Review of Industrial Organization 18: 175182, 2001. 2001 Kluwer Academic Publishers. Printed in the Netherlands. 175
Regulation and Cost Inefficiency
VAN KOLPINUniversity of Oregon, Department of Economics, College of Arts and Sciences, Eugene OR 974031285, U.S.A.
Abstract. The well known Averch Johnson effect states that rate-of-return regulation will inducecost inefficient production. This paper examines regulation induced inefficiency in broad set ofenvironments including arbitrary regulatory mechanisms, multiple outputs/inputs, uncertainty, timedynamics, price discrimination, and more. I show that the Averch Johnson effect applies throughouta wide variety of settings. Despite the generality of framework, my analysis is truly elementary anddoes not rely on KuhnTucker analysis or three dimensional graphics. I also provide results anddiscussion which clarifies the limits to Averch and Johnson-like insights in practical applications.
Key words: Inefficiency, regulation.
One of the best known results in regulatory economics was first presented byAverch and Johnson (1962). Their simple model of a regulated monopolist demon-strated that rate-of-return regulation induces cost inefficient production, a resultcommonly known as the Averch Johnson (AJ) effect. (See Baumol and Klevorick,1970; Sherman, 1985; and Train, 1991 for surveys of the literature.) This paperreexamines this result in the context of a much broader set of environments thanthat conceived in the traditional literature including nonlinear regulatory mechan-isms, uncertainty, time dynamics, multiple outputs/inputs, price discrimination, andmore. Despite this added generality, my proofs are truly elementary and highlightthe essence of the AJ effect without the use of KuhnTucker analysis or geometricgymnastics.
My work offers fresh insights in several dimensions. The first lesson is a ped-agogical one. The AJ effect is traditionally established either by solving a formalconstrained optimization problem with KuhnTucker methods (as in Averch andJohnsons seminal paper), or through the use of three dimensional geometric argu-ments (as in Zajac, 1970; and Bailey, 1973). I argue that the driving force of theresult is both more transparent and more general if one instead clearly identifiesthe two fundamental assumptions that are imposed. In particular, capital must bereplaceable with labor local to the regulated optimum and, secondly, the regulatedoptimum is not itself an unconstrained local optimum. By bringing these twopivotal assumptions to the forefront, proof of the AJ effect becomes transparent
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even to first time students of the material. (This is particularly noteworthy giventhat the AJ effect is standard material in popular undergraduate IO texts, such asCarlton and Perloff, 1999; and Viscusi et al., 1996.)
My results break new ground by dramatically expanding the realm of envir-onments in which the AJ effect is known to apply. Of equal importance, I alsoexamine the opposite perspective and provide a detailed analysis of when the AJeffect does not apply. I construct a general theorem characterizing all regulat-ory mechanisms immune to the effect as well as present a series of exampleshighlighting limits to the AJ effect in practical applications.
Another contribution of my analysis is less direct and relates to the new reg-ulatory economics promoted in such works as Laffont and Tirole (1993). Thisapproach stresses the importance of modelling the regulators objectives as well asthose of the regulated firm. A principal agent model emerges in which the regu-latory agent sets policy fully cognizant of the fact that the regulated firm will seekto optimize its own objective, subject to the regulatory constraints imposed. A dy-namic model such as this raises the possibility that a clever regulatory agent, armedwith a powerful arsenal of regulatory controls, might be capable of side-steppingthe AJ effect while still imposing limits on the return a monopoly can receive oncapital investment. To the contrary, I find that every less than comprehensive returnregulation, regardless of complexity, will induce cost inefficient production. If suchcost inefficiency is incompatible with the regulatory agents objectives, one canonly conclude that the agent must either micro-manage all inputs or abandon returnregulatory mechanisms altogether. This paper proceeds as follows. In Section II, Iexamine the classical Averch and Johnson framework. This analysis serves both tocontrast my approach with traditional presentations as well as motivate subsequentgeneralization. Section III presents my general model, assumptions, and results. Ishow that the AJ effect persists throughout all return regulatory environments. Ialso characterize all general regulatory mechanisms that do not suffer from the AJeffect. Section IV presents a series of examples showcasing limits to the Averchand Johnson result. Brief concluding remarks are offered in Section V.
II. The Classical Model
The classical Averch and Johnson model considers a monopoly employing labor(L) and capital (K) to produce a single homogeneous output (q) via a differentiableproduction technology f , i.e., L;K 0 and 0 q f .L;K/. Labor and capitalare purchased at strictly positive unit prices w and r respectively. A strictly positiveoutput price is determined by a differentiable inverse demand function P.q/ andprofit is characterized by .L;K; q/ D P.q/q .wL C rK/. I shall say that aproduction plan .L;K; q/ is fully employed if f .L;K/ D q and let 5.L;K/ D.L;K; f .L;K// denote the full employment profit function.
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LEMMA 1. A production plan is cost efficient if and only if it is fully employedand there is no other equally productive and fully employed production plan thatis more profitable.
This result is virtually a tautology. Cost efficiency must require inputs to be fullyemployed, else the original output would be feasible with a sufficiently small re-duction in input purchases. The fact that revenue depends only on output quantityin turn implies that the cheapest way to produce a given output level is also themost profitable and vice versa.
The AJ effect considers the implications of rate-of-return regulation. Such regu-lation constrains the profit the firm is allowed to earn from its capital. Letting > 0represent a given regulated rate of return, regulated profit effectively becomes.L;K; q/ D minf.L;K; q/; Kg:LEMMA 2. If (L,K, q) maximizes rate-of-return constrained profits, then giventhe capital level K, the labor employment level L also maximizes unconstrainedprofits.
This result also follows immediately. Indeed, if labor employment could be unilat-erally modified to increase unconstrained profit then a sufficiently small increasein capital would at most partially offset this gain while simultaneously relaxingthe profit constraint. As regulated profit would increase, the starting point couldnot have been an optimal response to regulation as assumed. (The fact that rate-of-return regulation will not dissuade the monopolist from employing labor in anunconstrained profit maximizing fashion is highlighted in Sherman, 1972.)
I now piece these two elementary lemmas together. Suppose a rate-of-returnregulation locally binds at the regulated optimum (in the sense that first orderconditions of an unconstrained optimum fail) and that positive levels of both inputsare employed. Lemma 2 implies that at the regulated optimum, the full employmentisoprofit curve has slope zero (as d5=dL D 0 and d5=dK 6D 0). But marginalproduct of labor must be nonzero (else d5=dLwould be strictly negative) implyingthe isoquant at the regulated optimum must have nonzero slope. It follows thatequally productive but more profitable production plans must exist and thus Lemma1 confirms cost inefficiency. As capital increases relax profit constraints, one mayalso conclude that too much (rather than too little) capital is employed.
PROPOSITION 1 (Averch and Johnson, 1962). Optimal responses to rate-of-return regulation use more capital than is cost effective whenever regulation islocally binding and both inputs are employed.
Recapping my proof in plain English: the traditional assumption that the regulatoryconstraint is locally binding and both inputs are employed directly implies that thecorresponding isoprofit has zero slope at the regulated optimum. As the corres-
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ponding isoquant cannot be zero sloped, there must be more profitable methods ofproducing the same output and cost efficiency must fail. (Note that I do not assumea positive marginal product for capital. See Sherman, 1985 for a discussion of thisissues significance, as well as a survey of relevant literature.)
III. A Generalized Model
The classical Averch and Johnson model has been criticized for its lack of dynamicstructure and narrow view of regulatory controls. I now introduce a general modelof monopoly regulation which allows for multiple inputs, outputs, and produc-tion periods, uncertainty, arbitrary regulation schemes, etc. This exercise providesseveral useful lessons. In particular, I show that the classical AJ-effect retains itscentral spirit in a very general framework and I characterize the class of all arbitraryregulatory controls that do not suffer from this effect.
The basic components of my general model include X the space of all inputprofiles, Q the space of all output profiles, f : X! Q the production function,R: Q!RC the revenue function, C: X!RC the cost function (defined overinputs), : XQ!RC the unregulated profit function defined by the differencebetween revenue and cost .x; q/ D R.q/ C.x/, and lastly, : X Q! RC the regulated profit function whose form is determined by the underlying marketdemand/costs and a given set of regulatory rules . A more detailed description ofthese components, along with expository examples follows below.
The input space of the classical model is assumed to be just two dimensional,while my general model imposes no fixed limits on the dimensionality of X. Thisallows for multiple physical inputs as well as stochastic and dynamic features.To be more precise, uncertainty is modelled by introducing state contingent inputconsumption. As a simple example, imagine a world in which demand is determ-ined by a stochastic variable which may either be high or low. If the state ofdemand is observed in advance, input consumption can be made state-contingent,effectively doubling the number of input variables the firm must choose. Inherentlydynamic situations can likewise be modelled by introducing time contingent inputemployment. As the dimension of X is arbitrary, such scenarios fit readily into thisgeneral framework.
The richness of the output space Q is analogous to that of the input space X as ittoo may be multi-dimensional and allows for the production of multiple outputs inmultiple states at multiple times. The monopolys production function is assumedto be a differentiable mapping f : X! Q.
The only requirements of revenues and costs are that both are differentiable andcosts are strictly increasing in X. This generality allows for multiple inputs andoutputs as well as market power in their purchase and sale. Firm profits (uncon-strained by regulation) are denoted by .x; q/ D R.q/ C.x/ for each feasibleproduction plan .x; q/.
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It is important to note that unlike the classical model, the cheapest way to pro-duce a particular output profile need not necessarily result in the full employmentof inputs. Indeed, if one commodity is produced as a byproduct of another, someoutput profiles may not be feasible unless excess quantities of the byproduct areproduced and then discarded. While this is surely a theoretical possibility, I shallassume that there is at least some nominal input usage affiliated with producingand bringing each product to market. (Thus I make a distinction between simplegeneration of a byproduct and the manufacture of this product into a saleable good.)I refer to this as the byproduct assumption and with it Lemma 1 can be extended tomy general model. (Details are presented in an earlier version of this paper whichis available upon request.)
The precise manner in which regulated profit differs from the unconstrainedprofit function depends on the nature of regulation imposed. Examples mayinclude profit constraints, price constraints, taxes, subsidies, or virtually any otherregulatory mechanism. I shall say that is a return regulation if it represents anallowed return which is a strictly increasing continuous function of some subset Kof input variables (capital). The regulation constrained profit function is in thiscase defined by .x; q/ D minf.x; q/; .xK/g; where xK denotes the vector ofcapital goods purchased and .xK/ the corresponding maximal allowed return.Note that need not represent a rate of return as in the classical model, but isinstead an aggregate level of return which need not be linear. (This generality isparticularly germane given that capital may in practice often be a composite ofplant, equipment, etc.) The classical fixed rate-of-return scenario of course remainsand is characterized by the special cases for which is linear.
Optimal response to return regulation requires employment of labor inputs(those outside K) in an unconstrained profit maximizing fashion. This result fol-lows analogously to the classical case and thus Lemma 2 also extends to mygeneralized setting. Fundamental to any investigation of AJ-like effects is a de-gree of replaceability amongst inputs. Given an input profile x, I shall say thatcapital inputs are locally replaceable at x if the marginal impact they have onproduction can be replicated by some marginal change in labor inputs. Note thatif multiple outputs are produced, incremental changes in one input may inducechanges in more than one output and replicating this effect may be nontrivial.While replaceability may be essential for a discussion on AJ-like effects, itis not a vacuous requirement. As in the classical setting, Lemmas 1 and 2 canbe used to confirm the presence of an AJ-effect in my general framework. If areturn regulation locally binds at the regulated optimum (in the sense that firstorder conditions of an unconstrained optimum fail) and capital inputs are locallyreplaceable, Lemma 2 can be used to show that the full employment isoprofit andthe isoquant corresponding to the regulated optimum cannot be tangent. Lemma 1then immediately implies that cost inefficiency must prevail. (Details are presentedin an earlier version of this paper and are available upon request.)
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PROPOSITION 2. Optimal responses to return regulation are cost inefficientwhenever regulation is locally binding and regulated inputs are locally replace-able.
The question naturally arises as to which regulatory mechanisms do not sufferfrom an AJ effect. I shall say that is demand based if t...