this for granted, firm U can extract more rent from its production. Finally, this result is robust to a change in the regulatory framework. In a RamseyBoˆıteux 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 result 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.

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, firm 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 profit with the extra cost of T U , that is, if there exists q˜1 such that   q˜1 = argmax p1 (q1 ) q1 − C D (q1 ) − H0 − p0 q1 q1

and p1 (˜ q1 ) q˜1 − C D (˜ q1 ) − H0 − p0 q˜1 ≥ 0. 9

This has been motivated by a remark of a referee.

9

If it exists, then it is characterized by the first order condition which yields a solution noted q1∗ (p0 ). The second order condition is assumed to be satisfied. At the first step, firm U maximizes its profit subject to the constraint that firm D is maximizing its own profit under its participation constraint    q1 = q1∗ (p0 ) , U max H0 + p0 q1 − C (q1 ) st p1 (q1∗ ) q1∗ − C D (q1∗ ) − H0 − p0 q1∗ ≥ 0. p0 ,H0 Because leaving profits to firm D is costly to firm U , the participation constraint of firm D is binding at the optimum, π D = 0. This yields, omitting the arguments,   max p1 (q1∗ ) q1∗ − C D (q1∗ ) − C U (q1∗ ) . p0

This program is the same as that of firm V , the vertically integrated firm and attains its maximum for the value q1 = q1vi . Therefore, the optimal tariff for firm U to set is p0 = cU .
This yields q1∗ cU = q1vi which is the argument that maximizes the objective function of firm U . Finally, the fixed part is given by the participation constraint. Firm U gets π U

= π vi , while social welfare is S1 q1vi − p1 q1vi q1vi . Proof of lemma 2. When it faces T U (q1 ) = π vi +F U +cU q1 , the regulator maximizes social welfare under the constraint π D ≥ 0. This constraint is binding and social welfare becomes
S1 + λp1 q1 − (1 + λ) C D + T U
= S1 − p1 q1 + (1 + λ) p1 q1 − C D − C U − π vi .

With q1 = q1vi , social welfare is S1 q1vi − p1 q1vi q1vi > S1 (0) and the regulator accepts the tariff.

Proof of proposition 1. Lemma 2 sets that S1 q1vi − p1 q1vi q1vi > S1 (0). Therefore, one can find some ε > 0 such that the left hand side minus ε remains greater than S1 (0). This means that, when it faces the no-regulation tariff with ε/ (1 + λ) more in the fixed part, the regulator gets more than the acceptation threshold S1 (0) when it makes firm D produce q1vi . Thus, the regulator still accepts this two-part tariff thanks to which firm U obtains π vi + ε/ (1 + λ) > π vi . Given T U , the regulator solves the following program 
 max S1 + λp1 q1 − λπ D − (1 + λ) C D + T U q1 ,t

10

under the participation constraint of firm D: π D = t ≥ 0. Because leaving rents to firm D is costly, π D = 0. This yields the standard first order equation inducing an outcome noted q1∗ (p0 ). The acceptance condition is   S1 (q1∗ ) + λp1 (q1∗ ) q1∗ − (1 + λ) C D (q1∗ ) + H0 + p0 q1∗ > S1 (0) . Firm U maximizes its profit with respect to p0 and H0 , subject to the acceptance condition and the reaction of the regulator. For a given p0 , the acceptance condition defines an upper limit to the value of H0 . As firm U ’s profit is strictly increasing in H0 , the constraint is binding at the equilibrium and the objective function of firm U becomes max p0


 1  ∗ S1 − S1 (0) + λp∗1 q1∗ − (1 + λ) C D∗ + C U ∗ . 1+λ

Except for the constant S1 (0), this objective function is (1 + λ)−1 times the objective function of a regulator who would be surpervising the vertically integrated firm. Therefore, the optimal price is p0 = 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) + F U 1+λ  viR viR

 = p1 q1 − C U q1viR − C D q1viR +

H0 =

 1  viR viR S1 − S1 (0) − pviR + FU. 1 q1 1+λ

From the acceptance condition, the social welfare level is S1 (0) and the final outcome is q1viR . The beginning of the proof ensures that U ’s final profit is higher than π vi . Proof that the upstream firm’s rent is a decreasing funtion of λ. Recalling section 3, SWviR stands for the highest social welfare in a situation where both firms are vertically integrated. By proposition 1, the rent of the upstream firm is πU =

 1  SWviR −S1 (0) . 1+λ

Then, with a slight abuse of notation on SWviR , on can get   1 d SWviR dq1 1 dπ U = − SWviR −S1 (0) . 2 dλ 1+λ dq1 (1 + λ) q1 =q viR dλ q1 =q viR 1

1

The last term is clearly negative. Moreover, SWviR , as a function q1 , is maximized for the production level q1viR . Therefore, the derivative of SWviR with respect to q1 in q1 = q1viR is equal to zero and the rent of firm U is decreasing in λ.

11

References Ballard, C., Shoven, J. and Whalley, J. 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 Hariton, C. 2000. “Rent extraction by an unregulated essential facility.” Working paper 20.07.538, Gremaq, Universit´e de Toulouse I. Laffont, J.-J. and Tirole, J. 1993. A theory of incentives in procurement and regulation. Cambridge, MA: Massachussets Institue 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 Institue of Technology Press.

12