Regulated Competition under Increasing Returns to Scale

• Published date: 01 June 2016
• Date: 01 June 2016
• DOI: http://doi.org/10.1111/jpet.12172

REGULATED COMPETITION UNDER INCREASING RETURNS

TO SCALE

THOMAS GREVE

University of Cambridge

HANS KEIDING

University of Copenhagen

Abstract

In the classical models of regulation economics, a mechanism that se-

cures truthful revelation involves paying a subsidy to the firm. In this

paper, we investigate whether it is possible to create a regulatory mech-

anism under a no-subsidy constraint that induces the firm to report its

private information truthfully. We consider a number of firms operat-

ing under regulated competition and with increasing returns to scale

technology. It is shown that in equilibrium each firm chooses to report

truthfully without receiving any subsidy. The use of competition may

give rise to an efficiency loss due to the increasing returns to scale.

However, we show that our mechanism may still be better, from a so-

cial welfare point of view, than the case of monopoly regulation that

involves no subsidy.

1. Introduction

The interest in regulation of markets characterized by either monopoly or oligopoly

has a long history (see, e.g., the survey by Armstrong and Sappington 2007), and the

privatization of industries formerly owned and managed by governments, mainly in the

field of public utilities, has promoted an increased concern about regulation, often in

a context of market failures in the form of increasing returns to scale or asymmetric

information.

In this paper we consider such a case, where there are increasing returns to scale in

production. In the context of public utilities, this may occur for companies providing

services to the consumer (such as electricity or natural gas) which they either produce

themselves or acquire in a market where large buyers obtain considerable rebates. As is

well known, optimal allocation in a market with increasing returns to scale occurs at a

level of output where price equals marginal cost, so that pricing according to marginal

cost (see, e.g., Joskow 1976) can be sustained only if the producers are paid a subsidy.

Thomas Greve, University of Cambridge, Cambridge, CB3 9DD, U.K. (tg336@cam.ac.uk). Hans Kei-

ding, Department of Economics, University of Copenhagen, Oster Farimagsgade 5, DK-1353 Copen-

hagen K, Denmark (hans.keiding@econ.ku.dk).

Received September 30, 2013; Accepted September 15, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (3), 2016, pp. 327–345.

327

328 Journal of Public Economic Theory

Throughout this paper, we assume that subsidization of producers is not possible,

so that the welfare optimum cannot be achieved. We shall not discuss reasons for or

justification of this assumption, which is taken as given here as in many other contexts,

such as, e.g., the theory of Ramsey pricing (cf. Hagen and Sheshinski 1986). Even so,

regulation serves the purpose of achieving an allocation which is welfare-superior to

monopoly or to an oligopolistic equilibrium for the case with more than one firm.

In particular, we shall compare regulation of a single firm, a monopoly, with a reg-

ulated competition between two firms, under the conditions of increasing returns to

scale and no subsidization. This comparison is not altogether trivial, since on the one

hand, the increasing returns to scale tend to favor production in a single plant, but on

the other hand the competition between two firms may lead to lower prices and larger

output.

As mentioned above, we shall assume that there is asymmetric information about

production cost which is private information for the firm in the case of monopoly and

for each firm if there are several firms. Thus the regulator must try to overcome the

informational advantage of the firm (or firms). In the case of a single firm, this takes

us to the theory of regulated monopoly, now under conditions of increasing returns

to scale.

There is a considerable literature on regulation of monopolies under asymmetric

information. In Loeb and Magat (1979), subsidies are used as incentives to surpass

the information asymmetry. Baron and Myerson (1982) present a mechanism that

induces the regulated monopoly to report its cost truthfully. We shall use the ideas of

Baron and Myerson in our treatment of regulated monopoly, but because subsidization

is not allowed the regulation which emerges cannot implement a welfare optimum,

and truthful revelation is obtained by allowing the firm a profit which is no less than

what could be achieved by misinformation of the regulator. The loss of welfare due to

smaller output and to the deliberate closing down of production when cost is too high

may be considerable.

As an alternative to the regulated monopoly, we then consider a case with two firms

both engaged in production, a regulated duopoly. Since we have increasing returns to

scale, a marginal cost equilibrium, where price equals marginal cost in each of the two

firms, would entail negative profits in both firms, and negative profits in at least one firm

if the regulator is free to redistribute profits between firms; thus, we cannot achieve a

welfare optimum in a regulated duopoly.1Accepting this, the regulation must come

as close to the welfare maximum as possible without subsidies, meaning that market

revenue should equal total cost of production, possibly with an acceptable profit mar-

gin. We consider one such regulation, where the firms are receiving regulated incomes

which allow for transfers of market profits from one firm to another but no overall sub-

sidization. However, the regulation depends on the level of cost of the two firms, which

is private information, and it is assumed that firms send messages about their true cost.

Having received the messages, the regulator proceeds according to the largest of the two

messages, but using regulated incomes which favor the firm with the smallest message.

It is shown that truthful revelation is an equilibrium; however, the firm with the lowest

cost can maintain an informational rent because the regulator acts as if both firms have

the higher cost.

1The result of Gradstein (1995) about the possibility of achieving a welfare optimum in regulated

oligopoly does not apply when there are increasing returns to scale, since it uses only the first-order

conditions for profit maximization, not taking into account the nonnegativity condition.