¹ Docile is used in this paper in its literal meaning: teachable.

² See Dworkin, R., “What Is Equality? Part 2: Equality of Resources”, Philosophy and Public Affairs, vol. 10 (1981), pp. 283–345 Google Scholar, where the author defends a definition of comprehensive resource equality. See Roemer, J. E., “Equality of Talent”, Economics and Philosophy, vol. 1 (1985), pp. 151–87CrossRefGoogle Scholar, for a discussion and criticism of Dworkin's proposal for how to equalize resources, and Roemer, J. E., “Equality of Resources Implies Equality of Welfare”, Quarterly Journal of Economics, n.v. (Fall 1986), pp. 751–84CrossRefGoogle Scholar, for an argument that equality of resources, comprehensively conceived, implies equality of outcome. Equality of educational opportunity, as I conceive of it in this essay, does not require equality of educational outcome or attainment (an unrealistic goal), but it does require some compensation — that is, more than [equal exposure to education] requires.

³ This description of the educational process doubtless strikes some readers as overly mechanistic. It presumes children, teachers, books, and school buildings interact in certain well-defined ways to produce educated (skilled) children. In general, different schools possess different ‘educationaltechnologies’ — which is to say, the processes of interaction may differ across schools. I defend this economic abstraction of the educational process as useful for comparing voucher and public educational regimes. For other purposes, it may not be the right abstraction.

⁴ A [vector of skill levels] is a list of the degrees ofthe various skills that a person has. A [set of vectors of skill levels] refers to a complete specification of the degree of each skill each person has.

⁵ By [bright], I mean docile. There is no intended implication that docility is correlated with some kind of natural intelligence.

⁶ The formal models, definitions, and proofs of theorems are presented in Roemer, J. E., “The Economics of Equal Educational Opportunity: Public and Voucher Regimes”, Department of Economics Working Paper No. 360, University of California, Davis (1990).Google Scholar

⁷ That children do not consume in the first period is a simplifying and harmless assumption.

⁸ This is merely for expositional simplicity. All results are true with many competing firms and schools. The essential assumption is that firms and schools are price-takers, not price-makers.

⁹ For example, the school provides the child with a fellowship that pays more than the costs of his tuition and living expenses. Negative tuitions occur when the student is a particularly valuable input in the educational process: for instance, he plays the violin magnificently, which adds to the musical skill acquisition of other students in the school orchestra.

¹⁰ His labor is inelastically supplied at the full amount.

¹¹ The parent's labor is also inelastically supplied.

¹² This is not price discrimination in the usual sense — that is, charging different prices to different consumers for the same product. Children of different types are indeed different goods, as far as the school is concerned.

¹³ Suppose it is true that parents who send their children to private schools, in a society where such intergenerational borrowing cannot be arranged, also leave bequests to their children. We can infer that such parents would not have borrowed against their child's income even were that possible.For if they would have but cannot, then we should observe zero bequest levels: such parentswould spend all their [discretionary] income on the child's education. If the bequest level is positive, then the parent did not face a tight constraint with regard to the level of education she wished her child to have.

¹⁴ This voucher system differs from some in the literature —in particular, that of Coons, J. and Sugarman, S., Education by Choice: The Case for Family Control (Berkeley: University of California Press, 1978)CrossRefGoogle Scholar, where parents are not permitted to purchase additional education for their children in voucher schools.

¹⁵ In most actual voucher proposals, public schools continue to exist. But unless public schools were to be subsidized with funds additional to the vouchers — a phenomenonthe voucher system is meant to prevent — then public schools should behave as profit maximizers as well. Profits of publicschools would be distributed to citizens (or, equivalently, would decrease the education tax bill to citizens). Another difference one could maintain between the two types of school is that public schools might educate students only up to the level of the public syllabus, while private schools would offer the option to go further. Public schools, that is, might accept only vouchers but no cash from parents.

¹⁶ Coons and Sugarman, Education by Choice, p. 195.

¹⁷ Because, for instance, it lacks information specifying which children are ofwhich type.

¹⁸ This assumes some separability in the education of type 1 and type 2 children, so that costs of educating children are not very sensitive to the mix of children in the school.

¹⁹ In reading this paper before several audiences in Europe and the United States, I have occasionally heard the objection that a social norm against the differential pricing of children does, or would, not exist if a voucher system werecomprehensively adopted. This objection has only been made in the United States.

²⁰ This is to be distinguished from the static effect of unequal educational opportunity in such a voucher system.

²¹ I am assuming that a relatively small reduction in taxes is at issue, small enough so that if implemented, few parents who formerly chose the public school option would now find the private school option more attractive.

²² It is in general the case that children of poor families require more educational resources to reach the same level of skill attainment as children of middle-class families; if taxes are levied as a proportion of income or the value of property, it is therefore likely that, given a social commitmentto equal educational opportunity, the middle class will subsidize the poor through either public education or vouchers.