Are Labor Unions Consistent with the Assumptions of Perfect Competition?

The percentage of U.S. workers organized by a labor union has steadily declined from a peak of 35 percent in 1954 to 12.9 percent today (U.S. Bureau of Labor Statistics 2005). Institutionalists have suggested policies to revitalize the labor movement, but such a task is difficult in today's ideological

In order to restore labor's strength, effective policy must resonate with "the nation's commitment to individualism, self-reliance, and economic freedom" (Toruno 2004, 281). A formidable ideological obstacle, however, is the perfectly competitive model (PCM) under which resources are efficiently allocated as if by an invisible hand, without need for institutional intervention.

The PCM resonates with "the image of a social order dominated by self-reliant individuals carrying on economic activity without the need for government oversight" (Torufto 2004, 274). The PCM is praised as an "intellectual triumph" (Lipsey et al. 1999, 288) under which "things do not get any better" (Boyes and Melvin 2005, 583). Since a labor union within the PCM is superfluous and can only distort market outcomes, it "represents a wrench in an otherwise mellifluously running machine, an unsightly weed to be extirpated" (Woodbury 1987, 1786). The PCM also forms the basis of the so-called monopoly face of labor unions whereby unions are believed to "raise wages above competitive levels [causing] harmful economic effects" (Freeman and Medoff 1984, 6).

Despite voluminous criticism of the PCM and its assumptions, orthodox economists believe that given the PCM assumptions, deductive logic proves that resources are efficiently allocated without need for institutional intervention. But is this true? Is this conclusion logically deductible from its assumptions?

The purpose of this paper is to demonstrate that this conclusion cannot be derived from the PCM assumptions without making ex post facto violations. Correction of the logical errors, in fact, leads to the opposite conclusion that resources within the PCM cannot be allocated efficiently without institutional intervention and that a labor union can efficiently allocate resources within the PCM. So rather than inhibiting individualism, self-reliance, and economic freedom, labor unions enable individuals to operationalize these values within the PCM.

This paper will focus on perfect competition in the labor market and will critique the PCM from within this model. The first section will critique the logical errors of the PCM; the second will offer a revised argument; and the third will discuss the implication of these findings.

Logical Errors in the Perfectly Competitive Model

This section will accept all PCM assumptions as true as well as the narrow neoclassical view of efficiency in order to demonstrate the logical flaws in the PCM. Once corrected, the next section will prove that the PCM cannot allocate efficiently resources on its own without institutional intervention.

To sharpen our argument, let us focus on firm A, a representative firm in industry X, which is assumed to operate in a perfectly competitive labor market. For ease of exposition we assume this firm also operates in a perfectly competitive product market, which allows market price to be constant, so that the marginal revenue product (MRP) equals the value of the marginal product (VMP), defined as the extra dollar value in output obtained from an extra unit of labor.4

The labor demand curve of firm A, illustrated in figure 1, is downsloping and equals the MRP. The firm's labor supply curve is perfectly elastic at the industry wage, We, and also equals its marginal wage cost (MWC), defined as the absolute change in the total wage cost resulting from the employment of an additional unit of labor. Firm A will maximize its profits by hiring Qe units of labor, where MRP = MWC. To the left of Qe, the MRP exceeds the MWC, inducing the firm to hire more labor. To the right of Qe, the MWC exceeds the MRP, inducing the firm to reduce its units of labor.

Since firm A can obtain all the workers it wants at We, it has no incentive to offer a higher wage. If, however, firm A offers a lower wage, it will not attract any labor because each worker has an opportunity cost of at least We and can find employment elsewhere. Specifically, since "the labor market [is] free of barriers to entry . . . workers are free to change jobs or move to labor markets that pay higher wages, if they wish to do so" (Ayers and Collinge 2004, 513).

Ease of exit, it is assumed, protects workers in the PCM because, "if a worker is dissatisfied with a job, he or she can quit and find a better one" (Reynolds et al. 1998, 407). ease of exit/entry is the cornerstone of the PCM (Prasch 2004, 148). It is clear why exit is preferred to other corrective mechanisms such as voice:

[Exit] is neat-one either exits or one does not; it is impersonal... and it is indirect-any recovery on the part of the declining firm comes by courtesy of the Invisible Hand as an unintended by-product... [whereas] voice is just the opposite of exit. It is ... far more "messy." ... [I]t implies articulation of one's critical opinions. . . . [It] is direct and straightforward rather than roundabout. (Hirschman 1970, 16-17)

Given costless mobility, it is assumed that if a wage less than We is offered, all affected workers will exit, creating a shortage of workers which will return the wage to We. By ensuring that all dissatisfied workers exit, efficiency is achieved by the market's invisible hand, rendering institutional intervention superfluous since "workers who have a legitimate dissatisfaction or grievance have a readily available and low (zero) cost means to solve the problem-quit and find a job elsewhere " (Kaufman 2004b, 360). Thus, according to orthodoxy, there is no need for institutional intervention within the PCM which will only generate inefficiencies. Specifically, a higher union wage will force unionized firms to substitute capital for labor, thus creating unemployment.

The perfectly competitive model arrives at its conclusion by imposing ex post facto restrictions on three assumptions of the PCM: exogenous preferences, rationality, and profit maximization, each of which will now be explained.

The assumption of exogenous preferences is integral to the PCM because it purports to demonstrate that individuals acting alone, free from coercion, will gravitate toward an efficient outcome: "Tastes are part of the individual's freedom. If some workers prefer to live in the country that is simply a fact that science must accept" (Deising 1982, 31). The PCM, however, violates this assumption by restricting preferences so that all disaffected employees will exit.

Orthodox economists might object that given costless mobility, a worker is irrational for not leaving. Why not leave if it costs nothing? This objection, however, ignores the nexus between preferences and behavior. If, for example, the costs of attending a movie are zero but an individual would rather pay to attend a baseball game because he or she prefers to watch a baseball game rather than a movie, it is rational to pay to attend a baseball game. Likewise, if an individual prefers to use voice rather than exit, even though exit is costless, that behavior is rational because it is consistent with the individual's preferences. By denying voice as an option for redress, the PCM becomes tautological: The desired end is free of institutional intervention, so individuals are denied voice, which precludes the formation of institutions. Voice and individual freedom-the hallmark of democracy-should be fully embraced.

By restricting preferences and thereby the opportunity to choose the type of redress, the PCM denies freedom, since freedom is actualized by choice representing free will (van Staveren 2001, 26, 69). Such a person, denied the opportunity to choose, is thus "reduced to the mechanical calculation of an algorithm."

The second violated assumption of the PCM is rationality. Choice implies an array of alternatives; without alternatives there can be no choice and, without choice, rationality is absent (Casson 1990, 4). If each dissatisfied individual is assumed to mechanically react the same without thoughtful consideration, rationality is not exercised. Freedom, choice, and rationality are inextricably interwoven.

The third violated assumption is profit maximization. If each dissatisfied person is assumed to exit, he or she must have a place to exit to; that is, an existing firm must be able to hire an additional worker who wants to leave. But such a firm, by definition, is not maximizing profits. This problem is illustrated in figure 2.

At point A, the firm maximizes profits by equating the MRP to the MWC and hires Qe units of labor. If the firm hires Qe+I workers, it will operate to the right of point A, where the MWC exceeds the MRP by be, and the firm will lose revenue. If, however, the firm were to maximize profits by hiring an additional worker, then by definition it was initially operating to the left of point A, where the MRP exceeds the MRC by ef. To employ more (or less) than Qe units of labor violates the assumption of profit maximization.

If full employment is assumed, as it is in the long run, and each firm is maximizing profits, then the exit option is not viable since no firm has an incentive to hire an additional worker. But with less than full employment, slack exists, allowing a firm to hire an additional worker, but such a firm was not maximizing profits. Whether or not the exit option is viable in the short run depends on the speed of adjustment. With instantaneous adjustment, the exit option is not viable since all firms are maximizing profits. If however, we assume noninstantaneous adjustment, some firms have excess capacity and would be willing to hire additional workers, but this violates the assumption of profit maximization.

The orthodox economist might object that a disaffected worker could exit and offer to work elsewhere for a lower wage. But why? Why not stay and use voice? This assertion reveals the orthodox bias favoring exit and a more insidious bias favoring the worker's subservience to the firm: it is the responsibility of the worker to exit.

It is interesting to note the selectivity bias of neoclassical economics eagerly appropriating the invisible hand metaphor while ignoring Adam Smith's powerful insight that the relationship between employers and employees is intrinsically unequal:

It is not... difficult to foresee which of the two parties must, upon all ordinary occasions, have the advantage in the dispute, and force the other into a compliance with their terms. ... In all such disputes the masters can hold out much longer. A landlord, a farmer, a master manufacturer, or merchant, though they did not employ a single workman, could generally live a year or two upon the stocks which they have already acquired. Many workmen could not subsist a week, few could subsist a month, and scarce any a year without employment. (Smith 1976, book I, 74-75)

Employees rely on wages to meet needs, defined as a demand that if not met will intensify with time; whereas a want if not met will either remain at the same intensity or diminish with time (Prasch 1995, 809). Employees cannot totally withdraw from the market if needs are not met, whereas employers are at least three steps away from experiencing unmet needs: they can first sell their wares, then their business, then their labor (Prasch 2004, 148). Furthermore, even the words "employee" and "employer" presuppose an asymmetrical relationship (Kaufman 2004a, 20). The assumption of costless mobility ostensibly equalizes this inherent difference but only after ex post facto violations of the initial assumptions.

A Revised Argument

In this section we accept the initial assumptions of perfect competition while not imposing any ex post facto restrictions. Proper deductive reasoning will demonstrate that given the assumptions, the PCM is not capable of efficiently allocating resources without institutional intervention. We assume that representative firm A operates in both a perfectly competitive labor market and a perfectly competitive product market.

As shown in figure 3, firm A maximizes profits by hiring Qe units of labor at the industry wage and incurs a total wage bill of (We)(Qe).

Firm A has no incentive to offer a wage higher than We because at that wage it can obtain all the labor it wants. But given full employment, the exit option does not exist, so the firm might reduce its wage offer to some or all of its workers, thus increasing short-term profits. This is a variation of Huw Dixon's (1990) argument that if each firm within a perfectly competitive industry is maximizing profits, any individual firm might raise prices knowing that it will not lose all its customers, since no firm has an incentive to deviate from its profit-maximizing output. As a reminder, the PCM acknowledges the possibility of a lower wage offer but assumes the affected worker(s) will exit.

If Firm A offers WI to all workers, it will enjoy a rent equal to W^sub 1^WeAB; whereas if firm A offers W^sub 1^ only to the last worker hired, it will enjoy a rent equal to ABCD. Firm A is not a monopsonist, since it is one of numerous firms in the industry and does not control the wage by adjusting the amount of labor it hires; rather it hires Qe workers with the possibility of offering a lower wage to all, none, or some of its workers.7

Given the PCM assumption of exogenous preferences, a worker confronted with a lower wage has three options: exit, voice, or loyalty (Hirschman 1970). He or she will exit if he or she prefers exit, if a job is available, and if he or she prefers not to be stigmatized for leaving the employer. He or she will use voice if he or she prefers voice or is stigmatized for leaving, or if the exit option is not viable. The worker will remain loyal if he or she is submissive to the firm's interests, prefers to wait until conditions improve, or prefers inaction.

If we assume variable labor intensity, a fourth option emerges: the worker remains at the firm but varies his or her work effort such as postulated in the following relationship, I = I(W-W*, p) where I = labor intensity, W = the wage, W* = the opportunity wage, and p = the probability of being caught shirking (Fairris and Alston 1994). Although this paper assumes constant labor effort, the assumption of variable labor effort does not detract from its conclusions.

Given the PCM assumptions of exogenous preferences and rationality, it is conceivable that when offered a lower wage, an individual might prefer to use voice, even with costless mobility. Paraphrasing Paul Deising (1982), if an individual prefers voice to exit, this is a simple fact that the model must recognize. Furthermore, with full employment, the exit option is not viable and voice becomes an effective means of redress (Hirschman 1970, 33). But even with a viable exit option, an individual should be able to choose the type of redress if the model is consistent with the values of self-reliance, freedom, and individualism.

An orthodox economist might object that if a lower wage is offered, the employer would hire an additional worker(s) until the lower wage equals the lower MRP. But where would the firm obtain the extra labor, given full employment? And why would a worker seek a lower wage elsewhere?

An individual who prefers voice might hesitate to reveal his or her true preferences for fear of employer retribution (Freeman and Medoff 1984, 9). However, cooperating with similar workers will reduce such fear and concomitantly increase the efficacy of voice. "Collective action," as John R. Commons wrote, "means liberation and expansion of individual action; it is literally the means to liberty" (1950, 35). A labor union in this sense "does not supplant a competitive labor market with a monopolistic combination of workers; rather it supersedes single worker bargaining by a simple agent who represents many workers" (Pencavel 1991, 4).

Since the PCM cannot guarantee every worker the value of his or her MRP, institutional intervention becomes a possibility. Such a union is organic and voluntarily chosen by the affected workers. Not all workers would join such a labor union, rather only those with a wage offer less than their marginal products. The threat of unionization might compel the firm not to offer a lower wage, but for this threat to be viable, voice must be recognized as an efficacious means of redress. It is unlikely that a union in the PCM would demand a wage greater than We because such a wage necessitates either the existence of market power, blocked entry, or the firm's possession of a differentiated cost function, and under such conditions, perfect competition no longer exists (Booth 1995, 95).

Frank Taussig (1939) acknowledged the possibility of a union forming in pure competition in order to secure the industry wage which might otherwise be allusive.8 However, he assumed immobile labor, whereas this paper assumes the more stringent assumption of costless mobility. And H. Gregg Lewis (1980) argued that a union in a perfectly competitive industry could secure a public good but only by offering its members a lower wage. Lewis, however, assumed that the union could not raise the wage above the market-determined wage, whereas this paper argues that a labor union in the PCM could raise the wage to the competitive level.

It is interesting to note that individuals in the PCM do not remain isolated and disconnected from each other, despite the PCM assumption of independent utility functions. Given rationality and exogenous preferences, cooperation and collective action becomes a legitimate and reasonable course of action. Thus, contrary to orthodoxy, an efficient labor union is consistent with the assumptions of the PCM. This is not to say that a disaffected worker will passionately pursue unionization or that he or she will relish the social connection with other disaffected workers; rather, that he or she views social cooperation as a de facto necessity, for as van Staveren (2001) noted, "paradoxically, people need to relate to each other if they want to become independent; that is, economically speaking they can only secure a living by interacting with others" (20). It is no accident that the impetus for ameliorative social and labor legislation began after a competitive labor market was implemented.

Not until 1834 was a competitive labor market established in England.... Yet almost immediately the self-protection of society set in: factory laws and social legislation, and a political and industrial working class movement sprang into being. It was in this attempt to stave off the entirely new dangers of the market mechanism that protective action conflicted fatally with the self-regulation of the market system. It is no exaggeration to say that the social history of the nineteenth century was determined by the logic of the market system. (Polyani 1944, 83)

Conclusion

In an essay written almost half a century ago, George Stigler noted that perfect competition "has proved to be a tough and resilient concept [which] will stay with us in recognizable form for a long time to come" (1957, 9). Unfortunately, his prognosis remains true. This paper has demonstrated, however, that the orthodox assertion that resources are efficiently allocated without need for institutional intervention can only be deduced from the PCM assumptions by committing three ex post facto violations. Correction of the logical errors and proper deductive reasoning leads to the conclusion that a labor union can achieve a Pareto optimal allocation of resources within the PCM. So rather than an imperfection within the PCM, a labor union should be viewed as an organic and voluntarily chosen method to redress an inequity. A labor union is thus consistent with the values of self-reliance, freedom, and individualism even in the idealized and hermetically sealed PCM.

Acceptance of this correction, however, will be ideologically difficult for orthodoxy because of its intrinsic antilabor view that unemployment is caused by high and rigid wages (Levin-Waldman 2004, 142). But if, as this paper has demonstrated, a labor union can efficiently allocate resources within the PCM-something the market is unable to do itself-then it cannot distort an otherwise competitive equilibrium.

This does not imply that unions do not raise wages, nor that unions do not cause inefficiencies, for evidence indicates otherwise, justifying to some extent its monopoly face.9 Rather, this paper has argued that since the PCM cannot guarantee that every worker's wage will equal his or her MRP, a labor union, by equating the wage and the MRP, can promote efficiency within the PCM. Without an automatic mechanism ensuring that everyone will receive his or her wage, a range of indeterminancy exists within the PCM, where the wage is determined by differences in relative bargaining leverage. Smith recognized that

Masters . . . sometimes enter particular combinations to sink the wages of labour even below the [actual] rate . . . but such combinations are frequently resisted by a contrary defensive combination of the workmen; who sometimes too, without any provocation of this kind, combine of their own accord to raise the price of their labour. The usual pretenses are, sometimes the high price of provisions; sometimes the great profit which their masters make by their work. (1976, book I, chap. 8, 75)

Differences in relative bargaining strength are in turn influenced by full employment, voice, and the availability of exit.

The assertion that a labor union is incompatible within the PCM is an enabling myth "serv[ing] as powerful social control mechanism enabling] the upper strata to maintain dominance over the lower" (Dugger 1989, 608). This myth, given the imprimatur of the inexorable will of the market, "weakens the credibility of those who would reform the market, dashes the hopes of those dispossessed by the market and hides those who benefit from the particular way the market has been instituted" (609).

Orthodox economists are so enamored by perfect competition that they are wont to construct real world economies to conform to the idealized PCM, a veritable blending of idealization and ideology (Thurow 1983, 21; Canterbery 1987, 181-2). A labor union, viewed as an imperfection within the PCM, is also viewed as an imperfection in the real world since it prevents the realization of the ideal. Thus, policies that strengthen labor unions and move society away from the nineteenth century ideal of perfect competition are not endorsed by orthodoxy.

Labor unions, like all institutions, are not infallible. But to judge a labor union against an idealized standard which itself is obtained only by ex post facto violations is an invidious and undeserving stigma that needs to be erased. While it is unrealistic to expect orthodoxy to jettison the PCM, or to attenuate its anti-union bias, at the very least it is hoped that this paper will expose this enabling myth and demonstrate that labor unions are essential even within the PCM. As Stephen Woodbury has noted, "Collective bargaining is one method of handling the problems that inevitably arise in relations between workers and management" (1987, 1786). Not only is this patently true in the real world, but as this paper has demonstrated, patently true in the idealized PCM world as well. Rather than idealize a nineteenth century Utopia, orthodoxy should create and support institutions that enable all to participate and reach their full potential.