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This paper describes a contract theory of public finance of college education that explains why everyone pays for the college education of a lucky minority. The contract provides gambles that families desire. Optimizing the contract determines the taxes paid by all members of society, fees paid by those whose children go to college, the fraction of children who are admitted to college, and the quality of college education. Changes in wealth lead to changes in taxes and admissions, but fees and quality are invariant. The practice of using a cutoff level of precollege achievement to determine admission to college is justified by the theory.