I. Introduction, 395.—II. The model, 397.—III. Competitive entry and long-run equilibrium, 402.—IV. Welfare analysis of industry equilibria, 405.—V. Conclusion, 408.

[This paper models the dynamics of the earnings distribution among successive generations of workers as a stochastic process. The process arises from the random assignment of abilities to individuals by nature, together with the utility maximizing bequest decisions of their parents. A salient feature of the model is that parents cannot borrow to make human capital investments in their offspring. Consequently the allocation of training resources among the young people of any generation depends upon the distribution of earnings among their parents. This implies in turn that the often noted conflict between egalitarian redistributive policies and economic efficiency is mitigated. A number of formal results are proven which illustrate this fact.]

Affirmative action policies have come increasingly under attack in recent years. Both in the courts and in public discourse questions have been raised about the legitimacy of government efforts on behalf of blacks and other racial minorities.' The criticism seems to have two central themes. First, it is argued that those policies which have been tried have not had a noticeable effect on the economic standing of minority group members. (See James Smith and Finis Welch.) They thus constitute yet another example of costly but ineffective government regulation, according to this view. The second theme strikes more deeply at the foundation of these policies. Its adherents argue that even if effective programs could be designed, they ought not be implemented. There have been philosophical and empirical arguments advanced to support this conclusion. Essentially, the philosophical argument states that it is wrong for government to intervene on behalf of certain groups (and thus, necessarily, at the expense of others); this amounts to reverse discrimination-a visiting of the fathers' sins upon the sons.2 The empirical argument concludes that, moral issues aside, such intervention is unwarranted because the consequences of historical discrimination have been (or will soon be) largely eliminated. (See B. Wattenberg and W. Wilson.) In this essay I would like to offer a defense of affirmative action policies against the second of these thematic criticisms. That is, I shall hold in abeyance questions concerning the efficacy of particular programmatic efforts, and concentrate instead on whether government should in principle be taking actions to facilitate economic progress for minority group members. This would seem to be the logical first step in constructing an intellectual basis for affirmative action policies. Of course, philosophers and legal scholars interested in theories of distributive justice have devoted considerable attention to this question in the past ten years. (See R. Dworkin and T. Nagel.) The approach adopted here differs from these earlier efforts in two ways. First, I shall endeavor to meet the empirical argument directly, by pointing to evidence which suggests that significant racial economic disparity persists. Secondly, I will treat the philosophical argument in a manner in keeping with the economist's traditional approach to the question of the desirability of laissez-faire. This approach is based upon the concept of failure. Intervention is favored over laissez-faire when, because of some externality, the outcome is inefficient. Below I argue that an analogous market failure contributes to the maintenance of economic inequality between racial groups in our society. As such, intervention which redresses this inequality is warranted.

This essay examines interconnections between "race" and economic inequality in the United States, focusing on the case of African-Americans. I will argue that it is crucially important to distinguish between racial discrimination and racial stigma in the study of this problem. Racial discrimination has to do with how blacks are treated, while racial stigma is concerned with how black people are perceived. My view is that what I call reward bias (unfair treatment of persons in formal economic transactions based on racial identity) is now a less significant barrier to the full participation by African-Americans in U.S. society than is what I will call development bias (blocked access to resources critical for personal development but available only via non-market-mediated social transactions). By making these points in the specific cultural and historical context of the black experience in U.S. society, I hope to contribute to a deeper conceptualization of the worldwide problem of race and economic marginality.

Consider the problem of a buyer purchasing a (costlessly) storable good at a fixed price under threat of interruption of trade. Suppose there are two distinct and exhaustive regimes: either one can buy as much as desired at the going price, or one can purchase nothing at all and must rely accumulated stocks for consumption. The market moves randomly over time between these two states, which will be referred to here as on and off, respectively. Given the stochastic process governing the evolution of market regimes, the price faced when the market is on, and the intertemporal preferences of the buyer, one may inquire as to the optimal acquisition rate for storage and consumption when the market is on, and the optimal usage of accumulated stocks when the market is off. Solutions for these problems could then be used to ascertain the degree to which buyer (and seller) welfare is affected by the probabilistic curtailment of trading opportunities, and the willingness to pay of the buyer for greater security of supply. As well, the possibility of inferring from purchase and storage behavior the buyer's perception of the likelihood and duration of trade interruptions may be explored. This paper presents a general solution to this problem for stationary environments. That is, assuming intertemporal preferences to be representable by the expected present value of a uniformly discounted, time-independent flow utility function, and taking the stochastic process governing change in regimes to be stationary Markov, optimal behavior and associated expected discounted utility are derived. The method employed adapts to this context the dynamic programming arguments of my 1981 paper, and is similar in structure to that employed in the analysis of resource depletion with technological uncertainty in Partha Dasgupta and Geoffrey Heal (1974) and Dasgupta and Joseph Stiglitz (1981). There are many industrial markets in which these considerations are important. Recent events in the world oil market have stimulated much interest in the study of strategic mineral reserves (see, for example, Thomas Teisberg, 1981). In markets where demand fluctuates randomly and prices are inflexible (for example, the industrial market for natural gas), the possibility of stochastic rationing has important implications for firm behavior (see Dennis Carleton, 1978). The prospect of strike upstream, or lag in the delivery of goods order has significant implications for inventory holdings in some industries. The framework of this paper may even be adapted to the study of labor supply and savings behavior over the life cycle for a worker facing intermittent and uncertain unemployment.

A key question concerning affirmative action is whether the labor-market gains it brings to minorities can continue without it becoming a permanent fixture in the labor market. We argue that this depends on how the policy affects employers' beliefs about the productivity of minority workers. We study the joint determination of employer beliefs and worker productivity in a model of statistical discrimination in job assignments. We prove that, even when identifiable groups are equally endowed ex ante, affirmative action can bring about a situation in which employers (correctly) perceive the groups to be unequally productive, ex post.