A graphical exposition of the economic theory of regulation.

Beard, T. Randolph ; Kaserman, David L. ; Mayo, John W. 等

I. INTRODUCTION

Historically, many if not most economic theories have advanced in three fairly distinct stages, progressing from descriptive to graphical to mathematical formulations, generally in that sequence. The economic theory of regulation, however, has been an exception to this normal order of progression. The fundamental corpus of this theory was laid out initially in the descriptive discussions provided by Stigler (1971), Posner (1974), and others. From these early presentations, however, the theory was subsequently formalized mathematically by Peltzman (1976) and Becker (1983) without passing through the graphical stage of its development. (1)

Regardless of the chronological order of the progression of this theory, however, we believe that a fully developed graphical exposition is likely to be of considerable value even now. At least two considerations support this view. Specifically, by making this theory more accessible to a wider audience and by better illustrating the basic underlying mechanics behind it, the likelihood of significant future advancement, we believe, is enhanced. Indeed, currently there remain a number of observed regulatory phenomena that have yet to be satisfactorily explained by the existing theory (e.g., the deregulation movement and the specific pattern of observed cross-subsidies). (2) An improved understanding of the fundamental components of the theory should facilitate its further advancement and lead to an expanded ability to explain a broader range of regulatory practices. We illustrate this point through a variety of applications to provide an improved understanding of, inter alia, the markets likely to be chosen for regulation, the propensity of regulatory benefits to be spread across interest groups, the symbiotic nature of regulation and cross-subsidization, and the economics of deregulation. We also are able to depict graphically the relationship between the economic theory of regulation and the traditional normative model of regulation, which assumes that regulators maximize social welfare.

The article is organized as follows. In section II, we briefly describe the regulator's general optimization problem--viz., what precisely is being maximized and what constraints apply to that maximization problem. The latter topic--the constraints--will be of primary interest here. Section III presents the formal graphical analysis of these constraints by deriving what we label the regulator's "benefits budget constraint." As its name suggests, the benefits budget constraint defines the locus of maximum benefits the regulator is able to deliver to the affected interest groups. Importantly, that constraint is determined by the prior, unregulated market equilibrium price and output and by general market parameters, such as demand elasticity, costs, and so on. Section IV describes the resulting regulatory equilibrium. Section V, then, applies the graphical tools developed in sections II-IV to explain a number of commonly observed regulatory phenomena. Here, both the ability to provide new insights and the pedagogical value of the graphical approach are illustrated. Finally, section VI concludes.

II. THE REGULATOR'S GENERAL OPTIMIZATION PROBLEM

The economic theory of regulation postulates that regulators will attempt to maximize some objective function (most generally, the regulator's utility) by implementing regulatory policies that benefit (and, by necessity, harm) particular interest groups. (3) The benefits provided to these groups are then used to "purchase" from them the objects that are directly valued by the regulator--that is, the direct arguments contained in the regulator's objective function. The distribution of these benefits and harms across the affected groups (which is determined by the regulator's choice of a particular regulatory policy) is selected to maximize the value of the regulator's objective function.

The ability of any specific interest group to curry regulatory favor, then, will depend on the capacity of that group to deliver the objects of value to the regulator in exchange for the benefits provided by the regulatory process. That is, each interest group has a "production function" that transforms benefits received by that group into the objects directly valued by the regulator. The literature in this area has identified at least three likely sources of utility for regulators--votes, income, and ideological rewards--that may be provided by regulated parties. The affected groups--for example, consumers, producers, and/or subsets of each--reward (or punish) regulators when the latter use their legal coercive powers to create benefits (or losses) for the former. They reward them by "producing" the objects that regulators value--that is, the direct arguments of the regulator's utility function.

Although regulators may not care directly about the welfare of either producers or consumers, the benefits and costs imposed on sellers and buyers by regulation constitute the bases of regulator rewards. Thus, although regulators may care only about their own incomes, campaign contributions, or personal ideological goals, whenever these direct sources of utility continuously depend on the benefits received by producers and consumers, then we can write the regulator's utility as a continuous function of the underlying benefits.

Assume two interest groups that receive regulatory benefits of [B.sub.i], i = 1, 2. Generally, we expect either [B.sub.1] > 0 aud [B.sub.2] < 0 or [B.sub.1] < 0 and [B.sub.2] > 0 will hold. (4) That is, with only two interest groups, we expect that one group will gain from regulation and the other group will lose. (5) This expectation is particularly likely to hold where, as we will assume, the regulator's only control instrument is the market price. As a result, the graphical analysis that applies will tend to focus on the second and fourth quadrants of the [B.sub.1], [B.sub.2] space.

Given these benefits from regulation, then, the two affected interest groups will undertake actions that either reward or punish regulators by influencing the values of the arguments that enter the regulator's utility function. Following the prior literature, let these arguments be votes, V, income, Y, and ideological values, I. The regulator's utility function, then, is given by

(1) U = U[V([B.sub.1], [B.sub.2]), Y([B.sub.1], [B.sub.2]), I([B.sub.1], [B.sub.2])] = U([B.sub.1], [B.sub.2]),

where V(*), Y(*), and I(*) represent the production functions through which regulatory benefits (inputs) are converted into utility-generating outputs. (6) Given this formulation, then, regulator utility depends on (1) the values that regulators place on V, Y, and I; (2) the ability of affected interest groups to "produce" these utility-yielding outcomes; and, ultimately, (3) the benefits delivered to the affected groups.

If we assume a declining marginal product in each interest group's ability to deliver the outcomes valued by the regulator--V, Y, and I--the indifference curves associated with (1) in [B.sub.1], [B.sub.2] space will tend to exhibit the normal properties of such curves. That is, they will be downward-sloping and convex toward the origin. They are not, however, confined to the positive quadrant; because, as noted, the operative benefit values will tend to fall in the second and fourth quadrants where either [B.sub.1] or [B.sub.2] is negative.

One of the principal postulates of the economic theory of regulation is that given some level of discretion over the regulatory decisions they render, regulatory commissions will choose to implement policies that maximize their own utility (equation [1]) rather than some index of overall social welfare. (7) Such maximization, however, is subject to an extremely important constraint. Namely, the ability of the regulator to supply benefits to various interest groups by using the coercive powers of the state (granted to the regulatory commission by the enabling legislation) to alter the otherwise unregulated industry equilibrium is constrained by the particular circumstances exhibited by the market that is to be regulated. That is, the underlying characteristics of the market--the level of demand, the elasticity of demand, the structure of costs, and, importantly, the natural (unregulated) structure of the market (monopoly, competitive, or oligopoly)--all constrain the ability of the regulator to deliver benefits to particular interest groups. (8)

This constraining influence of the prior market structure has been recognized in the literature (see Peltzman, 1976, pp. 223-24; Jordan, 1972). It stems from the fact that regulation produces benefits and costs principally by altering the industry equilibrium away from its unregulated state. As a result, the location of the unregulated equilibrium and other prior market parameters provide the principal constraint on the regulator's ability to deliver benefits to the various interest groups through regulation. With only two interest groups, moving the market price away from its unregulated state is likely to benefit one group (say, consumers) and harm the other group (say, producers). As a result, the frontier of maximum feasible benefits will be downward-sloping in [B.sub.1], [B.sub.2] space. Thus, the benefits budget constraint is given by

(2) [B.sub.1] = f([B.sub.2]),

with f' < 0. The regulator's general optimization problem, then, is to maximize (1) subject to (2). In the following section, we develop a graphical representation of the regulator's benefits budget constraint and demonstrate how that constraint is influenced by the prior (unregulated) market equilibrium and other market parameters.

III. THE BENEFITS BUDGET CONSTRAINT

To facilitate our derivation of the regulator's benefits budget constraint, we make use of four simplifying assumptions. First, we assume a linear market demand and constant costs. Thus, we assume

(3) Q = [alpha] - [beta]P,

and

(4) C = cQ,

where Q is quantity demanded and produced; P is price; C is total cost; and [alpha], [beta], and c are positive constants. (9) This set of assumptions is reflected in Figure 1. Second, we assume that there are only two relevant interest groups--producers and consumers. As a result, benefits provided to one group will be associated with (though, in general, not equal to) costs imposed on the other group. Third, we assume that price is the regulator's only control variable but that the regulator has complete control over this variable within certain well-defined limits. Finally, we assume that regulation costs the regulator nothing per se, that is, there are zero direct costs of regulating the market. This is, of course, an obvious simplification. However, our results do not depend on zero administrative costs, and we maintain this hypothesis only for convenience.

[FIGURE 1 OMITTED]

Given these assumptions, the regulator can move price away from its unregulated equilibrium to create benefits (and costs) for the two affected interest groups. Importantly, we shall assume that these benefits and costs of regulation are given by the changes in consumer surplus, CS, and producer surplus, PS, brought about by these price movements. The benefits budget constraint, then, is the frontier of maximum benefits (surplus changes) that can be delivered to one interest group for a given level of costs imposed on the other interest group by altering price away from its unregulated equilibrium value. This focus on surplus changes is a fairly stringent assumption that warrants some explanation.

To begin, consider the ordinary consumer utility function U(x) ([equivalent to] U[x.sub.1], [x.sub.2]], say) of conventional microeconomics. Assuming preferences are well behaved, U(*) is (semi-)-continuous and monotonic. Let [X.sup.o] = ([x.sup.o.sub.1], [x.sup.o.sub.2]) be some bundle. Then, consider a new bundle ([x.sub.1], [x.sub.2]) given by [x.sub.1] = [x.sup.o.sub.1] + [dx.sub.1], and [x.sub.2] = [x.sup.o.sub.2] + [dx.sub.2]. We can write (trivially) U [equivalent to] U([x.sup.o], dx), where dx = ([dx.sub.1], [dx.sub.2]). To be able to express preferences in terms of dx alone, however, we would have to impose a requirement that U([x.sup.o], dx) = U([x.sup.o])V(dx), such that [x.sub.a] is preferred to [x.sub.b] if and only if V([dx.sup.a]) > V([dx.sup.b]), where [dx.sup.a.sub.1] = [x.sup.a.sub.1], and so on. Such a requirement is not generally reasonable for consumers. As a consequence, a formulation of consumer utility in terms of changes in goods only is not sensible.

Analysis of the regulator's problem wherein we assume that regulators gain utility from changing the existing distribution of surpluses, however, is rather different from the analysis of the consumer's problem. Such a focus rules out regulatory "extortion" of the form "unless you provide me with benefits such-and-such, I will deprive you of the benefits you are currently receiving." Thus, our assumption that regulator utility arises from changes in market outcomes implies that the status quo (i.e., non-regulated equilibrium) allocation of surpluses has a special status that is inherently different from all other potential allocations (see McChesney, 1990, for a contrary view).

Although the idea that the unregulated status quo is different from other allocations of surpluses seems apparent, the prior analyses by Peltzman (1976) and Becker (1983) accord no special role to the inherited market structure. As a consequence, these theories cannot generally explain the decision to regulate or deregulate an industry. Only the external form of preexisting regulation can be described. Additionally, only the total levels of surpluses matter in such models; consequently, no representation of preferences in surplus change terms is necessary or useful.

An examination of both the probable sources of regulator benefits and the incompleteness of regulation, however, suggests that changes in surpluses are potentially significant elements in the regulator's calculus. For example, suppose a regulator establishes a high price but fails to fully restrict entry or impede nonprice competition among regulated rivals. In that case, regulation yields only transitory benefits to sellers who eventually compete away regulatory rents. We may then observe "monopoly" pricing but no concomitant profits among the regulated firms. As a result, these firms will have no incentive to expend resources to maintain their (worthless) monopoly status. When such rent dissipation is expected to obtain, then, the status quo offers no opportunity for extortion by the regulatory authority, and only "transitional gains" can be reliably exploited by regulators. (10)

Here, however, we assume that regulators are able to restrict entry so that the price changes they adopt will produce more or less permanent profit changes. In that case, regulatory benefits are represented by the surplus changes. Although regulatory extortion can then potentially arise, we assume that it is not commonly practiced--regulators do not collect benefits by threatening to change price away from the status quo but rather by actually doing so. The status quo, then, becomes the unique no-regulation state, with surplus changes to consumers and producers representing the benefits delivered by regulation.

With the linear demand and constant costs assumed, consumer and producer surpluses are given by

(5) CS(P) = ([[alpha].sup.2]/2[beta]) - [alpha]P + ([beta]/2)[P.sup.2],

and

(6) PS(P) = -[alpha]c + ([alpha] + [beta]c)P - [beta][P.sup.2],

respectively. These two quadratic functions are shown in Figures 2 and 3. Here, [P.sub.C] and [P.sub.M] are the competitive and monopoly prices, respectively. Assuming that regulators are unable to set price below the competitive level and unwilling to set price above the monopoly level, [P.sub.C], [P.sub.M] provides the economically relevant region of prices. (11) Within this region, both functions are monotonic. CS is a negative function of price, and PS is a positive function of price.

[FIGURES 2-3 OMITTED]

Given these two surplus functions, the benefits that can be delivered to the two interest groups by regulatory pricing decisions are given by the changes in the relevant surpluses caused by altering the market price away from some initial, unregulated level. These surplus changes are

(7) [DELTA]CS(P) = CS(P) - [bar]CS,

and

(8) [DELTA]PS(P) = PS(P) - [bar]PS,

where [bar]CS and [bar]PS are consumer and producer surpluses realized in the prior, unregulated industry equilibrium, respectively. These unregulated equilibrium surpluses are exogenous constants. They are given by equations (5) and (6) evaluated at the equilibrium price and output determined by the prior market structure.

Substituting equations (5) and (6) into equations (7) and (8) and solving for the associated price changes, we obtain

(9) [DELTA]P([DELTA]CS) = [([alpha] - [beta][bar]P) [+ or -] [square root of ([([DELTA] - [beta][bar]P).sub.2] + 2[beta]([DELTA]CS))] /(-2[DELTA]CS),

and

(10) [DELTA]P([DELTA]PS) = [[beta][DELTA][P.sup.*] [+ or -] [square root of ([([DELTA] - [beta][bar]P).sub.2] + 2[beta]([DELTA]CS))] /(2[DELTA]CS),

where [bar]P is the unregulated equilibrium price and [DELTA]P* is the change in price that will result in price being set at the monopoly level (i.e., [DELTA][P.sup.*] = [P.sub.M] - [bar]P).

Interestingly, which sign is associated with the radical in each of these equations is determined by the direction of the price change brought about by regulation. Specifically, if [DELTA]P > 0, then [DELTA]CS < 0 and [DELTA]PS > 0. Consequently, in this case, the positive sign must apply in equation (9), and the negative sign must apply in equation (10). (12) Analogously, if [DELTA]P < 0, then [DELTA]CS > 0 and [DELTA]PS < 0. In this case, then, the negative sign must be used in equation (9), and the positive sign must be used in equation (10).

Because the prior market structure determines whether regulation will lead to [DELTA]P greater than or less than zero, that structure in turn determines which set of signs applies in each of these equations. As a result, we get different expressions for equations (9) and (10) for different prior market structures. That is, we will get different benefits budget constraints for different starting points (where such starting points are given by the unregulated market equilibria).

These benefits budget constraints are found by equating equations (9) and (10) (using the appropriate radical signs for each starting point) and solving for [DELTA]PS as a function of [DELTA]CS (or vice versa). Although a general analytic solution to this problem is unobtainable, we are able to draw the necessary inferences regarding first and second derivatives to determine the general shape and location of the resulting function for any given prior market structure. In the following subsections, we present the results for three such structures: competition, monopoly, and oligopoly.

Case 1: Regulating a Competitive Market

Assume that the prior market structure is competitive, with an unregulated equilibrium at [P.sub.c], [Q.sub.c] in Figure 1. (13) At this equilibrium, consumer surplus is

(11) [bar]C[S.sub.c] = (1/2)[([[alpha].sub.2]/[beta]) - 2[alpha]c + [beta][c.sup.2],

and producer surplus is

(12) [bar]P[S.sub.c] = 0.

[FIGURE 1 OMITTED]

In this case, regulation can only increase the market price, reducing CS and increasing PS relative to their initial, unregulated values. The locus of resulting changes in CS and PS--which are, in fact, the benefits of regulation delivered to these two groups--define the regulator's benefits budget constraint. That constraint is depicted graphically in Figure 4. It shows the maximum benefits (or minimum losses) that can be delivered to one group while holding the benefits (or losses) to the other group constant as price is increased from its prior, unregulated (competitive) equilibrium level.

[FIGURE 4 OMITTED]

Several properties of this constraint are worth noting. First, the function has a non-positive slope throughout the relevant range, reaching a slope of zero at the monopoly price. As regulators increase the benefits provided to producers, they must simultaneously decrease the benefits (or increase the losses) provided to consumers. Second, the function falls entirely within the second quadrant within the permissible price range, [P.sub.C], [P.sub.M]. Starting from a competitive equilibrium, it is not feasible to increase consumer surplus or to decrease producer surplus. Third, the function is concave. (14) A given increment in the benefits provided to producers as price is raised requires that an increasing increment in losses be inflicted on consumers. Fourth, the function begins at the origin. (15) This property indicates that it is feasible to provide zero benefits to both interest groups simply by not regulating. No regulation--leaving price at its unregulated equilibrium--yields no benefits from regulation. (16) Fifth, the slope of the benefits budget constraint (with [DELTA]PS on the vertical axis) is greater than minus one (i.e., less than one in absolute value) at all positive values of [DELTA]PS. This property reflects the deadweight social welfare loss created by raising price above the competitive level. (17) That is, the (negative) change in consumer surplus will exceed the (positive) change in producer surplus. Sixth, the slope of the benefits budget constraint for regulation of a competitive market at [DELTA]PS = [DELTA]CS = 0 equals -1. That is, at P= [P.sub.C], a marginal change in price yields an equal (though opposite) change in producer and consumer surplus. Seventh, within the general properties described, the specific shape and location of the benefits budget constraint will depend entirely on the parameters of the market demand and cost functions. As a result, shifts in demand and/or changes in production technology or input prices will alter the ability of regulators to produce benefits from regulation, thereby altering the benefits budget constraint. In addition, any change in the prior, unregulated market structure (e.g., a shift from monopoly to competition or vice versa) will also alter this constraint.

Case 2: Regulating a Monopoly

Next, assume that the prior market structure is monopolistic, with an unregulated equilibrium at [P.sub.M], [Q.sub.M] in Figure 1. (18) At this equilibrium, consumer surplus is

(13) [bar]C[S.sub.M] = (-[alpha]c/4) + ([[alpha].sup.2]/8[beta]) + ([beta][c.sup.2]/8),

and producer surplus is

(14) [bar]P[S.sub.M] = (-[alpha]c/2) + ([[alpha].sup.2]/4[beta]) + ([beta][c.sup.2] /4).

In this case, regulation can only decrease the market price, increasing CS and reducing PS relative to their initial, unregulated values. The resulting benefits budget constraint is shown in Figure 5. Again, it shows the maximum benefits that can be delivered to one interest group holding the benefits delivered to the other group constant.

[FIGURE 5 OMITTED]

Clearly, many of the same properties that applied to the benefits budget constraint for regulation of a competitive market hold here as well. Specifically, this constraint is concave and downward-sloping. In fact, for a given market demand and cost curve, the benefits budget constraint for regulation of a monopoly market will be identical to that for regulation of a competitive market except that it is shifted downward and to the right so that P = [P.sub.M] is now located at the origin. Otherwise, the two curves are the same. The entire constraint, then, is located in the fourth quadrant in this ease. Moreover, the slope of this constraint is equal to 0 at P = [P.sub.M] (the origin) and -1 at P = [P.sub.C]. We note also that given the relative slopes of the benefits budget constraints at the origin (-1 for competition, 0 for monopoly), "no regulation" seems a more likely outcome in competition than in monopoly. We touch on a related issue later.

Case 3; Regulating an Oligopoly

Finally, consider the case in which the prior market structure is oligopolistic. For comparison purposes, we assume arbitrarily that the unregulated oligopoly equilibrium output falls precisely halfway between the competitive and monopoly equilibria. (19) At this equilibrium, consumer surplus is

(15) [bar]C[S.sub.o] = (9[[alpha].sup.2]/32[beta]) - (9[alpha]c/16) + (9[beta][C.sup.2]/32),

and producer surplus is

(16) [bar]P[S.sub.o] - (3[[alpha].sup.2]/16[beta]) - (6 [alpha]c/16) + (3[beta][C.sup.2]/16),

in the absence of regulation.

In this case, regulation may either increase the market price toward (or to) the monopoly level or decrease the market price toward (or to) the competitive level, thereby benefiting either producers or consumers, respectively (while, of course, harming the other group). The resulting benefits budget constraint is shown in Figure 6.

[FIGURE 6 OMITTED]

Once again, this function exhibits many of the properties associated with the two preceding benefits budget constraints. Indeed, the curve itself is identical to the two preceding benefits budget constraints except for its location. It is simply shifted so that its midpoint now lies at the origin. There are, however, two substantive differences revealed here. First, the oligopoly benefits budget constraint extends into both the second and fourth quadrants. This result stems from the regulator's ability to either raise or lower price away from its initial, unregulated equilibrium value. (20) Second and importantly, this function does not extend as far into either of these quadrants as the two previous constraints. In fact, the two segments of this constraint correspond precisely to the terminating halves of the two prior benefits budget constraints, where these halves have both been shifted to meet at the origin. This second property stems from the more limited distance that price can be moved in either direction beginning from a point that is midway between [P.sub.C] and [P.sub.M]. As we will illustrate, these differences have important economic implications for the economic theory of regulation.

IV. REGULATORY ENVIRONMENT

Given the characteristics exhibited by a particular market--viz., the prior market structure and underlying market parameters--regulatory equilibrium is attained at the tangency between one of the regulator's convex-toward-the-origin indifference curves and the benefits budget constraint presented by that market. As explained earlier, the former will depend on the regulator's preferences and the affected interest groups' ability to deliver the particular outcomes valued by the regulator--votes, income, or ideological rewards--while the latter is determined entirely by prior market conditions. To both illustrate the relevant concepts and demonstrate their applicability to explaining regulatory behavior, we present one such regulatory equilibrium in Figure 7.

[FIGURE 7 OMITTED]

Here we are assuming that the prior market structure is competitive, yielding the benefits budget constraint AB. Regulator preferences (incorporating the two interest groups' ability to "produce" rewards for the regulator) are reflected in the indifference curves labeled [I.sub.R], with preference ordering [I.sub.R] < [I.sup.'.sub.R] < [I.sup.''.sub.R]. Constrained utility maximization, then, occurs at the regulatory equilibrium [E.sub.R], yielding positive benefits to producers of [DELTA]P[S.sup.*.sub.c] and negative benefits to consumers of [DELTA]C[S.sup.*.sub.c]. These benefits, of course, are created by setting the regulated price above the unregulated (competitive) equilibrium level. (21)

Clearly, the location of [E.sub.R] along the benefits budget constraint will depend on the regulator's marginal rate of substitution of changes in consumer surplus for changes in producer surplus. The smaller this value (i.e., the more willing the regulator is to substitute producers' interests for consumers' interests) the closer the equilibrium will be to point B, which results when price is set at the full monopoly level. As noted earlier, however, the slope of AB at point B is zero. (22) Consequently and importantly, regulators will select this extreme value only if their indifference curves are horizontal--that is, only if they place no value on consumers' interests at all. Therefore, this analysis suggests that regulators generally will tend to set price below the full monopoly level when regulating a competitive market.

Location at the opposite end of AB (i.e., at point A), however, does not require such extreme preferences. Recall that the slope of the benefits budget constraint at point A, which is the no-regulation option, is -1. As a result, regulators may have a marginal rate of substitution that is greater than zero (i.e., they may be willing to trade some consumer benefits to obtain some producer benefits) but nonetheless choose not to regulate a competitive market. Obviously, this corner solution will occur whenever the regulator's marginal rate of substitution of [DELTA]CS for [DELTA]PS is greater than or equal to one at point A. (23) Thus, this analysis also suggests that competitive markets may go unregulated even though producers stand ready to reward regulators for imposing a regulatory-sanctioned price increase. They may simply be unable to reward them enough.

The application of our simple graphical analysis of regulatory equilibrium illustrates how this apparatus can be used to generate insights into observed regulatory behavior. In the following section, we expand our application of this analysis to provide graphical explanations of several commonly observed patterns of such behavior.

V. ILLUSTRATING SOME OLD (AND NEW) THEORETICAL RESULTS

If our graphical approach is to provide a useful supplement to the existing theoretical literature, it should be able to explain (hopefully, more clearly) the same set of phenomenon that have already been explained by prior analyses. In addition, the value of this alternative approach is further heightened if it can also provide insight into previously unexplained (or inadequately explained) patterns of behavior. In the subsections that follow, we illustrate how the graphical tools we have developed here satisfy both of these standards.

Application 1: Regulation Tends to Occur in Extreme (Monopoly or Competitive) Market Structures

Several prior studies of regulatory behavior have noted (and, to varying degrees, explained) that regulation tends to occur in extreme market structures--that is, in markets that are either naturally monopolistic or naturally competitive (see Jordan, 1972; Peltzman, 1976; 1989). That is, regulation of oligopolies is comparatively rare. A straightforward explanation of this observed behavior is provided by a comparison of the three benefits budget constraints that apply to these alternative market structures. Such a comparison is facilitated by examination of Figure 8.

[FIGURE 8 OMITTED]

We have graphed all three constraint functions together in the two curves labeled ABC and DBE. The benefits budget constraint applicable to regulation of a monopoly market is represented by the segment BC on the former curve. The benefits budget constraint applicable to regulation of a competitive market is represented by segment AB on that curve. Finally, the benefits budget constraint applicable to regulation of an oligopoly market is represented by the curve DBE. Notably, although this last curve extends into both quadrants two and four, it does not extend as far into either as the benefits budget constraint associated with one of the extreme prior market structures--competition or monopoly. Starting from an oligopoly (intermediate) equilibrium, the distance to either the monopoly price or the competitive price is not as great as it would be if we were to begin from the opposite extreme equilibrium (e.g., moving from competitive equilibrium to the monopoly price). In addition, the benefits budget constraint for oligopoly lies everywhere to the southwest of the corresponding benefits budget constraints of the two extreme market structures. In fact, segment DB of the oligopoly benefits budget constraint corresponds to segment AF of the competitive benefits budget constraint, with this latter segment shifted to the origin. Similarly, segment BE corresponds to segment GC of the monopoly constraint, also shifted to the origin.

Given these benefits budget constraints, then, the question is: Under which market structure or structures are we relatively more likely to observe an equilibrium at a point away from point B? That is, under which prior market structure are we more likely to observe regulation? To answer this question, we note that the net gain to regulators from regulating a market is given by the increase in utility caused by locating at a point other than B--which, of course, is accomplished by moving price away from its nonregulated equilibrium value. Without drawing indifference curves, it is apparent from Figure 8 that such gains are likely to be much more substantial if benefits budget constraint AB or BC (rather than DE) applies. For oligopoly, the no-regulation option is an interior solution, whereas for monopoly or competition it is a corner solution. Therefore, the graphical analysis immediately suggests a common finding reported in prior studies--that regulation will tend to be more common in situations for which the prior market structure is at one or the other extreme, either monopolistic or competitive. Regulation of oligopolies will tend to be relatively less common (but by no means ruled out). One might further argue that "abstinence" from further regulation is more likely with a competitive industry than a monopoly.

A review of the previous discussion establishes another, related result. It is less probable that in an initially competitive market one would observe a move to full monopoly than that an initially monopolistic market would be regulated to produce fully competitive prices. This conclusion arises simply from the fact that it would require a regulator's marginal rate of substitution of [DELTA]CS for [DELTA]PS to equal zero for a competitive market to be regulated at the monopoly outcome.

Application 2: Regulation Tends to Spread the Benefits/Costs of Exogenous Changes across the Affected Interest Groups

Since the early work of Peltzman (1976) and others, it has been widely argued that when changes occur in underlying market conditions (e.g., when technological change alters costs), the resulting benefits or costs will tend to be spread across the various interest groups affected by the regulatory process. (24) This fundamental prediction of the economic theory of regulation is also readily explained by the graphical approach we have developed.

Consider Figure 9. Here, we assume that a competitive market is being regulated. The initial underlying market conditions generate a benefits budget constraint of AB, yielding a regulatory equilibrium of [E.sub.R]. Now suppose that a technological advance occurs that lowers production costs. The impact of such a change is to shift the applicable benefits budget constraint from AB to A[B.sup.']. That is, the new constraint is steeper, allowing a greater amount of benefits to be delivered to producers for a given reduction in benefits to consumers. (25)

[FIGURE 9 OMITTED]

Given this new constraint, regulatory equilibrium shifts from [E.sub.R] to [E.sup.'.sub.R]. The gain to producers from regulation increases and the loss to consumers decreases, both by less than the full change made possible by the technological advance. That is, the benefits resulting from that advance are spread across both of the affected interest groups.

Application 3: Cross-Subsidies are a Prevalent Feature of Regulated Markets

Over the years, many authors have noted the prevalence (if not ubiquitous presence) of cross-subsidies in regulated price structures (see Posner, 1971). Under Faulhaber's (1975) definition of a cross-subsidy, one group of consumers of the regulated firm's output is charged a price that exceeds the unit stand-alone costs of production, while another group of consumers is charged a price that falls below the marginal costs. This phenomenon is readily seen within the context of our model.

Specifically, assume two demand curves representing purchases by consumer groups 1 and 2. Given these demands, the regulatory benefits delivered to the favored (i.e., subsidized) group 1, [DELTA]C[S.sub.1], are given by the change in that group's consumer surplus caused by lowering the regulated price [P.sub.1] below its unregulated equilibrium value. The regulatory benefits (or costs) imposed on the disfavored (subsidizing) group 2 are similarly given by the change in that group's consumer surplus, [DELTA]C[S.sub.2], where [DELTA]C[sub.1] > 0 and [DELTA]C[S.sub.2] < O. Presumably, the underlying cause of the regulator's preference for group 1 over group 2 consumers emanates from the former's greater ability to reward regulators by providing whatever objects form the arguments of the regulator's utility function. Producer interests (which are not depicted graphically) can be held constant under this analysis by holding profits fixed as [P.sub.1] and [P.sub.2] are varied.

Clearly, the same causal forces discussed earlier will be at work here as well. Namely, the prior market structure, the underlying market parameters (in particular, the price elasticities of demand for groups 1 and 2), and the affected interest groups' relative ability to reward regulators will determine both the benefits budget constraint and the regulator's indifference curves. Together, of course, these will determine the location of the resulting regulatory equilibrium and the pattern of cross-subsidies. As a general proposition, however, given differing demand elasticities and/or abilities to deliver rewards to regulators, some degree of cross-subsidization appears virtually certain to materialize. Thus, cross-subsidies are likely to be present in regulated markets.

Application 4. Regulation to Maximize Social Welfare

Suppose, as has been assumed in much of the normative work on regulation, that regulators have the objective of maximizing social welfare. That is, instead of maximizing some broadly defined utility function, regulators pursue pricing policies that solve

(17) MAX W = CS(P) + PS(P),

subject to the benefits budget constraint presented by the prior market conditions. What sorts of policy actions, then, would be implied by the economic theory of regulation if we replace equation (1) with equation (17)?

The answer to this question is readily illustrated in Figure 10. Given the above objective function, the regulator's indifference curves will be straight lines, all with a slope of -1. (26) Thus, the regulator's preferences are represented by the lines [I.sub.R], [I.sup.'.sub.R] in the graph.

Given these indifference curves and the benefits budget constraints implied by competition (segment AB of the curve labeled ABC) and monopoly (segment BC of this curve), it is immediately apparent that regulatory equilibrium will occur at [E.sub.R] (point B) in the former case and [E.sup.'.sub.R] (point C) in the latter case, where the slopes of the respective benefits budget constraints equal -1. Therefore, a social welfare maximizing regulator will set price at the competitive level (point C) in a monopoly market and will not regulate (point B) a competitive market. Moreover, although we have not included the benefits budget constraint for oligopoly in Figure 10, it should be apparent that with the indifference curves shown, oligopolies will also always be regulated with price set at the competitive level. Of course, it is the widespread departure from this implied behavior that provides empirical evidence that in general regulation is not social welfare maximizing.

[FIGURE 10 OMITTED]

Application 5: Regulatory Equilibrium can Shift from Regulation to Deregulation

Importantly, all three of the benefits budget constraints derived in section IV contain the no-regulation option as part of the feasible set of choices. Specifically, the origin at [DELTA]CS = [DELTA]PS = 0 represents the choice of leaving the naturally occurring market equilibrium undisturbed. As noted earlier, this option is a corner solution for the two extreme prior market structures--competition and monopoly--and an interior solution for oligopolies. Consequently, any of a number of changes in underlying market conditions (e.g., technological changes, demand shifts, or market entry) can cause the regulatory equilibrium to shift from regulation to no regulation. Deregulation, then, can become the optimal (regulator utility-maximizing) policy choice as a result of any of these exogenous changes. So, too, can the decision to abstain from regulating a market be shown to represent an optimal policy choice.

To illustrate this point, consider Figure 11. Initially, suppose the market is a natural monopoly. Consequently, regulators face the benefits budget constraint given by segment BC. Under this constraint and with regulator preferences represented by indifference curves [I.sub.R] and [I.sup.'.sub.R], regulatory equilibrium is achieved at [E.sub.R]. The market price is set below the full monopoly level and above the competitive level, producing negative benefits for producers and positive benefits for consumers. (27)

Now suppose some change occurs in the underlying market conditions that shifts the unregulated market equilibrium from monopoly to competition (e.g., a technological change dramatically reduces scale economies in this industry). As a consequence of this change, the new benefits budget constraint becomes segment AB. Given this new constraint (and with no change in the regulator's preferences), the new regulatory equilibrium shifts to [E.sup.'.sub.R] at point B. (28) Deregulation then becomes the optimal policy. (29)

It is important, at this point, to recall that the axes (and, therefore regulators' utility functions) are measured in surplus changes relative to the status quo, not in levels. The movement from [E.sub.R] to [E.sup.'.sub.R] in Figure 11 represents a change from regulated monopoly to deregulated competition. As a result, consumers gain and producers lose, even though the movement on the graph is to the northwest, suggesting the opposite (i.e., [DELTA]CS < 0 and [DELTA]PS > 0). Although the latter inference is correct given the original benefits budget constraint, BC, the levels of CS and PS from which the changes are measured must be recalibrated given the new constraint, AB. With this latter constraint, [DELTA]CS is at its maximum feasible value and [DELTA]PS is at its minimum value with deregulation (point B).

VI. CONCLUSION

The original insights provided by the early founders of the economic theory of regulation have provided the wellhead from which a substantial body of theoretical work has sprung. That work has greatly expanded our understanding of the economics of regulated markets in particular and interest group behavior generally. Numerous subsequent articles--both theoretical and empirical--and several new journals subsequently have appeared that have added to that understanding.

This body of literature, however, has never provided a complete and consistent graphical representation of the important underlying concepts and principal results of the economic theory of regulation. This article attempts to fill that void by providing a more fully developed graphical treatment of this theory. Hopefully, the conceptual tools developed here--primarily the benefits budget constraint--will facilitate both students learning the relevant theory and researchers developing further extensions and applications.

APPENDIX

In the text, we argue that the benefits budget constraints we derive are concave. Importantly, that property is not contingent on the assumption that demand is linear. Rather, concavity of the benefits budget constraints holds for nonperverse downward-sloping demands.

For any such demand, consumer surplus change is

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for P < [bar]P, where P denotes an initial price. (Note that we are integrating over prices, and s is the variable of the integration.)

Similarly, producer surplus change is

(A2) [DELTA]PS = X(P)(P - c) X([bar]P)([bar]P - c).

Note that, if [DELTA]P < 0, then [DELTA]CS > 0 and [DELTA]PS < 0 when [bar]P [less than or equal to] [P.sub.M].

Because both [DELTA]CS and [DELTA]PS depend on P, differentiation yields the conclusion that [DELTA]PS is (implicitly) a concave function of [DELTA]CS (i.e., the benefits budget constraint is concave) whenever we have

(A3) -X" * X * (p - c) - [X.sup'] * X + ([X.sup.'])2(p - c)>0

([A3] is obtained by simplification). This condition is quite familiar and is satisfied (for prices not less than marginal cost) by any demand curve X that exhibits greater price elasticity at higher prices. This may be seen by differentiating the elasticity expression E= ([X.sup.']p/X) with respect to price.

Thus, the benefits budget constraint is concave under very unrestrictive conditions. Therefore, the inequality indicated in (A3) holds.

It is likewise straightforward to show that the general benefits budget constraint is concave for [DELTA]P> 0. Thus, concavity of these constraints is not dependent on the assumption of linear demand.

(1.) Peltzman's (1976) paper contains some graphs that help explain his mathematical results. It does not, however, present a complete graphical explanation of the basic theory of regulation or of the dynamics of deregulation (of reregulation). The accelerated maturation of the theory has not prevented its rapid advancement and extension in a number of important directions. Indeed, the economic theory of regulation has found widespread acceptance in the fields of industrial organization and public choice and has provided a promising methodology for understanding a significant portion of political behavior in general. See, for example, Noll (1985; 1989) and Peltzman (1989). The potential for this theory to yield insight into the economic and political behavior of interest groups holds substantial promise that a general theory of collective action will eventually emerge that is analogous to the body of theory we now refer to as neoclassical microeconomics.

(2.) To our knowledge, the only formal theoretical treatment of the decision to deregulate an industry is that provided by McCormick et al. (1984). The explanation provided there, however, focuses on a built-in bias against deregulation and consequently fails to provide a full positive theory of the decision to deregulate. Our graphical approach, however, provides such a theory.

(3.) For convenience, we will generally refer to "benefits" only. Any harms imposed by regulation on interest groups are simply negative benefits.

(4.) This interrelationship between the benefits afforded any one group and the benefits to other groups is emphasized in the prior literature. See, for example, Becker (1983).

(5.) Our specification of the trade-offs in benefits afforded to one group versus another follows in the spirit of earlier work on the economic theory of regulation. See, for example, Becker (1983, p. 376).

(6.) Our analysis here is not dependent on the inclusion of all these arguments in the regulator's utility function. For instance, an alternative specification, congruent with Peltzman's (1976) analysis would include only V or "V and all others." The debate on what arguments properly belong in the regulator's utility function goes back to Peltzman's seminal paper and the comments on it. See, for example, Hirshleifer (1976) and Becker (1976).

(7.) This assumption separates the positive economic theory of regulation from the normative theories of optimal regulatory policies.

(8.) Beyond the market constraints that we explore here, political and legal constraints arise from the particular institutions within which regulators are made to operate. The role of these constraints, which is beyond the present analysis, has been explored in a growing literature beginning with Weingast and Moran (1983).

(9.) Although normative analysis of regulation has focused attention on declining average cost (or natural monopoly) conditions, our constant cost assumption here allows for the reality of regulation of a number of industries (e.g., trucking and airlines) that have (at least to an approximation) constant cost characteristics. The principal aspects of our subsequent analysis are, however, unaffected if we were to impose a declining cost structure.

(10.) On the subject of transitional gains from regulation, see Tullock (1975) and McChesney (1987).

(11.) Price cannot be set below the competitive level because of constitutional constraints that prohibit regulators from setting rates at nonremunerative (or so-called confiscatory) levels. Prices will not be set above the monopoly level, because at such levels both interest groups are harmed and, as such. supramonopoly pricing would be irrational.

(12.) This result arises because there are generally two levels of price (and. hence, two [DELTA]Ps) that yield the same change in producer surplus. Only the "smaller" of these is relevant, because the "larger" implies prices beyond the monopoly level.

(13.) Given our assumed market parameters, [P.sub.c] = c, and [Q.sub.c] = [alpha] - [beta]c

(14.) Concavity of the benefits budget constraint is not dependent on the specific (linear) functional form assumed here for the demand curve. A proof of general concavity of this constraint is contained in the appendix.

(15.) One can easily show from equations (7) and (8) that [DELTA]C[S.sub.c] = [DELTA][S.sub.c] = 0 at C[S.sub.c], P[S.sub.c]. That is, regulation yields no benefits unless it alters the market outcome away from its unregulated state.

(16.) As we shall illustrate later, identification of the no-regulation option along the benefits budget constraint becomes significant when we consider the decision of whether to regulate or deregulate an industry.

(17.) Note that we are assuming that first-degree price discrimination is not feasible. Otherwise, the benefits budget constraint would have a slope of -1 throughout.

(18.) Given our assumed market parameters, [P.sub.M] (1/2)[([alpha]/[beta])+c], and [Q.sub.M]= (1/2)([alpha] - [beta]c).

(19.) Given our assumed market parameters, the unregulated oligopoly equilibrium is [P.sub.o] = (1/4)[([alpha]/[beta]) + 3c], and [Q.sub.o] = (3/4)([alpha] - [beta]c).

(20.) As with the other benefits budget constraints. [DELTA]C[S.sub.o] = [DELTA]P[S.sub.o] = 0 at [bar]C[S.sub.o], [bar]P[S.sub.o]. That is, the no-regulation point is again found at the origin.

(21.) This result is consistent with prior empirical work. See, for example, MacDonald (1987) and Wilson (1994). Overall, these studies find that regulation of competitive markets tends to lead to higher prices.

(22.) Beyond point B, the benefits budget constraint curves back to the southwestern direction. Increasing price beyond the monopoly level reduces both consumers' and producers' surplus.

(23.) Whether, in fact, point A emerges as a regulatory equilibrium will, of course, depend on the ability of a given [DELTA]CS and a given [DELTA]PS to translate into an argument (e.g., votes) in the regulator's utility function. This transformation will depend on a variety of factors, such as the relative cost of organizing consumer versus producer interests. For a discussion of the nature of these production functions, see Becker (1983).

(24.) Indeed, many of the more recent incentive regulation schemes, including price cap regulation, formalize such benefit/cost spreading through the sharing requirements imposed.

(25.) It is important to note that the basis on which the new benefits budget constraint is formulated is the initial (pre-technological change) competitive equilibrium. Our thanks to Sam Peltzman for pointing this out.

(26.) With the objective function given by equation (17), d[DELTA]W = [(d[DELTA]CS/dP)dP] + [(d[DELTA]PS/dP)dP] = 0 along any indifference curve. Thus, the slope of this indifference curve is (d[DELTA]ACS/d[DELTA]PS) = -1.

(27.) At this point, there is ample empirical evidence that such intermediate regulatory outcomes often occur. See, for example, Mayo and Otsuka (1991) who find that regulated cable rates were held below monopoly levels but above competitive levels. See also, Caudill et al. (1993).

(28.) Structural changes in underlying market conditions could also alter the ability of the affected interest groups to provide rewards to regulators. Consequently, regulator indifference curves could change as well. Obviously, such a change could either reinforce or offset (partially or completely) the result shown here.

(29.) Clearly, a dramatic shift from a prior market structure that is a natural monopoly to one that is fully competitive is not required to shift the regulatory equilibrium to the no-regulation corner solution. In Figure 11, any change in market conditions that increases the absolute value of the slope of the BC segment could have this effect. Similarly, a shift to an oligopolistic market structure could yield the same outcome. Thus, there is a large set of circumstances that could plausibly cause a regulator to abandon price controls altogether. Deregulation is not a mystery in this model.

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T. RANDOLPH BEARD, DAVID L. KASERMAN, and JOHN W. MAYO *

* We thank Willis Emmons, Jeff Macher, Sam Peltzman, Dennis Quinn, Bennet Zelner, and seminar participants at Auburn University, the University of Florida, and Georgetown University for helpful comments. All errors are our own.

Beard Associate Professor, Department of Economics, College of Business, Auburn University. Auburn, AL 36849. Phone 1-334-844-2918, Fax 1-334-844-4615, E-mail [email protected]

Kaserman: Torchmark Professor, Department of Economics, College of Business, Auburn University, Auburn, AL 36849. Phone 1-334-844-2905, Fax 1-334-844-4615. E-mail [email protected]

Mayo: Dean and Professor of Economics. Business and Public Policy, McDonough School of Business, Georgetown University. Washington, DC 20057. Phone 1-202-687-6972, Fax 1-202-687-2017, E-mail [email protected]