Ken Arrow (1998) asks, “What has economics to say about racial discrimination?” He replies – entirely correctly – that racial “segregation within an industry – that is, firms with either all black or all white labor forces” – may be explained by economic theory, but “the hypothesis of employer discrimination does not at all explain segregation by occupation, [and] discriminatory tastes of other employees … may explain segregation [by firms] within industries but not segregation by occupation[s]” (p. 95), that are filled by racially distinct persons within firms. Becker (1957) and Akerlof and Kranton (2000 and 2010) offer economic theories that deal with social identity differentiation, but these lack rational choice theory foundations, insofar as they impose a utility indicator function as a primitive concept via persuasion, rather than such a function being entailed by derivation from a preference ranking relation defined on a set of outcomes, with restrictions imposed both on the set and the relation. This is a methodological weakness of their work relative to that of Arrow and Debreu (1954). A more serious difficulty with these contributions is that they ascribe a utility function to each individual in an economy, but I prove that assigning to individuals binary preferences, with or without their numerical representation as utility indicator functions, entails the impossibility of interpersonal social-identity diversification, rendering all persons in society indistinguishable by identity. The information necessary to identify a person’s social identity is stripped off the model by the binariness restriction. A person in a binariness-salient model would simply not know against whom to discriminate. Economic theory is, therefore, endogenously color-blind, race-blind, gender-blind, ethnicity-blind, and in general, social-identity-blind. Everybody in the economy is White, or all persons are Black, or all female, or all Hispanics, and so on, but no two persons can endogenously have distinct social identities. This is also true of every player in a game, as in Nash (1951). However, if preferences are non-binary, interpersonal social identity diversification is possible, though their real-valued utility function representation is impossible. This begs the question as to what exact form preferences must take to support the specific utility function of Akerlof and Kranton, which also is non-traditional relative to the utility indicator function in Arrow and Debreu. As it happens, to exhibit diversity of persons by social identity, ascribing a utility function to a person is conceptually too restrictive. By substituting non-binary for binary preferences in the model of Arrow and Debreu, I extend their economic theory. The more general model I thus formulate has the following features: (i) there exists a social state in which all persons maximize their preferences on their feasible sets, (ii) endogenous interpersonal social-identity diversification characterizes this state of the economy, (iii) it is a free-market equilibrium without any state intervention, (iv) it is a Pareto optimal social state, and (v) a sizable proportion of Black workers are segregated into low-rank, low income jobs, whereas White workers in the same observable proficiency domain are placed in high-ranking, high-income jobs, thereby explaining occupational segregation within firms along a racial divide, which entails that (vi) income and wealth distributions vary by social identity. Thus free markets deliver a Pareto optimal state but it is fraught with remediable injustices. Further, my explanation meets standards Arrow sets for such a theory (see p. 21). (543 words)
