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