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. ...
