Conglomerates and regulation.

Calzolari, Giacomo ; Scarpa, Carlo

I. INTRODUCTION

Conglomerate firms account for a large part of developed economies. In 2008, the Bureau of the Census reported that about half of the sales in the United States was generated by multi-industry firms. Many of these horizontally diversified firms operate in highly regulated sectors, such as utility sectors, banking and financial sectors, as well as in completely unregulated ones. The multiple activities that characterize conglomerates naturally raise concerns on both the sides of regulators and rival firms in competitive markets. In both the United States and the European Union, it is feared that diversification may imbalance competition in the unregulated sectors (a "level playing field" argument), and affect negatively consumers in the regulated markets due to the increased complexity of the regulatory task. These concerns may also lead to a ban for regulated firms to operate in unregulated markets or, similarly, to run these activities with integrated productions. (1)

In this study, we investigate these issues studying a conglomerate that operates both in a regulated and an unregulated market. We analyze how competition and regulation interact by means of this type of firm, and if integrated production should be allowed.

These are central questions in market design of practical and theoretical relevance, and that have been at the center of an intense policy debate for at least three decades. Initially, the focus had been more on vertical integration and possible market foreclosure, but more recently, as a consequence of both important technological advancements and intense deregulation, the issue of regulation and competition has mainly involved horizontally related markets. In many cases regulated companies see, and try to exploit, opportunities of expanding their business into neighboring markets, which are open to competition.

Examples of this industrial development abound. For instance, most European local energy and gas utilities (e.g., in Italy, Germany, or Scandinavian countries) sell both to customers protected by regulated prices and to customers which can (and do) choose in the free market. In the same way, many regulated water companies also sell energy to free market customers. The French Veolia (very strong in regulated sectors such as water or environmental services) also generates electricity to be sold in the wholesale French market. Centrica in the United Kingdom operates both in gas and electricity transmission but also claims to be the United Kingdom's leading drain-cleaning service firm (through the brand name Dyno). GDF-Suez in France and other countries, RWE in Germany, and Enel in Italy all operate in regulated as well as unregulated markets in energy, water, and other utility sectors. In the United States, a major utility such as Pepco also offers energy management services. Regulated postal services are often jointly offered together with banking, insurance, and general financial services, for example, in France, Italy, Japan, and a similar proposal is currently debated in the United States as well. (2)

On the side of the firms, there are several reasons for expanding and diversifying into unregulated markets. However, the most commonly cited motivation goes under the heading "synergy," the buzz-word indicating economies of scope in the joint production and supply of horizontally diversified services. Indeed, in the mentioned sectors, common maintenance teams and, in general, any shared production facility allow to reduce both fixed and marginal costs of the different activities. Similarly, managing two or more distribution networks at the same time normally allows for significant cost savings. (3)

If on the one hand economies of scope are desirable because they increase efficiency in production, on the other hand interacting with those complex conglomerate firms may be difficult both for regulators and competing firms in unregulated markets. In particular, the actual amount of cost savings (i.e., the synergy) is generally unknown both to the regulator and to the competitors in unregulated markets, and it is private information of the conglomerate performing joint production. Indeed, the lack of information concerning the actual size of cost synergies is often lamented both by regulators and competing firms in terms of reduced market transparency: they may suffer a very substantial asymmetry of information. This has recently moved policy makers, regulators, and the academia toward an intense empirical research aiming to measure the actual magnitude of scope economies in multiproduct firms with an outcome that can be summarized with the words of the European Union Directorate-General of Energy and Transport in 2004 stating that the extent of separation "can only be decided on a case by case basis." (4) Although scope economies are often identified in empirical analyses, there is a significant variation due to unobserved heterogeneity which leaves open the aforementioned issue of asymmetric information: as reported in Panzar (2009), some regulators are nowadays led to argue that "the only way to ensure a level playing field is to prohibit incumbent firms that enjoy either de facto or de jure monopoly power in one market from participating in related competitive markets."

Interestingly, this view on unbundling has been a recurrent theme in utility sectors. During the 1980s, regulators and authorities were generally contrasting diversification into nonutility sectors by regulated firms, imposing restrictions ("Chinese walls"), and even mandatory breakup, such as in the case of AT&T (accused of subsidizing unregulated market activities with returns from the regulated and monopolized local telephone markets). During the 1990s, diversification became more common as documented, for example, in the U.S. electricity industry by the percentage of firms reporting also some unregulated activity which increased from 8% in 1980 to 34% in 1997 (Jandik and Makhija 2005). Since then, national authorities have become cautious again in allowing regulated firm to expand into unregulated sectors, although technologies have shown strong convergence within sectors (e.g., in the telecommunication industry) and, to a smaller extent, also across sectors (e.g., in electricity and gas).

In this study, we explicitly take the issue of complexity and asymmetric information brought about by conglomerate firms that affects both regulators and competitors. (5) In our model, the magnitude of scope economies is the private information of the conglomerate when it is allowed to run integrated productions, and both the regulator and the rival firms are uninformed. In this case, the optimally designed regulation accounts for the conglomerate's private information and, importantly, the actual behavior of this firm in the regulated market may reveal information to the unregulated market about the level of economies of scope and the conglomerate's costs. In other terms, the game in the unregulated market may or may not be one of asymmetric information, depending on the information generated by the regulatory process; this in turn affects the conglomerate's behavior in its regulated market, i.e., its incentive to disclose information to the regulator.

We show that the interactions between the regulated and the unregulated market depend on what type of competition takes place in the unregulated market. When firms compete in quantities (when capacity constraints are important, for example, as it is for some of the cases mentioned above), the regulator can more easily elicit information on scope economies, reducing distortions in the regulated sector. Acting as if economies of scope were small so as to obtain lenient regulation, the conglomerate would get the countervailing effect of inducing the rival firms to expand in the unregulated market. With price competition (when, e.g., conglomerates offer financial services), by contrast, the activities in the unregulated market and the associated informational externality complicate the regulatory process since behaving as if scope economies were small prompts an accommodating reaction by the rivals in the unregulated market. The regulator may thus be forced to apply a uniform regulatory policy (regardless of the actual size scope.

of the scope economies), so that no information is disclosed to rivals. Information is not the only channel connecting regulated and unregulated markets since a larger regulated output per se (i.e., independently of the actual and believed scope economies) implies smaller costs in the unregulated market for the conglomerate. This firm thus prefers a larger regulated output (a "top dog" strategy) under strategic substitutability in the unregulated market, as with quantity competition, and a lower regulated output (a "puppy dog" strategy) under strategic complementarity, as with price competition.

These results vindicate, at least in part, the general discontent of regulators, authorities, and also competitors with respect to the expansions of regulated firms into unregulated markets. Indeed, both regulation and competition are affected in a significant way by the activities of the conglomerate firm. On the one hand, a symptom of more difficult regulation is identified, for example, by the need to rely on uniform regulation. On the other hand, competitors will face a stronger rival when scope economies are significant and must rely on the informational externality of the regulatory policy to infer the actual dimension of this cost advantage.

We then move on to comparing welfare when the conglomerate is allowed to run joint productions for the two markets with that with compulsory separation preventing a firm from exploiting its economies of scope for the sake of transparency. On the one hand, if economies of scope are substantial, consumers in the two markets may benefit from the gain in efficiency. On the other hand, since scope economies is the private information of the conglomerate, the lack of information for the regulator and competitors affects and, as shown, it may distort the regulated price and competition in the unregulated market. (6) Unexpectedly we show that, even though horizontal integration causes transparency issues for regulation and for competitors, these adverse effects are systematically smaller than the efficiency gains from integration.

Among the many extensions that we consider, it is worth mentioning the possibility that integration brings about either diseconomies of scope (with some probability) or economies of scope (with complementary probability).

Although the optimal regulated quantities would be affected (actually reduced, as compared with the baseline model in the paper), the logic and the effects of the informational externality would be unchanged. Hence, the conglomerate may still prefer joint production, whilst separation may now become socially desirable.

The article is organized as follows: We conclude this section with a literature review, and introduce the model in the next section; Section III analyzes benchmark cases, with full information and separation of activities; Section IV derives optimal regulation when the conglomerate is allowed to integrate and investigates the interaction with the unregulated market; Section V uses these results to study the welfare effects of integration in the case of quantity and of price competition; Section VI discusses extensions and alternative modeling assumptions; and Section VII concludes. All the proofs are in the Appendix.

A. Related Literature

The early literature on diversification of regulated firms into unregulated sectors has initially emphasized the risks and the costs of this practice and, in particular, the undesirable possibility that the diversified conglomerate diverts resources and profits from regulated core-markets to unregulated ones. (7) Along these lines, Braeutigam and Panzar (1989), Brennan (1990), and Brennan and Palmer (1994) questioned the desirability of horizontal diversification addressing the possibility of cross-subsidies via cost shifting, in which an integrated firm attributes to the regulated activity costs that actually pertain to nonregulated ones and thus obtains higher regulated prices, while at the same time behaving more aggressively in the unregulated sectors. (8) The trade-off about horizontal diversification has been emphasized also in another pertinent analysis by Sappington (2003), with a model where effort can be allocated to regulated and unregulated activities. This paper shows that for diversification to be undesirable two conditions must hold at the same time: the regulator cannot control effort diversion and the firm can inflate expenditures (by cost padding) on unregulated activities. All these papers illustrate the potential risks of diversification in terms of cross-subsidies and effort diversion, while we emphasize the increased complexity and lack of transparency (in terms of adverse selection) that emerges when the regulated firm is allowed to diversify its activities in unregulated markets.

Lewis and Sappington (1989a) study a model where the costs of regulated activities are positively correlated with profitability in the unregulated sector. Within this setting and with a black-boxed description of profitability in the competitive market, they show how "countervailing incentives" may affect regulation. (9) A benefit of diversification is here that the regulator could learn something about the regulated firm's costs by observing its behavior in an unregulated market. Our analysis instead shows that this informational externality can be a "two-way street" in that when asymmetric information pertains the dimension of scope economies, the firm too can affect its rivals in the unregulated market that may obtain information observing actual regulation. Countervailing incentives have also been discussed by Iossa (1999) who considers the design of a regulated two-product industry with interdependent and unknown demand. She shows that whether an integrated monopolist or two separate firms is desirable depends on the interplay between the demand complementarity/substitutability of the two products.

Our analysis differs from all these papers in several respects. We emphasize that integrated production is both a source of scope economies but also of private information for the conglomerate with respect to the regulators and its rivals. The informational issues arise exactly from integrated production in that neither the regulator nor the rivals know the exact magnitude of scope economies. This is a different perspective with respect to that on effort diversion in the previous papers. Explicitly describing the unregulated market we can properly study if and when the regulated firm might have an unfair advantage in that market and how the rivals react to the information generated by regulation itself. The present study thus adds to the extant literature on pros and cons of horizontal diversification by illustrating a potential benefit that has not been considered.

This study is also related to the large literature on information sharing in oligopoly (surveyed by Vives 1999). With this respect, we illustrate how the availability of information in a market does not necessarily come from firms' information sharing decisions but may also result from an information externality of "third parties" such as the regulators of distinct markets. The paper thus naturally brings together two strands of literature, one on regulation and another on information sharing, which had been considered independent since now.

Finally, we suggest with our analysis a novel dimension of regulation that involves an information externality. The firm's regulated behavior in the regulated market can give other firms in the unregulated market a chance to infer the cost structure of the regulated firm which is also relevant for competition in the unregulated market. With this respect and with a more general perspective, this article also contributes to the contract theory literature by considering an environment in which (1) an agent (the conglomerate) has private information on how a contractible and a noncontractible action interact in her payoff (respectively the regulated output and the firm's activity in the unregulated market) and (2) the optimal (regulatory) contract set by the principal (the regulator) at the same time screens the agent's type and signals this private information to third parties (i.e., the competitors in the unregulated market). This informational externality also arises in different contexts. For example, Calzolari and Pavan (2006) study the optimal disclosure of information between two sellers who contract sequentially with the same privately informed buyer.

II. MODEL SET-UP

We consider a regulated natural monopoly (market R) and an unregulated oligopoly (market U). Demand functions in regulated and unregulated markets are independent, decreasing and (twice) differentiable. Inverse demand in the regulated market R is p(q) where q is output. The unregulated market U consists of n firms indexed by i = 1,..., n, each producing (possibly differentiated) output [y.sub.i with price [p.sup.U.sub.i]. Inverse demand functions are [p.sup.U.sub.i] ([y.sub.i], [T.sub.-i]) i = 1,..., n, where [T.sub.-i] denotes the vector of the outputs of other firms. The vectors of prices and outputs in the unregulated market are denoted by [p.sup.U] and Y, respectively. Competition in the unregulated sector takes place either in quantities or in prices.

A "conglomerate" firm operates in both markets, respectively producing outputs q and [y.sub.1] (index i = 1 will denote the conglomerate firm in market U). This firm may be allowed to run productions in the two markets jointly (integrated production), or may be forced to organize productions in separate units. In the latter case, separating productions makes impossible for the conglomerate to share assets and internal resources that may bring about cost savings. Formally, let C(q, [y.sub.1]; [theta]) denote the total production cost of the conglomerate with joint production, where [theta] is the scope economies parameter discussed below. If instead separation is imposed, the conglomerate's total costs is C(0, [y.sub.1]; [theta]) + C(q, 0;[theta]). Joint production thus generates a cost saving corresponding to

(1) C (0, [y.sub.1]; [theta]) + C (q,0; [theta]) - C (q, [y.sub.1]; [theta]) [greater than or equal to] 0,

which is nil when either q = 0 or [y.sub.1] = 0. The size of scope economies is parametrized by [theta], so that the expression in Equation (1) is nil if [theta] = 0 and, for any [theta]" [greater than or equal to] [theta]',

C(0, [y.sub.1];[theta]") + C(q, 0;[theta]") - C(q,[y.sub.1],[theta]") [greater than or equal to] C (0,[y.sub.1];[theta]') + C(q,0;[theta]') - C(q, [y.sub.1], [theta]').

with C(q, [y.sub.1]; [theta]") = C(q, [y.sub.1]; [theta]') if either q = 0 or [y.sub.1] = 0. Thus, the higher is [theta] the higher are scope economies and, if separation is imposed, [theta] has no bite on costs. (10) Assuming that the cost function is twice differentiable with respect to q and [y.sub.1], the previous conditions imply that (1) a larger output for one of the two markets induces a marginal cost reduction for the output in the other market, (2) this cost reduction is larger the higher is [theta] (and vanishing when [theta] = 0),

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

and (3) a higher value of [theta] (weakly) reduces the marginal cost for both outputs,

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The following simple specification of the cost function, that we will use in some examples, satisfies all the previous properties,

(4) [C.sub.1](q, [y.sub.1]; [theta])=c{q+[y.sub.1]) - [theta]q[y.sub.1].

The technology available to all other firms in market U (i.e., firms with index i = 2,..., n) is simply C([y.sub.i])=C(0,[y.sub.i];[theta]) and profits are

(5) [[pi].sub.i]([y.sub.i], [Y.sub.-i]) [equivalent to] [y.sub.i][p.sup.U.sub.i](Y ) - C([y.sub.i]).

When the firm is allowed to integrate production its total profit [PI] is (the apex I will stand for integration)

(6) [[PI].sup.I] (q,[y.sub.i], [Y.sub.-1];[theta]) [equivalent to] qp(q) + [y.sub.1][p.sup.U.sub.1] (Y) - C(q, [y.sub.1];[theta]) - T,

where T is a tax/transfer which is part of the regulatory contract in market R described below. If the conglomerate must keep apart its production for the two markets, its profit becomes [[PI].sup.S] + [[pi].sub.1]([y.sub.1],[F.sub.-1]) (the apex S will stand for separation) where

(7) [[PI].sup.S] [equivalent to] qp(q) - C (q, 0; [theta]) - T.

The regulator maximizes social welfare W which is a weighted sum of net consumer surplus in the two markets, firms profits and taxes (or transfers). Let [V.sub.j] denote gross consumer surplus in sector j = R, U. The welfare function is

(8) W =[V.sub.R](q) - qp(q) + [V.sub.U](Y) - Y[p.sup.U] (Y) + T + [alpha]([PI] + [n.summation voer (i=2)][[pi].sub.i]),

where Y[p.sup.U] (Y) = [[summation].sup.n.sub.i=1][y.sub.i][p.sup.U.sub.i] (Y) and the weight to profits is [alpha] [less than or equal to] 1. (11) The regulator sets the regulated quantity q (or equivalently the price p) and the transfer T, but cannot control any output or price in the unregulated market U. The role and feasibility of transfers in regulation has been thoroughly addressed in Armstrong and Sappington (2007). In some countries and for certain sectors, institutional constraints may limit the ability to pay transfers or specifically tax privately owned companies, although operating in regulated markets. In many other environments, transfers are instead feasible and actively used by regulators. (12) The regulator here equally cares for the surpluses of the two markets. This will allow us to account for the full effects of the decision to allow or not integrated production. (13)

As discussed in the introduction, the exact value of [theta] is private information of the conglomerate and neither the regulator, nor the competitors in the unregulated market know it. Assuming that [theta] is the only piece of private information is clearly a simplification which we employ to single out the effects of asymmetric information on economies of scope and of the complexity of conglomerates. Private information on scope economies is a distinctive trait of our analysis that naturally link regulated and unregulated market outcomes. It is common knowledge that scope economies can be either high or low, i.e., [theta] [member of] [THETA]= {[[theta].bar], [bar.[theta]]} with v = Pr ([theta] = [bar.[theta]]) = 1 - Pr ([theta] = [[theta].bar]), [bar.[theta]] [greater than or equal to] [theta]. The case of possible diseconomies of scope, i.e., [[theta].bar] < 0, is discussed in Section VII. (14)

The timing of the game is the following:

1. The regulator decides whether or not to impose separation of productions to the conglomerate firm, then accordingly sets and publicly announces the regulatory policy.

2. When allowed to integrate productions, the firm learns the size of scope economies, i.e., its type [theta]. It decides whether to be active in the regulated market and, if this is the case, regulation is enforced.

3. Finally, competition in the unregulated sector takes place.

Stage 2 indicates that the conglomerate is not obliged to participate the regulated market and will do so only if it finds it profitable. As we will discuss, if the firm wants to serve the regulated market, then it always prefers to bundle production in the two sectors, if allowed to do so. Finally, the execution of a regulatory contract (stage 2) naturally anticipates the determination of the equilibrium in the competitive sector (stage 3). Indeed, regulation follows procedures (such as regulatory lags that often last several years) and activities which are more difficult to modify than market decisions of private firms. Hence, once a particular regulatory policy is agreed between the firm and the regulator, it lasts for several years and the players in the unregulated market will take it as a fixed datum.

The exact magnitude of scope economies becomes clear to the conglomerate if it is allowed to integrate production and effectively does so. In this respect, we thus regard as impractical the possibility to condition the decision concerning joint or separate production on the realization of [theta]. This would require letting the conglomerate set up integrated production, learn [theta], and then subsequently impose separation if scope economies turn out to be low. Therefore, the regulator's decision on separation/integration cannot be made conditional on the specific regulatory policy and/or on the actual realization of [theta]. (15)

III. BENCHMARKS

In this section, we introduce two benchmarks which will help to discuss the pros and cons of integrated production in the presence of asymmetric information. We first analyze the case where separation of productions is imposed, and then we study the case with integrated productions and full information.

A. Optimal Regulation with Separate Productions

As there are no scope economies, and therefore no uncertainty, in the case of separate production, the regulated firm's profit in sector R with separation is simply as in Equation (7). Let firm i's equilibrium output in sector U be defined as [y.sup.S] which depends neither on [theta] nor on q and the associated profits [[pi].sup.S] = [[pi].sub.i] ([y.sup.S.sub.i], [Y.sup.S.sub.-i]) [greater than or equal to] 0. The regulator then maximizes Equation (8) with respect to q and T, subject to the participation constraint of the regulated firm, which assures that the conglomerate wants to serve (also) the regulated market, i.e., [[PI].sup.S] + [[pi].sup.S] [greater than or equal to] [[pi].sup.S]. Welfare can be written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which shows that, as usual, distributive efficiency would require to reduce as much as possible firms' profits in the two markets. The regulator then optimally sets the transfer at a level [T.sup.S], so that the participation constraint binds and the conglomerate earns no additional profits with respect to [[pi].sup.S]. Furthermore, the optimal regulated quantity [q.sup.S] is set efficiently, so that the price in the regulated sector is equal to the marginal cost, i.e., p([q.sup.S]) = [partial derivative]C([q.sup.S], 0; [theta])/[partial derivative]q. For future reference, we indicate with [C.sup.S] = ([q.sup.S], [T.sup.S]) this optimal regulatory policy when separation is imposed and with [W.sup.S] ([C.sup.S]) the associated welfare.

B. Integrated Productions and Full Information

Assume now that the conglomerate is allowed to integrate productions and all actors are fully informed on the precise level of scope economies [theta]. Consider the strategic variable [x.sub.i] for firm i in market U, so that [x.sub.i] = [p.sub.i] if competition takes place in prices and [x.sub.i] = [y.sub.i] for quantity competition. (16) Given the equilibrium choices in market U, we can express firms' profits and social welfare in terms of regulated output q and [theta]. Let the equilibrium output levels be [y.sub.1](q, [theta]), [y.sub.i](q, [theta]) i = 2,..., n (one could equivalently describe market U in terms of prices):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

and similarly for welfare,

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For a given (and here known) [theta], the regulator maximizes Equation (9) subject to the conglomerate's participation constraint

[[PI].sup.I] (q, [theta]) [greater than or equal to] Max {[[pi].sup.S], [[PI].sup.S]} = [[pi].sup.S]

where [[PI].sup.S] = 0, as discussed above. The regulator sets the T such that the participation constraint binds for any [theta] and no extra-profits are left to the conglomerate, i.e., [[PI].sup.I] (q, [theta]) = [[pi].sup.S]. Maximizing Equation (9) with respect to q, the optimal regulated quantity with full information and integration [q.sup.I.sub.FI] ([theta]) is such that

(10) p [[q.sup.I.sub.FI]([theta])) = SMC [[q.sup.I.sub.FI] ([theta]), [theta]],

where the right-hand side is the social marginal cost of q, i.e.,

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The price differs from the simple marginal cost [C.sub.q] for two reasons. As q affects firms' decisions in the unregulated market, the regulator internalizes the effect of q on market-power distortions in market U. This is illustrated by the second term on the right-hand side, where price-cost margin for each firm is weighted by the impact that q has on each firm's equilibrium output in that sector, where [partial derivative][y.sub.1] (q, [theta])/[partial derivative]q [greater than or equal to] 0 and [partial derivative][y.sub.i](q, [theta])/[partial derivative]q [less than or equal to] 0 for i [not equal to] 1. (17) Finally, by inducing the regulated firm to produce more in market R, the regulator reduces the profits of other firms in the unregulated market (since [partial derivative][[pi].sup.I.sub.i]/[partial derivative]q [less than or equal to] 0), thus increasing social welfare through enhanced distributive efficiency (the last term). Although these effects may be possibly conflicting, integration tends to expand regulated output, so that [q.sup.I.sub.FI]([theta]) [greater than or equal to] [q.sup.S], as illustrated in the explicit model of in Section IV-A. (18)

We indicate with [C.sup.I.sub.FI] = [{[q.sup.I.sub.FI]([theta]), [T.sup.I.sub.FI]([theta])}.sub.[theta][member of][THETA]] the optimal regulatory contract with integrated production and full information and with [W.sup.I.sub.FI] = [E.sub.[theta]] [[W.sup.I] ([C.sup.I.sub.FI]/[theta])] the associated (expected) welfare.

IV. REGULATION OF A PRIVATELY INFORMED CONGLOMERATE

When the regulator does not know the level of scope economies, he must rely on incentive compatible choices of the conglomerate. This can be obtained with a menu of type-dependent contracts C = [{(q([theta]),T([theta]))}[theta][member of][THETA]] which maximizes the (expected) social welfare and induces the conglomerate to choose the contract designed for a level of scope economies [??] which corresponds to the actual one [theta], i.e., the "declared" level of scope economies [??] is equal to the actual one [theta]. (19)

As a matter of fact, regulation does here two jobs at the same time: it allows to screen the actual level of scope economies and it may signal this information to the competitors in the unregulated market U. In fact, if it turns out that different levels of scope economies [??] are associated with different regulations, then rival firms may obtain information on [theta] by observing the actual regulated price [??] (which is clearly public information) or, equivalently, the quantity [??]. This is an important informational externality of regulation which allows competitors to update their beliefs about the level of the scope economies and then accordingly set their strategic variables in the unregulated market.

If optimal regulation is discriminatory with different quantities and prices for different values of declared [??], the updating process of rival firms is perfect. Without any loss of generality, we describe the updating process taking place through the observed regulated quantity so that v ([??]) [equivalent to] Pr ([bar.[theta]]|[??]) = 1 when [??] = q ([bar.[theta]]) and v ([??]) = 0 when [??] = q ([[theta].bar]). However, if regulation is uniform, the regulated quantity [??] does not depend on the firm's type and the competitors are not able to perform any updating, so that v ([??]) = v. (20)

We will denote with [y.sub.1] ([??], [theta], v ([??])) the equilibrium output in the competitive market for a conglomerate with (true) scope economies 0, producing a regulated output [??] and when the rival firms' updated beliefs are v ([??]). Similarly, let y ([??], v ([??])) be the rivals' output which clearly does not depend on the true level of scope economies but only on observed quantity [??] and associated [??]. Consistently with our notation, we will denote with [y.sub.1] ([??], [theta], 1), [y.sub.1] ([??], [theta],0) and y ([??], 1), y ([??], 0) outputs of a type [theta] conglomerate and of its rivals when the rivals believe that the true level of scope economies are either [bar.[theta]] or [[theta].bar].

Consider a conglomerate with scope economies [theta] which declares [??] and gets the contract ([??], [??]) [member of] C. This firm obtains a profit,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

However, by truthfully announcing, this firm obtains a profit [[PI].sup.I] ([theta]) = [[PI].sup.I] ([??], [theta]) with [??] = [theta]. Hence, any type of firm [theta] will truthfully announce the level of scope economies if

[[PI].sup.I]([theta]) [greater than or equal to] [[PI].sup.I] ([??]; [theta]) [for all][??] [member of] [THETA].

This incentive compatibility constraint for type [theta] can be conveniently rewritten as follows. Let [[PI].sub.U]([??], [theta], v ([??])) be the profit earned in the unregulated market U by the conglomerate with (true) scope economies [theta], producing [??] in sector R and thus inducing the rivals to believe that scope economies are [??], i.e.,

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the costs attributed to unregulated production is simply the incremental cost of [y.sub.1]. Then, incentive compatibility is guaranteed by the following equivalent condition

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In particular, the conglomerate with high scope economies [bar.[theta]] prefers not to mimic the one with small scope economies [[theta].bar] and vice-versa, respectively if

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

identifies the extra gain that type [bar.[theta]] obtains with respect to [[theta].bar] when they both produce the same regulated output q and induce beliefs v(q) on the rivals. ^

The declared scope economies [??] has here several interesting effects. First, as in standard models of regulation with asymmetric information, more efficient firms have incentives to understate their level of scope economies and to mimic less efficient firms in order to obtain more lenient and favorable regulation. This cost-efficiency effect is captured in the term [[DELTA].sub.[theta]][[PI].sub.U] ([q.bar],v([bar.q])) by the difference -[C([q.bar],[y.sub.1];[bar.[theta]]) - C ([q.bar], [y.sub.1]; [[theta].bar])] [greater than or equal to] 0. Indeed, if the efficient firm with type [bar.[theta]] mimics type [[theta].bar], it produces the same regulated quantity [q.bar] with a cost saving corresponding the previous cost difference.

However, the presence of an unregulated market generates two additional effects of the announcement. Rival firms observe the chosen regulated output [??] and they know that, because of scope economies (i.e., (2)), if [??] is large, their cost disadvantage with respect to the conglomerate is consequently large. Notably, this direct strategic effect is independent of the actual level of scope economies [theta]. We also have a beliefs-driven strategic effect which is the consequence of asymmetric information in market U and would not exist if rivals knew [theta]. Indeed, observing [??] the rivals are induced to believe a certain level of scope economies [??] and this affects again the perceived cost disadvantage with respect to the conglomerate, this time independently of [??]. Hence, these two strategic effects (direct and belief-driven) shape the incentives of the conglomerate to declare its type via the reaction of its rivals.

Anticipating all these effects, the regulator then determines the optimal regulatory policy [C.sup.*] maximizing the expected social welfare subject to the incentive compatibility constraints IC([theta]) as in Equation (13) and the participation constraints

[[PI].sup.I]([theta]) [greater than or equal to] [[pi].sup.S] [for all][theta] [member of] [THETA] IR([theta]).

Notwithstanding the strategic effects, for given q and v(q), the function [[DELTA].sub.[theta]][[PI].sub.U] is always positive, and this allows to show that participation of the efficient firm is always guaranteed, that the inefficient conglomerate obtains nothing more than its outside option, and that constraint IC([bar.[theta]]) binds at the optimum. (21) However, and notably, whether incentive compatibility for the inefficient firm (rewritten as in Equation (16) below) is relevant and affects optimal regulation, depends on properties of the regulated and unregulated market. This possibility affects optimal regulation, as explained in the next proposition.

Let the quantity [??]([theta]) be defined for any [theta] [member of] [THETA] by

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

with the indicator function I([theta]) = 1 if and only if the there are weak economies of scope, i.e., [theta] = [[theta].bar]. Let also the constant quantity [??] be

defined by

(15) p([??]) = [E.sub.[theta]] [SMC ([??],[theta]) + (1 - [alpha]) x v/1-v [partial derivative] [[DELTA].sub.[theta]][[PI].sub.U]([??], v)/[partial derivative]q].

We can state the following result.

PROPOSITION 1. 1. Optimal regulation is discriminatory, with quantity [q.sup.*] ([theta]) - [??]([theta]) for any [theta] if

(16)[[DELTA].sub.[theta]][[PI].sub.U]([??]([bar.[theta]),1) [greater than or equal to] [[DELTA].sub.[theta]][[PI].sub.U]([??]([[theta].bar]),0),

otherwise it is uniform with optimal regulated quantity [q.sup.*] ([theta]) = [??].

2. The profit of the conglomerate is

[[PI].sup.I]([[theta].bar]) = [[pi].sup.S]([bar.[theta]]) = [[pi].sup.S] + [[DELTA].sub.[theta]][[PI].sub.U] [[q.sup.*]([[theta].bar]), v ([q.sup.*]([[theta].bar]))].

To interpret the results in the Proposition assume for the moment that constraint (Equation (16)) is always satisfied, so that optimal quantities are discriminatory. Then, the regulator must guarantee the conglomerate with large scope economies (i.e., type [bar.[theta]]) an additional rent [[DELTA].sub.[theta]][[PI].sub.U] ([q.bar], v([q.bar])) which corresponds to the higher profit type [bar.[theta]] could obtain with respect to [[theta].bar] when asked to produce the same quantity q ([[theta].bar]) and rivals believe that scope economies are low. The (socially costly) rent of type [bar.[theta]] is an increasing function of the quantity designed for low scope economies (i.e., [partial derivative][[DELTA].sub.[theta]][[PI].sub.U] (q, 0)/[partial derivative]q [greater than or equal to] 0), so that the optimal q ([[theta].bar]]) is distorted downward relative to full information, and we (generically) have [q.sup.*] ([bar.[theta]]) > [q.sup.*] ([[theta].bar]) (which justifies the rivals' beliefs described above). If the conglomerate's incentives were solely driven by this cost efficiency effect, this monotonicity on regulated output would also guarantee that the low scope economies conglomerate (i.e., type [[theta].bar]) had no incentives to mimic type [bar.[theta]] since, otherwise, it would have to produce a large output [q.sup.*] ([bar.[theta]]) which is too costly given the low efficiency.

However, we know that incentives to announce the level of scope economies are here also affected by the two strategic effects which may either facilitate or hinder the regulatory process. Now, the role of the two strategic effects is best understood rewriting the incentive compatibility constraint for type [bar.[theta]] as follows,

(17) [[PI].sub.U]([bar.q],[bar.[theta]],1) - [[PI].sub.U]([q.bar],[bar.[theta]],0) [greater than or equal to] [[PI].sub.U]([bar.q],[[theta].bar],1) - [[PI].sub.U]([q.bar],[[theta].bar],0).

where [bar.q] = q ([bar.[theta]]) and [q.bar] = q ([[theta].bar]). This inequality corresponds in fact to Equation (16) in Proposition 1. (22) The left-hand side is the change of profits in market U for a type [bar.[theta]] conglomerate when regulated quantity is [bar.q] and rivals consequently believe scope economies are [bar.[theta]], as compared to profits with quantity [q.bar] and rivals believing [[theta].bar]. Similarly, the right-hand side is the same profit difference for a type [[theta].bar] conglomerate. (23)

With quantity competition in the unregulated market (i.e., strategic substitutability), a firm which appears to be more efficient induces its rivals to behave less aggressively, thus reducing their outputs and increasing its profits. If [bar.q] [greater than or equal to] [q.bar], then shifting regulated production from [bar.q] to [bar.q] induces a contraction of the rivals' outputs (for any given [theta] and associated beliefs) because of the direct strategic effect. Similarly, for the beliefs-strategic effect, declaring large scope economies induces the rivals to revise their beliefs and again contract their outputs. Both these changes account for an increase of profits [[PI].sub.U], so that both sides of Equation (17) become larger for the two strategic effects on the unregulated market. Furthermore, since higher scope economies amplify any change on profits [[PI].sub.U], the two effects make the left-hand side larger than the right-hand side, thus making the overall mimicking (potential) gain for type [[theta].bar] even less attractive. In other terms, incentive compatibility for the inefficient firm is less demanding than without the two strategic effects. A notable consequence, which will be explored in the next section, is that the regulated output may be incentive compatible even if standard monotonicity [bar.q] [greater than or equal to] [q.bar] is violated. (24)

If instead, the unregulated market is characterized by price competition (i.e., strategic complementarity), both the two strategic effects have adverse consequences on regulation. In fact, the conglomerate induces in this case an accommodating response of its rivals if it now shifts from production [bar.q] to [q.bar], so that the two strategic effects reduce both sides in Equation (17). As these changes are intensified by higher scope economies, the left-hand side decreases more than the right-hand side and the two effects make it more difficult to satisfy incentive compatibility for type [[theta].bar]. A consequence is that the incentive compatibility constraint IC ([[theta].bar]) may be violated even if regulated output is monotone. If this is the case, the regulator may be obliged to give up discriminating with respect to scope economies, thus resorting to uniform regulation, as indicated in the pricing condition (Equation (15)).

It now should also be clear that the two strategic effects increase the conglomerate's equilibrium profit with price competition and that, conversely, they reduce the rent when firms compete on quantities. In particular, noticing that the belief-related strategic effect would be absent if the rival firms were informed, we can state the following.

PROPOSITION 2. 1. With quantity-competition in the unregulated market, optimal regulation is discriminatory with quantities [q.sup.*] ([[theta].bar]) [less than or equal to] [q.sup.I.sub.FI] ([[theta].bar]), [q.sup.*] ([bar.[theta]]) = [q.sup.I.sub.FI] ([bar.[theta]]). The rivals' lack of information on scope economies reduces the conglomerate's profits.

2. With price-competition, optimal regulation may be either discriminatory with [q.sup.*] ([theta]) = [??] ([theta]) or uniform with a quantity [??], such that [q.sup.I.sub.FI], ([[theta].bar]) [??] [??] [less than or equal to] [q.sup.I.sub.FI] ([bar.[theta]]). The rivals' lack of information grants larger profits to the conglomerate.

The analysis in this (and the next) section shows that the nature of competition in the unregulated market plays an important role. Considering the several examples about diversification by conglomerate firms discussed in the Introduction, instances of either quantity or price competition are indeed relevant. For example, with regulated postal services jointly offered with financial or insurance products, we can conceivably see firms competing in the latter markets by setting prices. When instead firms operate in liberalized and deregulated segments of electricity or gas, whether strategic interaction is best described with price or quantity competition is debatable (depending also on the time horizon adopted in the analysis, as we know from) (this also explains the importance of the nonambiguous result of the next section on the desirability of integration, independently of the nature of competition).

The results in this section show that both regulation and competition are affected in a significant way by the activities of the conglomerate firm. In particular, the regulator may be obliged to give up with incentivizing regulation thus relying on uniform policies, and the competitors are also affected, as shown in the previous discussion. The possibility to run joint production may well put the regulator and the rivals in a more complicate environment, as it has been often claimed in real cases. The different effects at play and the reaction of the unregulated market will prove important also for the analysis in Section V in which we will investigate the desirability of integrated or separate productions. Before turning to this analysis it is instructive to present a simple model which allows to obtain some additional and interesting results. (25)

A. An Explicit Model

Let costs be described by Equation (4) and consider the following linear demands,

(18)

Market R : [p.sub.R] = [[mu].sub.R] - q, (with [[mu].sub.R] [greater than or equal to] c)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where m and [mu] are both larger than c, b [greater than or equal to] (n - 1) s [greater than or equal to] 0 and s and [gamma] are both positive and represent the substitutability parameter in the two environments. (26)

This model allows us to document some unexpected results. In the case of price competition, uniform regulation is more likely to take place the larger is the number n of competitors, the smaller are the degree of substitutability [gamma] and the maximum level of scope economies [bar.[theta]]. These results have intuitive explanations. The inefficient conglomerate with low scope economies will find it appealing to mimic the efficient one (so that pooling becomes optimal for the regulator) when the two types are not too different, since otherwise the standard cost-efficiency effect prevails thus making mimicking unprofitable. This is also the case when there are many competitors, so that the overall strategic effect is large and every rival firm will react less to the announcement that the conglomerate is efficient and, similarly, when the goods are poor substitutes, as when [gamma] is large, imitating the more efficient type would trigger a tough reaction by the competitors.

How does the intensity of competition affect the conglomerate firm's rent? Recall that market U is characterized by a suboptimal output level, which the regulator can affect by reducing the cost of the conglomerate in market U, thus making it more aggressive. This matters, first of all, as for the substitutability between the goods. When the products in the U market are closer substitutes, the regulator's decision on regulated output, by determining the conglomerate's marginal cost in the U market, has a stronger effect on unregulated prices. This is reflected into regulated quantities and consequently also [y.sub.1] and [p.sub.1] that increase in [gamma]. But then, as the conglomerate's rent is increasing in [q.bar], stronger substitutes may lead to larger rent. Therefore, independently of the type of competition, more substitutable products in market U (i.e., larger [gamma]) may also increase the informational rent.

As for the number of competitors, things differ depending on the type of competition. In general, notice that the larger is n the less distorted market U is, so that the regulator's interest in affecting the market is reduced. Hence, in this respect the regulated quantity should be increased to account for market power in U only to a lesser extent. With quantity competition, the two strategic effects induce the firm to produce more, and this effect is stronger the higher the number of competitors. Therefore, a more competitive unregulated market a fortiori induces a lower rent, which is the standard effect one would normally expect.

However, things are less straightforward with price competition, so much that the conglomerate's informational rent may be higher when the unregulated market is less concentrated. We know that with price competition and a more competitive market U, the two strategic effects are stronger and indeed the conglomerate's rent is increasing in n for given [q.bar]. When this second effect prevails (which requires that n is not too large and that the profit at stake in market U is large, i.e., that the demand intercept [mu] is large), then the overall effect of a larger n can be that the conglomerate's rent increases. Hence, unexpectedly if a regulated firm were to choose, it may well prefer to expand into a more competitive unregulated market.

V. THE DESIRABILITY OF HORIZONTAL INTEGRATION

We know that if the conglomerate is allowed to run integrated productions a problem of asymmetric information emerges both for the regulator and the rival firms in the unregulated market. In the previous section, we have illustrated that the conglomerate's incentives to report the actual level of scope economies are affected by the rivals' lack of information and inducing this firm to truthfully report may be more difficult, implying larger distortions on the regulated quantity.

Hence, the question is whether allowing the conglomerate to run integrated productions is desirable at all given that the asymmetric information affects both actual regulation and competition in the unregulated market.

Consider first price competition in the unregulated market. Because of strategic complementarity, if the rivals perceive that the conglomerate is more efficient they will react more aggressively. As a consequence, inducing the conglomerate to reveal the actual scope economies is more difficult, and regulation becomes less efficient. Hence a trade-off emerges: the greater technical efficiency which comes from integration indeed entails a larger distortion in the regulated price and a larger informational rent for the conglomerate. However, consider the contract [C.sup.S], which the regulator optimally designs for the case of separation. Applying this policy when the conglomerate instead integrates production raises a potential problem: with this contract, uninformed rivals would end up with no information on the magnitude of scope economies. However, with price competition (in general with strategic complementarity) the possibility that the regulated firm has lower costs makes rivals more aggressive even if they do not know exactly the magnitude of scope economies, thus inducing a larger welfare in the unregulated market. Hence, although regulation [C.sup.S] is suboptimal and leaves the rivals uninformed, with price competition it still allows to reach a larger welfare than with separate productions, thus making integrated productions even more desirable when an optimal regulatory contract is in place. (27)

Consider now quantity competition in the unregulated market. One cannot rely on the same line of reasoning as done above because with quantity competition leaving the rivals with no information may hurt the unregulated market. When the rivals do not know the value of [theta] and do not receive any information from the regulatory process (as it is the case when contract [C.sup.S] is the policy in place), they act as if the conglomerate had an "average" level of scope economies. In particular, when the real value of [theta] is [bar.[theta]], rivals underestimate scope economies and produce more than they would otherwise do. On the contrary, when they overestimate the level of scope economies, they reduce production and it may well happen that the contraction of total production of the n - 1 rivals exceeds the expansion of conglomerate's output. (28) Now, contract [C.sup.S] may then induce the following ranking for total output in the unregulated market Y ([q.sup.S], [bar.[theta]], v) [greater than or equal to] [Y.sup.S] [greater than or equal to] Y ([q.sup.S], [[theta].bar], v) and, since gross consumer surplus is a concave function of total output, the net effect of integration on (expected) consumer surplus in the unregulated market may be negative.

Nevertheless, we can obtain the following unambiguous result.

PROPOSITION 3. Irrespective of the type of competition in the unregulated market, letting the regulated firm integrate and run integrated production for regulated and unregulated markets is socially desirable, even if both the rival firms and the regulator do not know the value of scope economies.

The result for price competition has a simple proof as discussed above. As for quantity competition, we have seen instead that a clear trade-off emerges because leaving the unregulated market with no information negatively affects consumers in that market. To grasp the intuition of the proof consider the following reasoning. Consider a fictional environment in which the regulator is uninformed whilst the rivals are fully informed on [theta] and let us indicate the associated optimal policy with C'. Imagine now to employ regulation C' when rivals do not know [theta] as in our model. It follows that C', although suboptimal in this case, remains incentive compatible. To see this (the formal proof is in the Appendix), recall our discussion in Section IV showing that, when the rivals are uninformed and firms compete on quantities, the regulator will find it easier to elicit information by the conglomerate. In fact, the firm with large scope economies obtains a smaller profit and, at the same time, the inefficient firm finds it less convenient to mimic high scope economies when the rivals are uninformed. All this implies that even if regulation C' is designed for the case in which rivals are informed, with quantity competition in the unregulated market it remains incentive compatible also when applied to the case in which rivals are instead uninformed. Hence, although this policy C is potentially suboptimal in the latter case, it induces the conglomerate to declare exactly the actual level of scope economies. Hence, using this regulatory contract when rival firms are uninformed leads exactly to the same level of welfare as when they are instead informed. As a last step of the proof one then is left to show that in the informational environment in which the regulator does not know the level of scope economies but the rivals are fully informed on [theta], then integration is socially desirable. With this result (formally proved in the Appendix), we can conclude that by applying the contract C' in the environment of our model the regulator guarantees a surplus that, although not necessarily maximal, is still larger than that with separation.

Hence, despite the asymmetric information on the level of scope economies that integration brings about, and irrespective of strategic complementarity or substitutability in the unregulated market, integration is preferable to separation: the reaction of competition in the unregulated market can be ultimately turned to the benefits of consumers in the two markets and of overall welfare. (29,30)

VI. EXTENSIONS AND ROBUSTNESS CHECK

Our analysis is based on some specific assumptions which are not necessary to our results. In this section, we can show how we can generalize the model in different directions.

A. Cost of Public Funds

Raising funds from the taxpayer may be costly due to distortionary taxation. The regulation literature has contemplated this possibility introducing a shadow cost of public funds [lambda] such that each dollar transferred to/from the firm values 1 + [lambda] to society with [lambda], [member of] 0, 1]. (31) It has been shown that (see Armstrong and Sappington 2007) standard models of regulation with costly public funds are qualitatively equivalent to models in which the regulator weights firms' profit less than consumers' surplus (i.e., [alpha] < 1, as in the previous pages). However, it is here interesting to see whether the presence of the unregulated market has any additional role with this respect. With standard substitutions, the social welfare in case of integration becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

We have then two types of effects with respect to the model illustrated in the previous pages with [lambda] = 0. First, the informational rent [PI] now clearly costs more to the regulator since any dollar the regulator has to leave to the conglomerate in terms of rents has now the additional cost of the associated distortionary taxation. Whether regulation is discriminatory or uniform would not be affected, whilst the exact regulated quantity would be further distorted since the weight to the distortionary term (see the pricing rules Equations (14) and (15)) becomes 1 + [lambda] - [alpha]. The second line in the previous expression for W illustrates the second effect. Since a larger profit (net of transfer) to the regulated firm allows one to reduce T and thus distortionary taxation, the regulator has now a further incentive to favor the regulated firm against its competitors. In a standard model of regulation, the second line in W would simply induce a Ramsey pricing rule. In our environment, the optimal regulated price would be affected by this novel effect since the regulator would like to boost profitability of the conglomerate in market U thus increasing [[pi].sub.U] (see the definition, Equation (12)).

Although the proof of the desirability of integration in the previous section is not affected by the cost of public funds, this second effect clearly makes the payoff of integration even larger. (32) Therefore, our main conclusions about the desirability of integration would be strengthened.

B. Diseconomies of Scope

In our model, we have assumed that integration brings about an efficiency gain (namely, that [theta] > 0). However, in general we cannot exclude that integration may lead to diseconomies of scope if the two markets are not sufficiently close to allow the firm to exploit real synergies. This interesting possibility would be modeled in our environment by assuming that the "low type" [[theta].bar] is now associated with diseconomies of scope, i.e., [[theta].bar] < 0. It is simple to observe that the derivation of optimal regulation is unaffected by this possibility. Our reasoning about incentive compatibility would be unaffected (the high type still wants to mimic the low type, which in turn may be a fortiori induced to mimic the high type with price competition). Of course, we would have that the optimal regulated quantity for the low type would be now smaller than that with separation since by doing so the regulator can reduce the conglomerate's rent as usual and this would be also the case for the market power distortion in the unregulated market.

As for the desirability of integration of the conglomerate's activities, our previous result would be instead obviously affected. Indeed, one possible drawback of integration would be the risk of ending up with a conglomerate less efficient than with separate productions. However, for the same reasons illustrated in our previous discussion, the firm may still want to integrate since this gives the firm an informational advantage vis a vis the regulator. This simple observation may thus deliver a possible explanation of managers' desire to build their own inefficient "empires" which, prima facie, may be difficult to rationalize.

C. Endogenous Number of Competitors

Interestingly, our analysis could also be extended over a long-run horizon with free entry. Indeed, in this case the zero-profit condition (for rival firms) would make our arguments even simpler. Without going into analytic details, one may consider that with zero profits in the unregulated market what counts is really consumer surplus, so that allowing integration has a more straightforward impact on price and hence on welfare. In case production in the unregulated market entails a fixed cost, notice moreover that integration would also reduce the duplication effect noted by Vickers (1995) in a different set-up, where vertical integration is considered.

D. The Participation Constraint

We have assumed that the regulator must grant the conglomerate firm a total profit, which is not smaller than the one the firm can obtain in the unregulated market when deciding not to participate in the regulated market R, i.e., [[PI].sup.I]([theta]) [greater than or equal to] [[pi].sup.S]. In other terms, being also active in the regulated market cannot generate a loss to the conglomerate firm since the regulator cannot extract any of the profits that the conglomerate would have obtained by being active in the unregulated market alone. Hence, the conglomerate firm's participation constraint we have considered is standard but in the current framework has features, which are worth discussing.

If the regulated firm does integrate its activities with those in the unregulated market, two elements lead to increasing its profits (also) in this market. The first one is the cost reduction due to the economies of scope and naturally pertains to both activities since scope economies are, by definition, not attributable to a single one. The fact that the regulator is given the right to "tax" it away within the regulatory contract could be questioned, but also defended. A different apportionment of scope economies in which the conglomerate firm fully appropriates it is not defendable.

The second element is more subtle and pertains to the effect of expanding output in the unregulated market which is generated again by the efficiency increase of scope economies. From an "ex ante" perspective, the profit increase is uniquely due to integration and scope economies. However, "ex post" it may be accounted for as part of the profits attributable to the unregulated market where the conglomerate ultimately produces [y.sub.1] [((y([theta]), [theta], v(q([theta]))) and the rivals [Y.sub.-1]! (<y([theta]), v(q([theta]))). Now, one could consider the following profit in market U induced by those outputs (still excluding scope economies from costs):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Hence, the regulator could grant the conglomerate at least this profit, thus adding to the set of constraints of our regulatory program in Section IV also the following one, for any [theta]

[[PI].sup.I]([theta]) [greater than or equal to] [[PI].sup.I.sub.U](q([theta]), [theta], v(q([theta]))).

Now we can further develop our analysis in the previous pages with this additional constraint. With price competition, the expression [[PI].sup.I.sub.U] above is always smaller than [[pi].sup.S] which implies that the new constraint would be satisfied by the previous optimal regulatory contracts which then remains optimal. With quantity competition instead [[PI].sup.I.sub.U] [greater than or equal to] [[pi].sup.S]. We know that by increasing q the regulator expects that quantities in the unregulated market are increased thus limiting market power inefficiencies. However, with the new constraint she has to limit this expansion of q since otherwise [[PI].sup.I.sub.U], increases and a larger (total) profit [[PI].sup.I] has to be granted. In this case this constraint would introduce some additional technical difficulties in the derivation of optimal regulation ([[PI].sup.I.sub.U] is a type-dependent and endogenous outside option), but our result as for the desirability of integration remains unaffected.

E. Stochastic Regulation

In the previous pages, either the policy informs the rivals fully (discriminatory regulation) or it provides no information at all (uniform regulation). Differently, the regulator may try to "fine tune" information to the unregulated market. As the regulated price is naturally observable, a more sophisticated disclosure of information would require stochastic regulatory contracts that reveal information but only partially. (33) In view of the results in Calzolari and Pavan (2006) and of our results in Section IV, when competition in the unregulated market bears on quantities, full disclosure should be optimal, while with price competition less than full disclosure or even "no disclosure" may become optimal. Although the explicit derivation of these policies is technically challenging, it is important to notice that our results on the desirability of an integrated conglomerate would not be affected. Indeed, a more sophisticated regulatory policy that optimally controls for the information flow would actually make integrated production by the conglomerate even more beneficial.

VII. CONCLUDING REMARKS

We have analyzed optimal regulation of a conglomerate firm that serves both a regulated and an unregulated market. When the conglomerate is allowed integrate its production, economies of scope reduce costs, but the magnitude of these economies is known neither to the regulator nor to competitors in the unregulated market. Regulation would thus be distorted by asymmetric information and competition in the unregulated market may be also affected adversely. The regulator must therefore take into account how the unregulated market reacts to decisions in the regulated one, because this in turn affects the conglomerate's incentives in its regulated activity. A notable effect of regulation is an informational externality: the regulatory policy action conveys valuable information to the rival firms and its effects (on both markets) depend on the nature of competition in the unregulated market. Accordingly, we discussed optimal regulation and its distortions due to asymmetric information when competition in the unregulated market bears, alternatively, on quantities or on prices. We have shown that the nature of competition significantly affects regulation: with quantity competition this externality simplifies the task of the regulator, whereas price competition complicates it.

We then addressed the issue of desirability of integrated production in the conglomerate's activities, where a potential trade-off emerges. On one hand, allowing the conglomerate to integrate productions reduces its costs and, if this is at least partially passed on in the form of lower prices, then consumers may benefit (possibly in both markets). On the other hand, the conglomerate's private information may make the regulator's task more difficult, engendering distortions in regulatory policy and also making the unregulated market less competitive (with strategic substitutes). Notwithstanding this trade-off, we show that if uncertainty bears solely on the magnitude of scope economies then integrated production is socially desirable and if allowed to do so, the conglomerate will exploit this opportunity. (34) As usual, this result may inform policy recommendations only with caution since it just provides one piece of a complex picture in which previous analysis have emphasized the cons of diversification by regulated firms (see the discussion in the Introduction).

A few relevant extensions of the current framework can be conceived. So far, we have considered a situation, where the public authority deciding on integration and the one which sets the regulatory policy share the same objective function. In the European Union, while some structural decisions in sectors such as energy or transport are taken at European level, specific regulatory policies are decided by national regulatory authorities. In this case, it may well be that the regulated price dose not fully consider the surplus generated in the competitive sector.

This case has some similarities with our model, but it also entails a few differences. A sector regulator would in any case anticipate that the firm's incentives are affected by its activities in the unregulated market, so that the analysis of incentive compatibility, participation decisions and regulation (which we have carried out in Section IV) would be left qualitatively unaffected. However, a delegation problem would emerge, in that the sectoral regulator would have an objective function, which is not fully in line with the one of the regulator in charge of the structural decision. We leave this line of research to future work.

In the present study, there is a material difference between the conglomerate and its competitors active only in the unregulated market. An interesting extension would be to consider a more symmetric environment in which all firms are regulated in some sector (e.g., a domestic market) but also meet in a common (e.g., international) unregulated market. In this case, it could be reasonable to assume some correlation on scope economies, so that the informational externality would then be governed by the effects for information sharing among firms in common value environments.

Finally, in the present analysis we have considered simple pricing strategies in the unregulated market (when firms compete on prices). A multiproduct conglomerate, however, may also offer bundled discounts to its customers which are in fact another source of nonseparability in the conglomerate's profits such as scope economies. Relatedly, it is known that consumers in utility sectors exhibit relatively high switching costs. The complexity of (possibly nonlinear) bundled discounts may further increase these switching costs. Introducing the possibility of bundled discounts and its possible adverse effect on consumers and competitors in unregulated markets is another interesting line of research that we leave for future analysis.

APPENDIX

PROOF OF PROPOSITION 1

We can rely on the Revelation Principle in our environment in which regulation screens firm's type and at the same time signals it to the competitors. This possibility in mechanism design has been studied by the literature on sequential contracting with multiple principals which has shown under what conditions one can rely on the Revelation Principle and direct mechanisms when the same informed agent (the firm in our model) contracts first with an upstream principal (here the regulator) and subsequently interacts with downstream principals.

Calzolari and Pavan (2006, 2009) and Pavan and Calzolari (2009) show that the issues with direct mechanisms may occur for two reasons. First, when upstream allocations are observable (but not the upstream mechanism), direct mechanisms may fail to characterize all equilibrium outcomes (in particular those sustained by non-Markov strategies) since downstream players may be precluded to hold different out-of-equilibrium beliefs on the mechanism used upstream (by the regulator). However, this is not an issue in our environment since the regulatory mechanism is naturally observable. A second issue may emerge due to the observability of upstream mechanisms since payoff-irrelevant distinctions among mechanisms, that are not available with direct mechanisms, can be used as correlation devices for the principals' decisions. However, this is again not an issue here since we are considering pure strategy equilibria. Since y, is a moral hazard variable for the regulator, the appropriate reference for the application of direct mechanisms is here the Generalized Revelation Principle of Myerson (1982). In our simpler environment, the firm at the second stage does not contract with other principals but simply competes with its rivals in market U and the restriction to direct mechanisms is thus without loss of generality.

Finally, the Revelation Principle may be invalid if the announcement 9 had a direct effect on regulated firm's payoff. This is however not the case in our model since [??] only indirectly affects rivals' beliefs v ([??]) through the regulator's instruments (q ([??]), T ([??])).

Step 1. The regulatory program is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the objective is defined as in Equation (9) with the difference that outputs in market U also depend on beliefs v(q). (35)

The set of constraints IC([theta]) and IR([theta]) for any [theta][member of] [theta] can be rewritten as follows,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

For given quantity q and associated beliefs of the rival firms v(q), a more efficient firm obtains in market U a larger profit, so that [[DELTA].sub.[theta]] [[PI].sub.U] (q, v(q)) > 0 for any q > 0. Hence, constraints IC ([bar.[theta]]) and IR ([[theta].bar]) imply that IR ([bar.[theta]]) is slack and can be disregarded. This in turn means that constraint IR ([[theta].bar]) must be binding at the optimum. In fact, at least one of the two participation constraints has to be binding at the optimum, because, otherwise, the regulator could reduce both profits [[PI].sup.I], [[bar.[PI]].sup.I] by an equal amount, thus keeping incentive compatibility unaffected and increasing the objective function. Furthermore, constraint IC ([bar.[theta]]) must also be binding at the optimum.

In fact, reducing [[bar.[PI]].sup.I] the regulator is able to increase the objective function without negatively affecting IC ([[theta].bar]). Hence, she optimally reduces [[bar.[PI]].sup.I] as much as possible up to the point in which constraint IC ([bar.[theta]]) binds.

As for constraint IC ([bar.[theta]]), this can be written as

(A1) [[DELTA].sub.[theta]] [[PI].sub.U] ([bar.q], v ([bar.q])) [greater than or equal to] [DELTA].sub.[theta] [[PI].sub.U] ([q.bar], v ([q.bar])).

Note that if [bar.q] = [q.bar], then v ([bar.q]) = v ([q.bar]), so that [DELTA][theta][[PI].sub.U] ([bar.q], v) =

[[DELTA].sub.[theta]] [[PI].sub.U] ([q.bar], v) and constraint IC ([[theta].bar]) is trivially satisfied. The case with [bar.q][not equal to] [q.bar] will be treated in the next steps.

Step 2. Using step 1, we can now further rewrite program ([P.sup.I]) in the following equivalent way

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Hence, let [??] ([theta]) for [theta] [member of] [THETA] be solution of the following two first order conditions

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where v(q) = 0 for q = [??]([theta].bar]), v(q) = 1 for q = [??]([bar.[theta]) and generically we have [??]([bar.[theta]]) [not equal to] [??]([[theta].bar])

If [[DELTA].sub.[theta]] [[PI].sub.U] ([??]([bar.[theta]]), 1) [greater than or equal to] [[DELTA].sub.[theta]][[PI].sub.U] ([??]([[theta].bar]),0), then the optimal regulated quantities [q.sup.*]([theta]) are [q.sup.*] ([theta]) = [??]([theta]) for any [theta], because these quantities maximize the objective in (P') and satisfy the unique constraint IC ([[theta].bar]).

If instead [[DELTA].sub.[theta]] [[PI].sub.U] ([??] ([bar.[theta]]), 1) < [[DELTA].sub.[theta]] [[PI].sub.U] ([??] ([[theta].bar]), 0), quantities [??] ([bar.[theta]), [??] ([[theta].bar]) violate IC ([[theta].bar]), so that the optimal solution requires that IC ([[theta].bar]) binds. Thus, consider a pair of quantities q, [bar.q],[q.bar] such that [[DELTA].sub.[theta]] [[PI].sub.U] ([bar.q], v (bar.q])) = [[DELTA].sub.[theta]] [[PI].sub.U] ([q.bar], v ([q.bar])). This implies [bar.q] = [q.bar]. In fact, suppose on the contrary that [bar.q] [not equal to] [q.bar], so that v ([bar.q]) = 1, v ([q.bar]) = O and [[DELTA].sub.[theta]] [[PI].sub.U] ([bar.q], 1) = [[DELTA].sub.[theta]][[PI].sub.U] ([q.bar], 0) or equivalently [[PI].sub.U] ([bar.q], [bar.[theta]], 1) - [[PI].sub.U] ([bar.q], [[theta].bar], 1) = [[PI].sub.U] ([q.bar], [bar.[theta]], 0) - [[PI].sub.U] ([q.bar], [[theta].bar], 0).

This last equality is clearly genetically impossible unless [bar.q] = [q.bar], thus leading to a contradiction. Hence, when IC ([bar.[theta]]) binds optimal regulation requires pooling, so that quantities do not depend on [theta]. In this case, whatever its type [theta], the conglomerate firm is required to produce a quantity [??] independent of [theta]. This quantity can the be obtained by solving the following program,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where constraint 1C ([[theta].bar]) is omitted because, for what stated at the end of step 1, it is satisfied when [bar.q] = [q.bar] = [??].

Step 3. Given the optimal quantities [q.sup.*]([theta]) obtained in step 2, we then have that the profit of the conglomerate with low scope economies is [[PI].sup.I]([[theta].sub.bar]) = [[pi].sup.S] from IR ([[theta].sub.bar]) binding and for the efficient one is [[PI].sup.I]([bar.[theta]]) = [[pi].sup.S] + [[DELTA].sub.[theta]][[PI].sub.U] ([[q.bar].sup.*], v ([[q.bar].sup.*])) from IC ([bar.[theta]]) binding.

PROOF OF PROPOSITION 2

Step 1. We first derive the ranking on quantities [??] ([[theta].bar]), [??] ([bar.[theta]]) defined in the text of Proposition 1.

We show that the distortion [partial derivative][[DELTA].sub.[theta]][[PI].sub.U](q,v)/[partial derivative]q in the pricing conditions (Equations (14) and (15)) is positive independently of the type of strategic interaction in the unregulated market. To see this, for the generic strategic variable [x.sub.1] (price or quantity) of the conglomerate in market U consider the associated the first order condition,

[partial derivative]/[partial derivative][x.sub.1] [[PI].sup.I] ([??], [x.sub.1], [X.sub.-1]; [theta]) = 0.

This condition depends on [theta] through the marginal cost [partial derivative]C (q, [y.sub.1]; [theta])/[partial derivative][y.sub.1]. Now> the properties of the cost function (1)-(3) state that (1) this marginal cost is reduced by a larger q, due to scope economies and (2) this reduction is stronger the higher is [theta] (i.e., with large scope economies). Hence, for the implicit function theorem, it follows that the equilibrium profit [[PI].sub.U] (q, [theta], v) is increasing in q, in [theta] and that the profit increase caused by a larger q is larger the higher is [theta]. Hence, keeping constant the rivals' beliefs for (i.e., for a given v) we have

(A2) [partial derivative][[PI].sub.U] (q, [bar.[theta]], v)/[partial derivative]q [greater than or equal to] [partial derivative][[PI].sub.U] (q, [[theta].bar], v)/[partial derivative]q [greater than or equal to] > 0,

and then

(A3) [partial derivative][[DELTA].sub.[theta]] [[PI].sub.U] (q, v)/[partial derivative]q [greater than or equal to] 0.

With the sign of Equation (A3), we then obtain the ranking on optimal regulated output. In particular, if with full information scope economies induce a larger regulated out-put [q.bar].sup.I.sub.FI] [less than or equal to] [[bar.q].sup.I.sub.FI], then Equation (A3) implies [??] ([[theta].bar]) [less than or equal to] [??]([bar.[theta]) with strict inequality if [bar.[theta]] > [[theta].bar].

Step 2. Notwithstanding the monotonicity proved in the previous step. Proposition 1 illustrates that quantities [??] ([[theta].bar]), [??]([bar.[theta]]) may fail to be incentive compatible. Here we analyze when this is the case and we check whether these outputs satisfy constraint IC ([[theta].bar]). As illustrated in Ref (19), the incentive compatibility constraint for type [[theta].bar] is equivalent to

(A4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We now decompose this inequality into the three effects of cost announcement. To consider the simple cost-efficiency effect of announcement, let us fictitiously assume that outputs and [y.sub.1] do not depend on [theta] and q, in which case Equation (A4) would be

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

or equivalently

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

It is then immediate that properties of the cost function (1)-(3) imply that the previous inequality is satisfied by standard monotonicity, i.e., for [q.bar] [less than or equal to] [q.bar]. Hence, the cost-efficiency effect alone would imply that outputs ([??]([[theta].bar]), [??]([bar.[theta]])) are implementable.

We now add the direct strategic effect reintroducing the dependence of [y.sub.1] and y on [theta] and q, but keeping the rivals' beliefs unchanged. To this end lets assume that rivals are fully informed, so that even if regulated output is q ([??]) and real scope economies are associated to type [theta], rivals' beliefs are still such that Pr ([theta]|q ([??])) = 1. Constraint (Equation (A4)) would then be

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the notable difference with Equation (A4) is that rivals' beliefs on [theta] are always correct: independently of q then v(q) = 1 if type is [bar.[theta]] and v(q) = 0 if [[theta].bar] Now, from (1) to (3) we know that the marginal cost of [y.sub.1] is decreasing in q for any [theta], i.e., [[partial derivative].sup.2]C [q, [y.sub.1];[theta])/[partial derivative]q[partial derivative][y.sub.1] [less than or equal to] 0 and this marginal cost reduction associated with a larger q is larger the higher is [theta]. Hence, independently of the type of competition we have

These inequalities imply that for both the cost-efficiency and the direct strategic effects, constraint (Equation (A5)) is verified by the simple monotonicity condition for outputs [q.bar] [less than or equal to] [bar.q]

We are now left to study the belief-related strategic effect. Adding and subtracting [[PI].sub.U] ([bar.q], [theta].bar], 0) and % ([bar.q],[bar.[theta]],0) from Equation (A4), constraint 1C ([[theta].bar]) becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

or, equivalently

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The second line is negative whenever [q.bar] [less than or equal to] [bar.q] for the same reasons illustrated above on the direct strategic effect. On the contrary, the sign of the first line depends on the type of competition in market U. The function [[PI].sub.U] (q,[theta],1) - [[PI].sub.U] (q,[theta],0) uniquely refers to the effect of a change of rivals' beliefs for any q and [theta], that is for given marginal costs of y,. With quantity competition, or more generally with strategic substitutability, we clearly have [[PI].sub.U] (q,[theta],1) [greater than or equal to] [[PI].sub.U] (q,[theta],0), whilst [[PI].sub.U] (q,[theta],1) [less than or equal to] [[PI].sub.U] (q,[theta],0) with price competition or strategic complementarity. Furthermore, the absolute value [[PI].sub.U] (q,[theta],1) - [[PI].sub.U] (q,[theta],0) is increasing in [theta] because a smaller marginal cost of [y.sub.1] (induced by a larger [theta]) amplifies the change induced by different beliefs, so that we have

(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

From the signs in Equation (A7) and IC ([theta]) written as Equation (A6), we then obtain the following.

First, with strategic complementarity in market U the sign in Equation (A7) implies that monotonicity [q.bar] [less than or equal to] [bar.q] be not sufficient to satisfy IC ([theta]). When the (absolute value of the) first line in Equation (A6) is larger than the second line in the case [q.bar] = [??] ([[theta].bar]), [bar.q] = [??] ([bar.[theta]]), then quantities [??]([theta]) are not incentive compatible in which case optimal regulation is uniform and defined by Equation (15). As shown, quantity [??] is obtained from a pricing condition averaging with respect to type [bar.[theta]] and [[theta].bar], so that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] because two countervailing effects are at play. On the one hand, the distortionary term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in Equation (15) reduces [??]. On the other hand, the averaging with respect to [bar.theta]] and [[theta].bar] increases [??] as compared to [[bar.q].sup.1.sub.F1]. Furthermore, for the same reasons, we also have that [??] ([[theta].bar]) [less than or equal to] [??] [less than or equal to] [??] [less than or equal to] [??], so that [[DELTA].sub.[theta]][[PI].sub.U] ([??],v) [less than or equal to] [[DELTA].sub.[theta]][[PI].sub.U] ([??] ([[theta].bar]), 0) which implies that the conglomerate gains and that the regulator's task is complicated when the rivals are uninformed on the level of scope economies. Finally, if the first line in Equation (A6) is larger than the second line with [q.bar] = [??], ([[theta].bar]), = [??] ([bar.[theta]], then optimal regulation is discriminatory, [[q.bar].sup.*] = [??] ([[theta].bar]) [less than or equal to] [q.sup.I.sub.FI], [[q.bar].sup.*] = [??] ([bar.[theta]]) = [[bar.q].sup.I.sub.FI]. That the conglomerate gains from the rivals being uniformed can be seen in this case with discriminatory regulation by considering the firm's rent [[PI].sup.I] ([bar.[theta]]) = [[pi].sup.s] + [[DELTA].sub.[theta]], [[PI].sub.U] ([[q.bar].sup.*], 0) where [[DELTA].sub.[theta]], [[PI].sub.U] ([[q.bar].sup.*], 0) = [[PI].sub.U] ([[q.bar].sup.*], [[theta].bar], 0). For strategic complementarity, we have that [[PI].sub.U] [[theta].bar], 0) [greater than or equal to] [[PI].sub.U] ([q.bar], [bar.[theta]], 1) and also in this case the conglomerate benefits when the rivals are uninformed (the expression for [[DELTA].sub.[theta]] [[PI].sub.U] would be the smaller [[PI].sub.U] ([[q.bar].sup.*], [[theta].bar], 1) - ([[q.bar].sup.*], [[theta].bar], 0) were the rivals informed).

With strategic substitutability, the monotonicity [q.bar] [less than or equal to] [bar.q] implies that the incentive compatibility constraint (Equation (A4)) is satisfied from which it follows that optimal regulated quantities are q ([[theta].bar]), [??] ([bar.[theta]]) defined by Equation (14). This in turn gives the the comparison with quantities in the case of full information. Since the first line in Equation (A6) is negative the regulator's task is simplified by the rivals being uninformed. Furthermore, following the previous discussion, since for strategic complementarity [[PI].sub.U] ([q.bar], [bar.[theta]], 0) [less than or equal to] ([q.bar], [bar.[theta]], 1), the conglomerate gains a smaller rent [[PI].sup.I] ([bar.[theta]]) being the rivals uninformed. Finally, monotonicity [q.bar] [less than or equal to] [bar.q] is here sufficient but not necessary for incentive compatibility.

PROOF OF PROPOSITION 3

The proof is organized separating the study of quantity and price competition in market U, respectively strategic substitutability and complementarity.

Strategic complementarity (price-competition) in market U. Let [I.sup.*] be the information set in which neither the regulator nor the rivals know [theta], as in the model setup, and [C.sup.*] be the associated optimal regulatory contract illustrated in Proposition 1.

With information set [I.sup.*], contract [C.sup.s] satisfies all constraints IC([theta]) and IR([theta]) for any [theta] [member of] [THETA] because [C.sup.s] does not depend on [theta] and it is thus implementable. This allows to evaluate welfare with integration and information set [I.sup.*] when the regulator offers the contract [C.sup.s], i.e., [EW.sup.I] ([C.sup.S], [I.sup.*]). We can now compare this welfare with the that associated with separation [W.sup.S]. We now have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The difference between this expression for [EW.sup.I] ([C.sup.S], [I.sup.*]) - [W.sup.S] with the equivalent expression for [EW.sup.I] ([C.sup.S], I') - [W.sup.S] is that in the former rivals' beliefs correspond to their priors Pr ([theta] = [bar.[theta]] = v and Pr ([theta] = [[theta].bar]) = 1 - v and do not depend on q([theta]). In fact, in the information set [I.sup.*] they are not informed, contrary to I, and regulatory process associated with [C.sup.S] is totally uninformative.

However, with price competition facing an integrated conglomerate induces the rivals' to reduce their prices and this increases both consumers' surplus and total profits in the market U. Hence, both the first and the second line in [EW.sup.I] ([C.sup.S], [I.sup.*]) - [W.sup.S] are positive, so that we have

[EW.sup.I] ([C.sup.S], [I.sup.*]) [greater than or equal to] [W.sup.S].

Now note again that regulation [C.sup.S] is suboptimal with information set [I.sup.*], so that with the associated optimal regulation we have [EW.sup.I] ([C.sup.*], [I.sup.*]) [greater than or equal to] [EW.sup.I] ([C.sup.S], [I.sup.*]) which finally implies the result,

[EW.sup.I] ([C.sup.*], [I.sup.*]) [greater than or equal to] [EW.sup.I] ([C.sup.S], [I.sup.*]) [greater than or equal to] [W.sup.S].

Strategic substitutability (quantity-competition) in market U. We first prove that optimal regulation C' for information set I' is discriminatory and in particular we generically have [bar.q'] > [q'.bar]. Optimal regulation with information set Z can be obtained following the proofs of Propositions 1 and 2, keeping in mind that the unique difference consists in the rivals being fully informed. Exactly as in the with Equation (A3) we show that, generically, [partial derivative][[DELTA].sub.[theta]](q,v)/[partial derivative]q > 0, which immediately implies that the optimal regulation C' with information set I' is generically monotone [bar.q'] > [q'.bar].

Now we show that contract C' is incentive compatible and individual rational also with information Z*, i.e., it satisfies all constraints IC([theta]) and IR([theta]) for any [theta][member of][THETA]. This is again proved in step 2 of the proof of Proposition 2. In fact, the only difference between information sets [I.sup.*] and I is that in the former rivals are not informed, while they are informed in the latter. We know from the proof of Proposition 2 that with strategic substitutability the belief strategic effect due to the rivals' lack of information relaxes the compatibility constraint IC ([[theta].bar]), so that any pair of monotone outputs [bar.q] [less than or equal to] [q.bar] is incentive compatible (see Equation (A7) and related analysis).

This allows one to evaluate the welfare [EW.sup.I] (C', [I.sup.*]) that would prevail with information set [I.sup.*] if the regulator allowed the conglomerate to integrate its activities and offered the contract [C.sup.']. For what stated above, contract C' is discriminatory, so that it discloses perfect information on scope economies. Hence, the rivals' choices are the same in the two different information sets [I.sup.*] and I' so that [EW.sup.I] (C', [I.sup.*]) differs from [EW.sup.I] (C', [I.sup.']) uniquely as for the conglomerate's rent:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where for strategic substitutability we have [[PI].sub.U](q', [bar.[theta], 1) [greater than or equal to] [[PI].sub.U] ([q'.bar], [bar.[theta]], 0). It then follows

[EW.sup.I] (C', [I.sup.*]) [greater than or equal to] [EW.sup.I] (C', I').

As a final step, we now prove that

[EW.sup.I] (C', I') [greater than or equal to] [W.sup.S]

so that the two previous inequalities with the obvious

[EW.sup.I] ([C.sup.*], [I.sup.*]) [EW.sup.I] (C', [I.sup.*])

allow to finally have

[EW.sup.I] ([C.sup.*], [I.sup.*]) [greater than or equal to] [EW.sup.I] (C', [I.sup.*]) [greater than or equal to] [EW.sup.I] (C', I') [greater than or equal to] [W.sup.S].

Being independent of [theta], the regulatory contract [C.sup.S] is individually rational and incentive compatible when applied to integration with information set I', i.e., [C.sup.S] satisfies constraints IC([theta]) and IR([theta]) for any [theta] [member of] 0. This allows to evaluate the expected welfare with integration when the regulator offers the regulatory contract [C.sup.S] and rivals are fully informed, i.e., [EW.sup.I] ([C.sup.S], I'), and proceed with the following comparison:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where we have indicated with v([theta]) = 1 if [theta] = [bar.[theta]] and v([theta]) = 0 if [theta] = [[theta].bar] the rivals' degenerate beliefs. Both lines on the right-hand side are positive because the only difference between [EW.sup.I] [[C.sup.S], I') and [W.sup.S] is that in the former the conglomerate benefits of scope economies and is thus more efficient in market U. Thus, we have [EW.sup.I] ([[C.sup.S], [I.sup.']) [greater than or equal to] [W.sup.S]. Now, notice that regulation [C.sup.S] is suboptimal with information I', so that clearly [EW.sup.I] (C', I') [greater than or equal to] [EW.sup.I] ([C.sup.S], I') which proves the result that [EW.sup.I] (C', I') [greater than or equal to] [W.sup.S].

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GIACOMO CALZOLARI and CARLO SCARPA *

* We thank the co-editor Luke Froeb, two anonymous referees, Vincenzo Denicolo, David Martimort, John Panzar, Salvatore Piccolo, Wilfried Sand-Zantman, and Jean Tirole. We are also grateful to participants at several conferences and seminars. This article has been substantially revised while the first author was visiting Boston University in 2014 and substitutes a previous working paper "On regulation and competition: pros and cons of a diversified monopolist."

Calzolari: Department of Economics, University of Bologna and CEPR, Bologna 40126, Italy. Phone 0039-0512098489, Fax 0039-0512098493, E-mail [email protected]

Scarpa: Department of Economics and Management, University of Brescia, Brescia 25122, Italy. Phone 0039-0302988833, Fax 0039-0302988839/840, E-mail [email protected]

doi: 10.1111/ecin.12338

(1.) In the European Union, several Directives referring to utility services have stated that firms in regulated sectors that want to operate in competitive sectors as well must "unbundle," that is, separate the assets and the personnel of the two sectors. The unbundling may be of several types. The Directives require at least separate accounts and sometimes separate companies which may or may not belong to different shareholders.

(2.) According to the United Nations roughly 1 billion people in 50 countries have access to financial markets through their postal systems.

(3.) Alternative explanations also include multi-market strategies which may facilitate collusion. Or regulated activities may leave some free-cash flow that managers invest in unregulated sectors so they can then operate aggressively in those markets or just because they are "empire builders."

(4.) In a joint document issued by British sectorial utility regulators (OFWAT 1998), it is stated that for regulators, external auditors, as well as for rival firms, measuring scope economies is complex and often inconclusive, especially when conducted before integration takes place. Other interesting reports are those commissioned again by OFWAT in 2004 and the Cave 2009 Independent review of competition and innovation in water markets, commissioned by the UK government. For empirical analysis on scope economies in transport, gas, electricity, water, and other utility services, see Farsi et al. (2007), Farsi et al. (2008), Fraquelli et al. (2004), Piacenza and Vannoni (2004), Abbott and Cohen (2009), and Marques (2010). These works, although interesting and based on improving empirical methods and better data, do not allow to reach clear cut conclusions. Walter et al. (2009) and Saal et al. (2013) are meta-studies offering a very heterogeneous picture. Also event studies of abnormal stock returns of mergers in horizontally differentiated sectors are inconclusive as for scope economies (see Berry 2000 and Leggio and Lien 2000).

(5.) Our model can be also reinterpreted as one where consumers get higher utility from "one stop shop" (e.g., when joint billing lowers transaction costs): the cross-market effect goes through the utility function rather than economies of

(6.) It is well known from the literature on information sharing in oligopolies (see Sakai 1985 and Vives 1999, chapter 8, for a survey) that total welfare may be reduced when firms compete under asymmetric information.

(7.) With some delay, this literature was spurred by the intense debate against diversification of regulated firms during the 1980s, in the United States and other countries that culminated with the AT&T breakup.

(8.) In our analysis, the regulated service and unregulated service bear no vertical relationship, which is instead the case in Vickers (1995). In our study, the regulated firm's rivals do not need to purchase the regulated good, but still are affected by the cost saving that the integrated firm enjoys by operating both services.

(9.) Two main references for the literature on countervailing incentives in agency are Lewis and Sappington (1989b) and Maggi and Rodriguez-Clare (1995).

(10.) Economies of scope associated with fixed costs may well induce strategic effects in the unregulated market, as in our set up. In fact, with joint fixed costs F, proportional-to-outputs (i.e., q and [y.sub.1]) apportionment rules are often used in practical regulations so that, for example, apportionment attributed to product q would be F x q/(q + [y.sub.1]). This possibility is explored in Calzolari (2001). Chaaban (2004) studies the effects of various cost-apportionment rules for a joint fixed cost that is privately known by the multi-utility.

(11.) Costly public funds are discussed in Section VI. Different weights for profits of regulated and unregulated firms would not affect the analysis qualitatively.

(12.) For example, the U.S. railways companies receive federal funds (net of taxes paid) of the order of magnitude of several billions US$ per year (see http://www .bts.gov/publications/federal_subsidies_to_passenger_ transportation/). It similarly happens in Europe and for other sectors.

(13.) A sectoral regulator may evaluate the surplus in market U according to a weight 0 [less than or equal to] [beta] [less than or equal to] 1 and the associated profits with weight [[alpha].sub.r] (lower than [beta]). Although the main messages of the paper would be unaffected, we will discuss the consequence of this different assumption. Even if the sectoral regulator is given a narrower mandate (i.e. [beta] = [[alpha].sub.r] = 0), we expect that the decision to separate or not productions may be taken with a more general view also considering the unregulated market, as a competition authority would do. In the United States, for example, a non-sectoral agency such as the Security and Exchange Commission has often been given the power to approve or not diversification plans of utilities in the energy sector and also in telecommunications.

(14.) The restriction to two types clearly simplifies the analysis. With more (or a continuum of) types, optimal regulation may contemplate "bunching" for some subset of types, thus providing only partial information to the rival firms. However, also with just two types we will allow for regulatory contracts with or without bunching (respectively discriminatory or uniform regulation in the sequel). Hence, our analysis will consider regulation that can be informative for the rivals or not, thus covering all the relevant cases, in particular for the analysis on the desirability of integrated production (partially informative regulation could be dealt by simply mixing the arguments we actually use for those results).

(15.) In the sequel, we will nevertheless illustrate that even if one considers this possibility, no qualitative changes would emerge on our main results.

(16.) We assume that the usual conditions for an interior unique equilibrium in market U are met.

(17.) This departure from marginal cost pricing is typical in mixed oligopolies.

(18.) The regulator may be less concerned by the welfare in market U and, with the general setup illustrated in note 2, the social marginal cost would be [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. How ever, also in the extreme case in which the regulator is uniquely concerned by the welfare of the market R (i.e., [beta] = [[alpha].sub.r] = 0), still the integrated quantity would be larger than [q.sup.S], due to economies of scope.

(19.) In the Proof of Proposition 1, we explain why we can rely on the Revelation Principle in this dynamic environment where the regulatory contract both screens and signals.

(20.) Since in equilibrium all types [theta] will prefer to be active in market R, the decision to enter this market is uninformative. We assume that the conglomerate cannot credibly communicate [theta] to the rivals and since it chooses a contract in the given set C, one has only to define beliefs v over the elements in C. Finally, stochastic regulatory contracts are discussed in Section VII.

(21.) These results are proved in the Appendix showing that we can identify the binding constraints without the complications that emerge in problems without the single crossing condition (see Araujo and Moreira 2010).

(22.) Substituting [bar.[PI].sup.I] = [[PI].bar].sup.I] + [[delta].sub.[theta]][[PI].sub.U]]([q.bar], v([q.bar])) (since IC ([bar.[theta]]) binds at the optimum as shown in the Appendix) and [[pi].bar].sup.I] = [[pi].sup.S] (since IR ([[theta].bar]) also binds), constraint IC ([[theta].bar]) becomes [[pi].bar].sup.I] = [[pi].sup.S] [greater than or equal to] [[pi].sup.S] + [[DELTA].sub.[theta]][[PI].sub.U] ([bar.q], v ([bar.q])) which is equivalent to (17) and (16).

(23.) If only the cost-efficiency effect were at play, Equation (17) would reduce to C ([bar.q], [y.sub.1]; [bar.[theta]]) - C([bar.q], [y.sub.1]; [[theta].bar]) [greater than or equal to] C ([q.bar], [y.sub.1]; [bar.[theta]]) - C ([q.bar],[y.sub.1];[[theta].bar]]) which is satisfied by [bar.q] [greater than or equal to] [q.bar] for properties (2)-(3) of the cost function.

(24.) Absent the strategic effects, having the conglomerate with higher economies of scope produce more than the low scope economies one would be necessary for incentive compatibility.

(25.) All the results in this section would be clearly unaffected by the possibility that the regulator weights the welfare in the two markets differently, as in the model described in notes 2 and 3.

(26.) These systems of demand for market U are derived from utility [V.sub.U][[y.sub.1], y] = [mu] ([y.sub.1] + (n - 1)y) - 1/2 ([y.sup.2.sub.1] + (n - 1)[y.sup.2]) - [gamma](n - 1)[y.sub.1]y + (n - 1)(n - 2)[y.sup.2]] and in the case of price-competition m = [mu]/[gamma](n-1)+1, b = [gamma](n-2)+1/(1-[gamma])([gamma](n-1)+1), s = [gamma]/(1-[gamma]]([gamma](n-1)+1. The expressions and results discussed in this subsection are explicitely derived in the online Appendix available at http://www2.dse .unibo.it/calzolari/web/papers.html.

(27.) In the next section, we illustrate how this reasoning is affected when diseconomies of scope are possible.

(28.) In the explicit model of Section IV. A, this is the case when [Y.sup.S] - Y ([q.sup.S], [[theta].bar], v) = (n - 1) v[bar.q][bar.[theta]] - [q.bar]][[theta].bar][2 + v(n - 1)] is positive, for example, when [theta] is sufficiently low. Furthermore, this uncertainty over [theta] may even induce some rivals to exit the market, although this is not explicitly considered in the model.

(29.) As discussed in Section II, it is impractical to first let the firm integrate and then split it apart. Furthermore, although one might conceive a contract, where the decision to integrate is taken by the Government, conditional on the observed level of scope economies, even in that (probably implausible) situation our result that separation is dominated by allowing integration would anyway hold with similar arguments. The general principle of unbundling, often considered by regulatory authorities, is thus a dominated policy.

(30.) We have derived the results in this section with the more demanding environment in which the regulator equally cares for the welfare in the two markets. If instead he would be only concerned by the regulated market, letting the conglomerated operate under integrated production would be obviously optimal because any possible adverse effect of this decision would disappear.

(31.) This may be the consequence of inefficiencies in the use of public funds, distortionary taxation, or alternative use of the funds for public goods.

(32.) In our model information disclosure to the rivals would not be affected since whether regulation is discriminatory or uniform does not depend on X.

(33.) Interestingly, the optimality of stochastic regulatory contracts may emerge in a context in which, absent the informative role of the regulatory policy, the optimal contract would be deterministic, as in standard models of regulation with asymmetric information.

(34.) Other potential benefits of integrated production relate to the demand side. For example, customers would clearly find it advantageous having only one provider for both services (joint billing, lower transaction costs summarized in the expression "one stop shop"). Our model can be actually reinterpreted as one where consumers get higher utility from single bill: the cross-market effect may go through the utility function rather than the economies of scope that we have considered.

(35.) With the usual change of variables, maximization in program ([P.sup.I]) is equivalently taken over the contract [{(q([theta]), [PI].sup.I] ([theta]))}.sub.[theta][member of] [THETA]] instead of [{(q([theta]),T([theta]))}.sub.[theta][member of] [THETA]] In both cases, we will indicate the contract with C.