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Nepotism, discrimination, and the persistence of utility-maximizing, owner-operated firms: comment.

1. Introduction and Conclusions

In a recent thoughtful paper in this Journal, Singell and Thornton (1997) (hereafter ST) deviate from the traditional literature on discrimination that originates with Becker (1971) and Arrow (1972a, b, 1973) in three significant respects.(1) This comment criticizes these deviations, showing that the ST astonishing result that discrimination will persist in a competitive labor market is unjustified, that their unconventional definitions of owners with unbiased and biased preferences contradict an established result of economic theory, and that their unique attempt at modeling discrimination and nepotism is problematic, too. The next three sections deal with these issues in the above order.

The shortcomings of the ST analysis are due to two oversights: First, ST's crucial assumption that a positive externality arising from the ability to choose employees confers utility on the nonmarket goods discrimination and nepotism is unjustified. ST ignore the possibility that both discriminating and nondiscriminating owners may equally enjoy the process of choosing employees per se and that both types of owners (may) derive the same amount of utility from owning firms. Thus, discriminating owners lose an advantage that is wrongly conferred upon them by ST, and the ST result of the persistence of discrimination no longer holds. Second, ST overlook a basic result of economic theory that suggests that, in addition to tastes for discrimination (and nepotism), a crucial role in determining a desired composition of an owner's workforce is played by the differences in market wages of groups. Thus, ST's omission of the role of wage differentials is responsible for the shortcomings of their definitions of owners with biased and unbiased preferences and of their modeling of discrimination and nepotism as nonmarket goods.

By their very nature, the issues of defining and modeling tastes for discrimination and nepotism take economists to uncharted waters. This is partly responsible for the shortcomings of the ST model that this comment identifies. Thus, in order that further modeling in this area will be based on more sound foundations than economists' speculations, it may be advisable that theories and empirical evidence that other social scientists, like social and industrial psychologists or sociologists, have to offer will be taken into account.

2. Persistence of Discrimination in Competitive Labor Markets

ST claim that their "paper is the first to explicitly demonstrate how an owner operator who discriminates trades nonmarket for market consumption, and, thereby, can potentially compete and persist in a market with profit-maximizing firms" (1997, p. 916; emphasis added). The claim seems to be based on the ST modeling of discrimination as a nonmarket good yielding utility for a biased owner. As a result, they reach the astonishing result that discriminating firms will survive competition from otherwise identical but nondiscriminating firms.(2) This section suggests two arguments that cast doubts on the validity of the claim.

The first argument focuses on ST's justification for modeling the nonmarket good discrimination as yielding utility. Such a justification is crucial since the ST result about the persistence of discrimination stands or falls with it. Unfortunately, ST do not explain their attribution of utility to the nonmarket good discrimination except for claiming that "both nonmarket goods [nepotism and discrimination] provide a positive externality that arises from the owners' ability to choose who they employ" (1997, p. 907; emphasis added). However, even if an ability to choose employees was viewed by owners as yielding a positive externality, this would have not implied that practicing discrimination (or nepotism) per se must yield a positive utility, too. An ability to choose employees is a precondition for practicing discrimination (and nepotism), but this does not imply that the utilities from these two types of activities are synonymous or related in any particular way. Owners may enjoy being bosses and the activity of choosing employees whether they enjoy practicing discrimination (or nepotism) or not. And owners may be involved in the activity of discriminating against (favoring) a group whose employment reduces (increases) their utility as assumed by Becker and Arrow whether the activity of choosing employees per se is regarded as pleasant, unpleasant, or neutral. Thus, contrary to the ST claim, any utility derived from the mere activity of choosing employees does not provide discriminating owners an advantage over nondiscriminating ones who are otherwise maximizing profits. One has to conclude that ST do not provide a justification for their view that the nonmarket good discrimination yields utility and that their result regarding the persistence of discrimination is unsupported.(3)

A second argument suggests that, even if their modeling were correct, ST's claim would have exaggerated what could be proven. According to the ST model, the quantity of the nonmarket good discrimination (or nepotism), denoted by d (or n), is positive and yields utility if an owner's workforce composition is such that D/E [less than] [Beta] (or N/E [greater than] [Omega]), where [Beta] and [Omega] are, respectively, the proportion of the discriminated against and the favored groups in the labor force, D and N are, respectively, the number of workers from these groups that the owner employs, and E is the total workforce of the owner. As well, one can deduce from the first-order conditions of the ST model that an owner's optimal workforce composition depends on the wage differentials facing the owner and the owner's intensity of tastes for discrimination and nepotism (i.e., Becker's coefficients of discrimination and nepotism). Thus, a discriminating owner may well find it optimal to employ such a workforce composition that D/E [greater than or equal to] [Beta] and N/E [less than or equal to] [Omega]! And if wage differentials do not change because the labor market is already in equilibrium, there is no mechanism that ensures that owners with such workforce compositions will change them to those suggested by ST One has to conclude that ST cannot prove that d, n [greater than] 0 or that discrimination and nepotism necessarily yield utility even within their model.

3. Definitions of Owners with Unbiased and Biased Preferences

According to the ST definition, owners with unbiased preferences employ N/E = [Omega] and D/E = [Beta] and owners with biased preferences employ N/E [greater than] [Omega] and D/E [less than] [Beta]. ST ignore the possibility of owners who employ N/E [less than] [Omega] and D/E [greater than] [Beta] and leave their preferences undefined. This is unsatisfactory for two reasons: First, it was claimed in the previous section that a utility-maximizing owner might find it optimal to employ such a workforce composition. And if the market is in equilibrium, there is no mechanism that ensures that owners with such workforce compositions will not exist. Second, unless all owners have the same workforce composition of N/E = [Omega] and D/E = [Beta], there is a mathematical requirement that the said owners must exist. Under full employment, the weighted average of all the owners' workforce compositions have to be equal to [Omega], [Beta] for the said two groups of employees (N and D, respectively). And if some owners employ N/E [greater than] [Omega] and D/E [less than] [Beta], there must be others for whom the workforce compositions are N/E [less than] [Omega] and D/E [greater than] [Beta]. When there is unemployment, the argument is still valid, except for minor changes.(4)

It is clear that the ST definitions miss a group of owners that belongs in the analysis. If owners that employ N/E [greater than] [Omega] and D/E [less than] [Beta] are defined as having biased preferences and those that employ N/E = [Omega] and D/E = [Beta] are defined as having unbiased preferences, one wonders how ST would define the preferences of owners who employ N/E [less than] [Omega] and D/E [greater than] [Beta]. It must be concluded that the ST definitions leave much to be desired.

This discussion suggests that ST's attempt to classify discriminating and nondiscriminating owners on the basis of their observed workforce compositions is unsatisfactory. The traditional Becker-Arrow definitions that are based on whether employment of groups per se have direct effects on owners' utilities seem to be a better and more logical way of characterizing owners' preferences.

4. Modeling Nepotism and Discrimination

ST model quantities of the nonmarket goods discrimination and nepotism by the respective production functions d = [Beta] - [Phi](D/E) and n = [Phi](N/E) - [Omega] and the implicit assumptions of d [greater than or equal to] 0 according to whether D/E [less than or equal to] [Beta] and n [greater than or equal to] 0 according to whether N/E [greater than or equal to] [Omega]. Such modeling has two attractive features. First, the traditional Becker-Arrow modeling can be interpreted as assuming that d = D and n = N, so that the effects of owners' interactions with the discriminated against and preferred groups depend on their absolute numbers, D and N; the ST modeling suggests that they depend on their relative numbers, D/E and N/E. The latter formulation is as plausible as the former. Second, the ST modeling suggests that the labor force composition in the market, [Beta] and [Omega], affects the production of the nonmarket goods discrimination and nepotism by the firms. Put differently, the intensity of owners' feelings of discrimination (nepotism), or the disutility (utility) it yields, is predicted to change directly with (inversely to) the proportion of the discriminated against (preferred) group in the market labor force. The traditional modeling usually abstracts from this factor. However, it is exactly this situation that makes Cain (1986, p. 716-7) uneasy and is at the heart of his objection to an application of the nepotism model to whites in the U.S. "who constitute 85 percent of the labor force." As well, the ST modeling receives support from some social psychologists, for example, Allport (1954, p. 227-9), who see its merits.(5)

This discussion implies that discrediting the ST definitions of owners' preferences in the previous section does not automatically discredit their modeling of the nonmarket goods nepotism and discrimination. ST's specific formulation, that is, the above production functions of d and n, has to be evaluated on the basis of its own merits or shortcomings.

The problem of the ST modeling is that it disregards the case of owners who employ N/E [greater than] [Omega] and D/E [less than] [Beta]. ST are wrong to have ignored it for two reasons. First, as was already suggested, when owners are free to choose who they employ, this case cannot be ignored on the pretext that it is only temporary because there may be no market mechanism that ensures that. Second, since ST are explicit in viewing the production functions of d and n as technological relationships, there is a need to determine the values of n and d when an owner is forced to employ N/E [less than] [Omega] or D/E [greater than] [Beta] by circumstances such as pure chance or a union.(6)

When determining the values of n and d, it is tempting to suggest that the production functions of d and n imply that d [less than] 0 when D/E [greater than] [Beta] and n [less than] 0 when N/E [less than] [Omega]. Unfortunately, there seems to be no economic meaning for a negative quantity of a nonmarket good that reflects feelings such as discrimination or nepotism.(7) ST could have avoided the problem by defining the nonmarket goods so that, when D/E [greater than] [Beta], [Phi](D/E) [equivalent to] [Beta] by definition and d [equivalent to] 0, and when N/E [less than] [Omega], [Phi](N/E) [equivalent to] [Omega] by definition and n [equivalent to] 0. The disadvantage of such a solution is that it is arbitrary.

A more viable solution to the above problem is to adopt ST's ideas but to use them within a traditional Becker-Arrow model. Thus, the production functions of the nonmarket goods can be written as

d = [Theta](D/E, [Beta]) [[Theta].sub.D/E] [greater than] 0, [[Theta].sub.[Beta]] [greater than] 0, (1)

n = [Phi](N/E, [Omega]) [[Phi].sub.N/E] [greater than] 0, [[Phi].sub.[Omega]] [less than] 0, (2)

where [A.sub.i] is the derivative of A with respect to i. As well, one can specify that [U.sub.d] = [U.sub.n] = 0 for nondiscriminating owners and [U.sub.d] [less than] 0, [U.sub.n] [greater than] 0 for discriminating ones, where the owner is assumed to maximize the utility function U(d, n, . . .). And as suggested before, [Omega] and [Beta] are as perceived by the individual owner.

It seems useful to compare ST's formulation of the nonmarket goods nepotism and discrimination with their counterparts in the traditional literature, for example, Becker (1971) and Arrow (1972a, b, 1973). Translating the latter into the ST formulation, they become n [equivalent to] N and d [equivalent to] -D. The traditional modeling is based on the same sociological theory of personal interactions and social distance as ST's modeling. But as suggested above, the difference between the two models is that, in the traditional one, an increase in the absolute, rather than relative, number of interactions affects utility. It is interesting to note that, once the traditional modeling is transformed into an ST formulation, both nepotism and discrimination, that is, n and d, yield utility as in ST's model.(8) However, in the case of discrimination, this is only due to a mathematical manipulation rather than because discrimination yields utility!

1 ST do not replace the traditional framework because they identify shortcomings that they intend to overcome. Their rationale is based on their perception that it is wrong that, within this framework, "discrimination and nepotism which appear to be semantically equivalent, lead to opposite predictions for the long-run viability of utility-maximizing firms" (1997, p. 905). They refer to opposing predictions by Becker (1971) and Goldberg (1986). However, Sharir (1998) claims that the real culprit is the perception that these two models are based on identical (or semantically equivalent) assumptions.

2 ST are too cautious when they use the word potentially. Under their assumptions, an owner will increase the production of the nonmarket good discrimination (i.e., will discriminate) as long as its marginal utility is higher than its marginal cost (i.e., the marginal loss of utility from the inefficiency of production and a lower profit). Thus, contrary to Becker's model, the ST assumptions guarantee that discrimination does not disadvantage the discriminating owners.

3 The only idea that supports the ST view that this author can come up with is that discriminating owners may enjoy the turning down of job applications from the discriminated-against group. This idea implies that such owners must be disappointed when members of that group do not apply for a job in larger numbers since they are denied a source of raising their utility. While this is possible, the idea is not credible since it does not explain the behavior of discriminating owners. Contrary to what the idea would have predicted, there does not seem to be evidence that discriminating owners make more (than required) efforts to encourage job applications from the relevant group; if at all, the evidence is for the opposite behavior. Such evidence seems to contradict the ST view and to support the Becker-Arrow view about the (dis)utility from discrimination.

4 If the unemployed are D-type people, the existence of owners with D/E [greater than] [Beta] is no longer a mathematical requirement. However, there must still be owners who employ N/E [less than] [Omega], and they may well employ D/E [greater than] [Beta].

5 Note that Becker (1971, p. 117) thinks that the social psychologists misinterpret the data.

6 Another shortcoming of the ST modeling of n and d is the implicit assumption that the values of [Beta] and [Omega] are known. At issue is not only the dissemination of correct market statistics. Due to labor mobility (in and out of the labor force and among markets), there may be a question about the proper economic definitions of [Beta] and [Omega] in a market. This shortcoming can be overcome by arguing that the relevant [Beta] and [Omega] are either those deduced by owners based on their job applicants or they are as owners perceive them to be. In either case. [Beta] and [Omega] need not have the same values for all owners, but the ST modeling can be easily changed to reflect that by adding an appropriate subscript to them. However, within such an interpretation, affirmative action may also force owners to employ D/E [greater than] [Beta] or N/E [less than] [Omega].

7 Contrary to the Becker-Arrow treatment of discrimination as a bad and of nepotism as a good, ST treat discrimination also as a good. Within utility theory, the economic interpretation of a negative quantity of a good or a service is that the agent gives (sells) it away. There may be no economic interpretation for negative quantities of nonmarket goods that reflect feelings (of nepotism and discrimination) as they may not be discarded, given away, or changed. Note that the ST model of an owner's utility maximization is faulty because it does not take into account this economic and psychological constraint.

8 The traditional utility function can be written before and after the transformation as U(D, N, . . .) = U(- d, n, . . .) = V(d, n,...), where [U.sub.D] [less than] 0, [U.sub.N] [greater than] 0, D [equivalent to] -d, and N [equivalent to] n. One gets that [V.sub.d] = -[U.sub.D] [greater than] 0 and [V.sub.n] = [U.sub.N] [greater than] 0. Moreover, if [U.sub.DD] [less than] 0 and [U.sub.NN] [less than] 0, as is usually assumed, [V.sub.dd] = -[U.sub.DD] (1) [less than] 0 and [V.sub.nn] = [U.sub.NN] [less than] 0.


Allport, Gordon W. 1954. The nature of prejudice. Reading, MA: Addison-Wesley Publishing.

Arrow, Kenneth J. 1972a. Models of job discrimination. In Racial discrimination in economic life, edited by Anthony H. Pascal. Lexington, MA: Lexington Books, pp. 83-102.

Arrow, Kenneth J. 1972b. Some mathematical models of race discrimination in the labor market. In Racial discrimination in economic life, edited by Anthony H. Pascal. Lexington, MA: Lexington Books, pp. 83-102.

Arrow, Kenneth J. 1973. The theory of discrimination. In Discrimination in the labor markets. edited by Orley Ashenfelter and Albert Rees. Princeton, NJ: Princeton University Press, pp. 3-42.

Becker, Gary. 1971. The economics of discrimination. 2nd edition. Chicago: Chicago University Press.

Cain, Glen G. 1986. The economic analysis of labor market discrimination: A survey. In Handbook of labor economics, Volume I, edited by Orley Ashenfelter and Richard Layard. Amsterdam: Elsevier Science Publishers, pp. 693-785.

Goldberg, Matthew S. 1986. Discrimination, nepotism, and long-run wage differentials. Quarterly Journal of Economics 97:307-19.

Sharir, Shmuel. 1998. Employer's tastes for discrimination, nepotism and being boss: Modelling and implication for the persistence of discrimination. Macquarie Economics Research Papers No. 5/98.

Singell, Larry D., Jr., and James Thornton. 1997. Nepotism, discrimination, and the persistence of utility-maximizing, owner-operated firms. Southern Economic Journal 63:904-19.
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Title Annotation:response to Larry D. Singell, Jr. et al., Southern Economic Journal, vol. 63, p. 904, 1997
Author:Sharir, Shmuel
Publication:Southern Economic Journal
Date:Apr 1, 1999
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