the deceptively simple economics

The Deceptively Simple Economics of Workplace Diversity

EVAN O S B O R N E

Wright State University, Dayton, OH 45435

Legal, scholarly, and public discussion of work force diversity has proceeded largely without benefit of microeconomic theory. Existing analysis relies on incomplete information to explain why firms might have "unrepresentative" work forces. I buiM a model in which work force composition matters even given full information. My analysis both explains current labor-market trends and raises questions about the use by courts and government agencies of statistical evidence to test for employment discrimination.

I. Introduction

In recent years considerable effort has been devoted to enhancing "workplace diversity." Efforts to make work forces more closely "look like" some larger population take different forms. In the U.S., firms adopt, either on their own or with judicial prompting, work force composition targets.l In India, some university admissions and government jobs are reserved for various castes and ethnic groups. 2 In Canada, the Employment Equity Act requires employers to ensure "that persons in designated groups achieve a degree of representation in the various positions of employment with the employer that is at least proportionate to their representation (i) in the work force, or (ii) in those seg- ments of the work force that are identifiable by qualification, eligibility or geography and from which the employer may reasonably be expected to draw or promote employees.'3

The popular and scholarly discussion (e.g., Selmi, 1997) of work force diversity has charged ahead with little theoretical assistance from economists. I examine the question of the optimal mix of employees for a profit-maximizing firm. The existing economic analysis of this issue revolves entirely around incomplete information and assumes that diversity cum discrimination is a function of networks based on ethnic familiarity (Powell and Smith, 1994; Cornell and Welch, 1996) or reflects statistical discrimination (Coate and Loury, 1993; McCall, 1972; Selmi, 1995). Another ancestor of this paper is Breit and Horowitz (1995), who depict the optimal diversity of an unspecified institution as a trade-off between the transactions costs of dealing with members of different groups combined with a taste for variety in social interactions. They do not, however, explore why an organization might prefer more diversity to less. 4

I argue that the group composition of a work force can matter even under full information. Jurisprudence and legal scholarship can benefit from such an analysis, as they are dominated by a strain of thought best summarized by the Supreme Court in

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1977 in International Brotherhood o f Teamsters v. U.S.: "It is ordinarily to be expected that nondiscriminatory hiring practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired. ''5

There is as yet no economic analysis of this proposition's validity and, in particular, of such terms as "qualifications" and "eligibility." I provide a compact description of what a work force should look like, so that meaningful comparisons can be made with reality. The model can also accommodate, where appropriate, the claim of Team-

sters that the proper comparison is between a firm's work force and the general population, which turns out to be true only under some circumstances even after considering productivity differences among groups. In addition to its theoretical insights, the paper should aid courts in determining whether discrimination has occurred. Section II pre- sents the basic model; Section III describes its equilibrium and comparative statics; Section IV extends it to analyze other workplace-diversity issues; and Section V exam- ines its public-policy relevance.

II. T h e B a s i c M o d e l

At first glance, concern for workplace diversity as such is puzzling given full information. Why should a firm prefer a work force with certain proportions of "profiles" (e.g., race, ethnicity, national origin, sex, and age) to any random sample of workers? Pro- file-specific requirements imply that employees of different profiles contribute to profit in differing proportions. One way to think about the problem is as a firm that manu- factures one product for sale in many markets. The product contains multiple characteristics, and each market values only some of them. The firm seeks the optimal combination of characteristics, given that product demand in each market differs depending on the mix of characteristics and that the cost of producing each characteristic varies. For example, a newspaper firm may operate in a city with a large number of ethnic groups which, ceteris paribus, will pay a higher price for the paper if the paper's coverage of its community is greater. In a public-sector context, it is often asserted that police officers of particular ethnic groups are best-suited to patrol neighborhoods populated substantially by those groups. The analysis will readily generalize to the case in which profiles as such are irrelevant to profits. This baseline model may describe many manufacturing work forces. For example, the ethnicity of the automobile worker who installs the clutch is likely to be irrelevant, ceteris paribus, to both the rate at which he can install them and to consumers' willingness to pay for the car.

Demand. Let there be m profiles, indexed by i. Each profile defines a market, a type of worker, and a characteristic. Each market contains some number n i of identical consumers. Demand for the product in each market is given by

Qi = niaixi - P" (1)

x i is the amount of characteristic i contained in each unit of the good sold to consumers of profile i, Qi, and P is the product's price. Equation (1) is thus a horizontal

EVAN OSBORNE 465

summation o f n i identical demand curves, Qi = a i x i - P" ai scales the willingness to pay of an individual in market i, given the amount of "his" characteristic x i in the product. a i depends on such conventional factors as consumer wealth and the elasticity of sub- stitution between the good and other unmodeled goods. Arbitrage insures that the price is identical in all m markets.

This depiction of product demand assumes that consumers in each group are exclu- sively concerned with price and the amount of "their" characteristic per unit of Q i " In reality, consumers might be interested in general characteristics (e.g., world or national news) as well as characteristics of particular interest to them (e.g., coverage of their community), but both assumptions allow for more clarity as well as less cumbersome mathematical notation. Either one could be relaxed without affecting my main conclusions. A general version of the problem, which does not allow for closed-form solutions but can accommodate this and other less-restrictive assumptions, is found in an appen- dix available to readers on request.

Supply. Characteristics are each produced according to

X i = L ? i. (2)

Ct i measures marginal productivity, and L i is the labor of profile i hired. Equation (2) reflects the idea that members of a particular group are the only ones able to produce characteristics of value, broadly defined, to that group. Assume ~ i < 1 V i, so that labor yields diminishing returns in the production of all characteristics.

There is again some simplification in assuming that characteristic i can only be produced by hiring workers of profile i. Any characteristic valued by one market might be produced, perhaps at greater cost, by workers of other profiles. The implications of relaxing this assumption are explored in Section IV. In addition, productivity is for now assumed to be immutable. 6

The cost of producing a given amount of characteristic i in a single unit of output, called r Wi) , is obtained by inverting (2):

-0~ i C i ( X i , W i ) = W i X i . ( 3 )

Assume that the firm is a price taker in labor markets, w i is the exogenous wage for each worker in group i and is a function of the other opportunities available to each group. 7

The next step is to convert the production of characteristics into the production of output. In this framework each unit of output is simply a basket of characteristics, and I temporarily assume that it is costless to bundle characteristics together as output. The cost of producing any amount of output, C(Q, w, x), is then simply the amount of output multiplied by the cost of characteristic production in each unit of output: 8

m m rn -~

C(Q,w,x) = Qi=I ]~ ci(wi'xi) = (,~=lQi)(,~lWi'Xi'= = ). (4)

Note that total output Q is simply the sum of sales in all m markets, so that Q = Z Q i.


Ill. E q u i l i b r i u m a n d C o m p a r a t i v e S ta t i c s

The firm maximizes profits subject to wages, characteristic technology, and demand. Its profit expression is thus

ni~ = (mt~ = -~i rt = e Q i - [Qi wi,xi )]- i=1 1 1

(5)

Since the industry is competitive, a firm treats its price as exogenous, and the only choice variables in its optimization problem are characteristics x r The marginal cost of producing another unit of x i is

MCi = ( w i / o ~ i ) x i ( l - a i ) /~ ~ Qi. i=1

(6)

The additional cost of another unit of a characteristic in one unit of output is multiplied by total output sold in all m markets (ZQi). The model is closed by the standard equilibrium condition for perfect competition: namely, price must equal average cost of a unit of output. Note: While the individual firm optimizes over characteristics, competitive equilibrium requires that the total cost of each identical unit of output, which is the sum of characteristic costs, equal the price for the entire product. Substituting from equation (3), the equilibrium condition is thus:

m -O~ i

P = Y~ w ix i . (7) i=1

Thus, total revenue at any production level is given by

m m m m --0~' - O P

TR=P ]~ Qi = ]~ wix i t( E n ia i x i -m E wix i t). i=1 i=1 i=1 i=1

(8)

Differentiating equation (8) with respect to X i yields the marginal revenue pro- vided by another unit of x i. Equating it to the marginal cost of characteristic i in equation (6) and substituting for both the various Qi via equation (1) and for price via equation (7) gives the equilibrium condition:

. . ( l_~ i ) / t~ i m m m Wi/(Xi)Xi i=1• niaixi -- 2m(wi/~i)xi(l-ai)/~ti i=IZ wixi -~ + nia i i~=lWiXi -~i.

m

. , . (1-~i)/ct i ~ niaix i - m(wi/(Xi)xi (l-~176 ]~ Wixi -~ = ~Wi/O~i)X i i=1 i=1

(9)

After collecting terms, equation (9) reduces to the solution for xi:

X; = ~176 [ (niai~i) / (mwi) ] (10)

EVAN OSBORNE 467

Note that there may be a comer solution, i.e., one in which at competitive equilibrium some markets do not purchase the product. In that case, firms will produce no x i for those markets and hire no workers of that profile. The competitive price is then calculated by only considering the cost of producing for the remaining markets. The entry into new markets when comer solutions are no longer optimal because of parameter changes is explored in Section IV.

Labor hired is obtained by inserting the expression in equation (10) back into the production function:

L? = . . . . . . . 1/(1-0~i) , l(niaiOti)/(mwi)l (11)

From inspection of equation (11), the following comparative-statics proposition is obvious:

Proposition 1: Equilibrium labor hired from profile i is an increasing function of market size (ni) and the parameter denoting willingness to pay for individuals of profile i (ai) and a decreasing function of the wage for workers of that profile (wi).

More labor of a particular profile will be hired as market demand for the characteristic produced by workers of that profile is greater or the cost of hiring those workers is lower. These results are as expected, but the relation between physical productivity and hiring is surprisingly ambiguous:

Proposition 2: Labor of profile i is an increasing function of productivity of type i only if the number of other markets is sufficiently small and~or the wage for profile i is sufficiently small or demand in market i is sufficiently high.

Proof" Differentiating equation (11) with respect to d i yields the comparative-statics derivative

dL i 1~(1-or i) [(2-ai)/(l-cti)] 2 (--j-S-Z) = (x i [(niai) / (mwi) ] [1 / (1-ai ) ] log[(nia i~i ) / (mwi)] . (12 )

utL i

This expression is positive if and only if

1 < (niaitxi)/(mwi). (13)

Inequality (13) can be rearranged as

(mwi)/(niai) < o~ i. (14)

If the inequality is reversed, a rise in a i lowers the firm's equilibrium hiring of workers of profile i.


Intuitively, an increase in physical productivity a i will lower the production cost of a unit of x r However, increased production of that characteristic makes the product more valuable to consumers in market i. They bid up its price, lowering quantity demanded in the other m - 1 markets. If the negative effect on profits in other markets is sufficiently large relative to the positive effects on own-market profits, then each finn responds to greater productivity by reducing the use of more-productive group i labor. Thus, if there are many other markets or the wage in market i (wi) is sufficiently high, the intercept and market size in market i (ai, ni) are sufficiently low or the productivity parameter (O~i) is sufficiently high, the latter effect dominates and an increase in a i leads to a decrease in L i.

Equation (14) reveals the importance of other-market effects. The finn must take account of sales changes in other markets when it adjusts the product's characteristic mix in response to increased labor productivity in that profile. For example, if the level of general human capital (e.g., education) in workers of a particular profile rises, rais- ing their productivity in manufacturing "their" characteristic, the firm does not neces- sarily hire more workers of that type.

IV. Extens ions and Impl icat ions

This section extends the basic model. The formal requirements to obtain the results are available to readers on request.

Entering New Markets. If a market's willingness to pay (given by ai) or size (given by ni) is sufficiently low relative to the cost of producing its characteristic (given by a i, wi), it may be optimal to avoid the market entirely, so no workers of this profile are hired. Over time poorer markets may become wealthier, the comer solution may no longer be optimal, and finns will seek to (further) diversify their work forces by adding workers from the new market. For products with highly profile-specific characteristics, increased diversity may be essential as new markets arise (e.g., through immigration) and become more prosperous. Firms in such industries that diversify their work forces will succeed at the expense of those that do not. Firms in cultural industries, such as media products and recorded music, may find greater diversity particularly compelling, for reasons described below, as more markets raise their willingness to pay as their wealth increases.

Other Workers As Imperfect Substitutes. The basic model can also be extended by allowing other workers to produce characteristics, albeit at higher cost. Under such circumstances a finn may desire a multi-profile work force even in the production of a particular characteristic. In this case, profit maximization requires that each worker's marginal revenue product be equated to his wage in the production of all characteristics, not just the own one. A firm will hire workers from all groups for which the marginal productivity of the first worker exceeds that worker's wage. Even if workers (e.g., reporters) of one profile are the best at producing a characteristic (e.g., covering that community), workers of other profiles may be hired to do so if they are sufficiently productive relative to their wage. Other things (including wages) equal, characteristics

EVAN OSBORNE 469

will still be produced disproportionately by own workers, but work forces with some or all groups hired to produce characteristics are certainly possible.

Bundling Costs. I have assumed that it is costless to integrate workers of different profiles. But there may be "bundling costs" associated with, for example, training workers of different profiles to work together or with workplace frictions among such workers. Such bundling costs could occur when multiple types of workers produce the same characteristic, as discussed above, or in the one-profile, one-characteristic basic model. In the former case, sufficiently high bundling costs would lead firms to use only the workers who can most efficiently produce a given characteristic. To hire workers of a particular type to manufacture a characteristic to which they are not best-suited might be optimal in the absence of bundling costs but not with them.

In the basic model, a firm may again elect not to enter certain markets because the bundling costs of incorporating the new workers exceed the benefits of producing for those consumers. A newspaper fearing that productivity will suffer when its existing work force is combined with the workers needed to serve a new market may elect to leave it unserved. In other words, it will only cover that community to the extent that other markets are interested in it. Even if there are economies of scale or scope in serving joint markets, such economies can be outweighed by bundling costs. If such costs decline (for example, because employee hostility to different types of workers has declined) characteristic production and employment will become more diverse, particularly if productivity differences are not great across profiles, and firms will expand into more markets.

There is some evidence that bundling costs deriving from animus by workers toward workers of different profiles have diminished. Data compiled by the National Opinion Research Center and various polling organizations indicate sharp increases in the last fifty years in the percentage of whites who believe that blacks should have as good a chance as whites at any sort of job and who are willing to live in integrated neighborhoods and to send their children to integrated schools (Schuman et al., 1997). Although such data are not a perfect proxy for the issue of interest here, the costs involved when workers of different profiles work together, they do allow the inference that such frictions have declined significantly during this period. 9 Such declines in bundling costs are surely an important factor in the drive by many large employers to diversify work forces, coming on the heels of efforts in the 1960s to persuade consumers and prospective employees that if profiles were irrelevant to productivity they were irrelevant to compensation (e.g., claiming to be an "equal-opportunity employer").

A decline in bundling costs in profile-specific industries can mean that larger firms serving many markets becomes a more efficient market structure than highly special- ized firms serving one or a few profiles. For example, in cultural industries, such as recorded music, lower bundling costs should cause a change from many smaller firms specializing in one type of music to fewer broader firms serving many markets. Alexan- der (1994) has documented continuing consolidation in the recorded-music industry starting from the mid-1960s. Although he attributes it without further explanation to


technological shocks, the demand-side considerations outlined here may also play a role. Increasing wealth in historically less-served communities has induced larger firms to enter such markets and recruit the necessary work forces or to absorb the existing labels serving them. Consistent with the hypothesis, the increased efforts of mass-market news organizations to diversify their work forces is documented in Shepherd (1993). Although rigorous empirical evidence on concentration in news and cultural industries other than music is still absent, such concentration is increasingly noted (often with concern) by commentators. 10

V. From Theory to Evidence: Discrimination, Diversity, and the Law

The Law. In addition to explaining work force-diversity patterns, the theory is helpful in analyzing current antidiscrimination law and its enforcement) l The two primary governing rulings are Regents of the University of California v. Bakke 12 and Teamsters. The former defined the ways in which race and sex can be used in allocating job and other opportunities, while the latter described the proper role for statistical evidence. In Bakke the Supreme Court held that allocating such openings in education, employment, or elsewhere strictly on ethnic criteria is prohibited. However, ethnicity and sex may be used as one factor among several to distinguish among otherwise qualified candidates, and the ruling legitimized "temporary hiring remedies insuring that the percentage of minority group workers in a business or governmental agency will be reasonably related to the percentage of minority group members in the relevant population" (at 353).

In statutory law, Title VII of the Civil Rights Act of 1964 prohibits both "disparate treatment" by finns, i.e., willful discrimination against protected profiles, and proce- dures (e.g., job-skills tests) that have "adverse impact" on some profiles' wages and hiring. 13 With respect to the latter, Bakke and subsequent jurisprudence have estab- lished three conditions that must be satisfied to establish that an employment practice is discriminatory. The practice, though facially neutral (i.e., lacking group-specific requirements), must first cause outcomes (such as pay or promotion rates) that are significantly different for different profiles. Assuming the practice is clearly related to the job, there must be no alternative practice that achieves the same objectives without racially disparate results. The plaintiff can prevail if a facially neutral practice is meant to disguise actual discrimination. The defendant is allowed to present a defense of"bona fide occupational qualification" with respect to hiring based on sex, religion, and national origin, but not for race-based hiring) 4 Although Title VII originally did not allow an employer to offer "business necessity" as a defense to a claim of intentional discrimination, 15 the Supreme Court in Wards Cove v. Atonio accepted it if "a chal- lenged practice serves, in a significant way, the legitimate employment goals of the employer. ''16

A court may order a defendant held in violation to adopt plans with profile targets. In either case, the U.S. Supreme Court has allowed as evidence measures of disparities between work force composition and the population "qualified" to perform the job, as well as similar comparisons with respect to compensation and promotion. While Wards

EVAN OSBORNE 471

Cove significantly restricts the ability of public entities to implement group-specific hiring practices absent a specific history of discrimination, City of Richmond v. J. A. Croson upheld the ability of courts to mandate such programs for private entities in response to Title VII violations.l 7

Beyond Physical Productivity: A Superior Definition of Efficient Work Force Com- position. My analysis is a step forward in assessing "qualifications," the "relevant population" and other guidelines for government investigators. The public and scholarly discussion of whether groups are over- or under-represented in employment at particular finns, of which the excerpt from Teamsters in the introduction is eminently representative, has two weaknesses. The first is an erroneous definition of "qualifications." There is an exclusive focus on real or spurious differences in "physical productivity," i.e., whether different types of employees can produce different amounts of identical widgets. Work force composition is also compared to the makeup of some broad sur- rounding group, such as the population of the city or county of a company's labor market. The second problem is that the discussion ignores random variation in work force composition from firm to firm in a given industry. Such variation can be analyzed only after the expected work force is defined.

The analysis above provides a novel way of testing for employment discrimination. Discrimination occurs when the number of employees of a profile(s) is more or less than profit maximization would dictate (customer preferences for particular types of employees aside). Theories of why such behavior could survive in a competitive envi- ronment include a widespread taste for discrimination (Becker, 1971) or the asymmet- ric-information models cited in the introduction. My goal is to provide the proper baseline for measuring a finn's work force.

In legal scholarship, the description of what constitutes an optimal work force has often been reduced to an assertion, sometimes supported by casual economic sketches, that work force profile composition should closely resemble that of the population. Typical in this regard is the assertion by Katz (1991, p. 1037) that, given "no systematic differences in productivity between racial groups," the "representation of each race in the work force, or of any employer within such an industry, should approximate its representation in the general population" Such an analysis echoes uncritically the word- ing of Teamsters and begs the question of what "systematic differences in productivity" are.

Current legal scholarship and jurisprudence neglect the extent of characteristic- specific market demand. The traditional analysis can be represented by first defining a base case in which demand in each market is a function only of price and not product characteristics:

Pii = aini- Qi" (15)

Output is given by Q = L i a , where c~ is a profile-invariant productivity measure. In this case, it is trivial to sum the individual market demand curves and (assuming that the firm cannot price discriminate in the m different markets) obtain the optimal equi-


librium price, which then translates into m different Qi" There is then no reason that the typical finn's labor force should look any different from the population to which it markets the product, adjusted by differences in wages, w r The only step from here to the default legal reasoning in Teamsters and elsewhere is to incorporate differences in c~ i, which absent characteristic-based demand essentially measures general human capital. Reflexively assuming that this specification is true will lead to mistaken inferences about the presence of employment discrimination.

The Role of Random Variation. It is also critical to include the qualifying adjective "typical" above, because it is in industries described by equation (15) that random variation should be greatest. While a record label may require a very precise distribution of employee profiles, a firm for which profile composition is irrelevant is equally happy (absent bundling costs) with any random draw of workers. In the former the variation among firms will be small, but significant random differences may occur in the latter.

For any finn, the smaller the work force the greater the probability of failing a conventional statistical test of population versus actual work force composition. To claim that a firm discriminates is to reject a null hypothesis that the observed work force differs from the calculated optimal one because of chance. If each of h identical firms has 1 i workers and there are N workers in the population, so that hl i = N, then a conventional statistical test for discrimination takes the form

([1 i - Li[)/h < 13, (16)

where L i is the solution to (11) and 13 is the chosen standard of tolerance. 18 The left-hand side of (16) measures the firm's departure from expected optimal employment of profile i, and the probability that (16) is not satisfied is, by the Chebyshev inequality, greater as firm size is smaller. It is, however, true that if most or all firms in an industry fail such a test there is a stronger prima facie inference of industry-wide discrimination.

Defining Diversity Properly. Although current scholarship does not indicate it, the information requirements for current legal standards include both productivity and demand components. A three-part test for efficient diversity may thus be proposed: The optimal diversity of a firm's work force depends on the dispersion of demand for valued characteristics among identifiable markets (a i, ni), the specificity of the link between employee profiles and the production of these characteristics (o~i), and the cost of workers of different profiles (w/). A focus on physical productivity alone neglects significant components of the profit-maximizing firm's problem.

As a final caveat, the definition of the variables in the model, particularly the characteristics, is crucial. As argued above, national origin, race, and (usually) religion should be typically irrelevant for a manufacturing work force. 19 As an expectation, population diversity might be an excellent predictor of work force diversity in such a case, but random variation might lead to much greater departures for an automobile company than for a mass-market newspaper. This is because there is a very precise optimal profile composition in the latter case, while in the former any equal-sized random sample of equally productive workers yields the same profits.

EVAN OSBORNE 473

On the other hand, if employees of a particular profile are more productive in mar- keting automobiles to consumers of that profile and profiles differ in willingness to pay, then sales volume is the relevant "output" and the greater population is now a precise predictor of profit-maximizing diversity after it has been adjusted for demand differences in the various markets. For this class of employees the automobile firm will thus have a very precise index of optimal work force composition. In using employment, promotion, or wage statistics to infer discrimination, it is thus critical to define carefully characteristics, the extent to which producing them is specific to particular profiles, and the extent to which demand in different markets varies based on them. Such care would lessen the problem of probabilistic liability alluded to above and any presumption that firms for which market conditions in fact prescribe very precise work force composi- tions are discriminating. Finally, properly defining characteristics and their relation to employee profiles would prevent a finn that is engaging in Beckerian discrimination from claiming that it has few workers of a particular profile because it does not produce for that market. Such an argument will require proof of a relationship between an employee's profile and the product's characteristics, as well as a link between characteristics and product demand.

Finally, the analysis is somewhat similar for non-profit-maximizing entities, although their objective functions will surely be different. A university, for example, may know that students of a particular profile will only attend if there are a sufficient number of other students of that profile, and thus may find it optimal to pursue that group more intensively. Indeed, some institutions may view diversity as an objective in itself, because it directly contributes to, for example, the quality of education offered. This assertion is commonplace in educational and legal scholarship (Brest and Oshige, 1995).

VI. Conclusion

My approach for the first time connects profit maximization to work force composition given full information. Physical productivity, which dominates so much popular discussion of this issue, matters, but demand-side factors are also important. Defining a firm's optimal work force composition is nonsensical until at least the product's characteristics, the extent to which different markets value them, and the extent to which groups inherently differ in their capacity to provide them are precisely defined.

While the insights herein are derived from a basic model with full information regarding both supply and demand, it would be revealing and another departure from the existing literature to consider demand uncertainty. It may be that differences in consumer demand across profiles are uncertain, and thus more diversity is, up to a point, preferred, because more information is imparted to the firm about the product's markets. Such analysis would go hand-in-glove with the production-side analysis of the need to diversify work forces that can be inferred from statistical-discrimination models. Assumptions of this type might yield conclusions more in line with those of the immense biological literature on species diversity, which frequently argues (Goodman, 1975) that greater diversity is axiomatically better than less.

474 J O U R N A L OF L A B O R R E S E A R C H

N O T E S

1For example, Executive Order 11246 requires that federal supply and service contractors file an "affirmative action plan" that outlines their attempts to address underutilization of women, minorities, veterans, and others. Underutilization is defined in federal regulatory code at 41 CFR 60.2. i 1 as "having fewer minorities or women than would reasonably be expected by their availability."

21ndia's "reservations" program is described in Galanter (1991). The Indian government has considered but has not yet implemented reservations in private employment.

3Employment Equity Act, R.S.C. 1985 (2d Supp.), c. 23.

4Weitzman (1992) also explores optimal ecological diversity given that preserving it is costly, but again does not investigate the utility of greater diversity.

5431 U.S. 324.

6If this assumption does not hold, a worker might, for example, acquire language skills that would enable him to better produce a characteristic.

7Note that if there is a single alternate industry in which profiles are completely irrelevant, this reservation wage will be the same for each group.

8C can be compared to the standard textbook cost function. Its mathematical characterization is min wL s.t. X =f(L), where w and L are vectors of dimension m and X is an m • m diagonal matrix.

9They are also imperfect, though still suggestive, because of the increasingly multi-ethnic nature of U.S. neighborhoods, schools, and workplaces.

l~ an example, see Frank Rich, "Milli Vanilli News," New York ~mes, July 8, 1998.

1 qn what follows I take as given the objective of antidiscrimination law, that profiles should be irrelevant to hiring and compensation unless they intrinsically affect profits. One case in which profit maximization is never legal is customer taste for employers of particular profiles. It is illegal under antidiscrimination law to provide consumer surplus in this manner. See EEOC (1997), p. 3958. The governing case is Diaz v. Pan

American WorldAirways, Inc., 442 F.2d 385, 3 EPD & 8166 (5 th Cir. 1971), cert. denied.

12438 U.S. 265 (1978).

1342 U.S.C.A. w

1442 U.S.C.A. w (sex, religion, national origin), 42 U.S.C.A. w (race).

1542 U.S.C.A, w

16490 U.S. 642 (1989), at 659.

17488 U.S. 469 (1989).

iSFor ease of illustration, the term "population" is used under the assumption that the only industry is the one under examination. With multiple industries competing for the same pool of workers the analysis is more cumbersome but perfectly straightforward.

19Religion might be relevant if the employee's religious beliefs prohibit either working on certain days on which the employer has a compelling need to produce or certain employment practices.

EVAN OSBORNE 475

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