South Korea has the world's lowest fertility and an intense education race. Families devote nine percent of lifetime income to education, mostly to private tutoring with near-zero measured returns. I show that competition for coveted careers generates an assignment externality: when all families spend more, the admission bar rises and children become costly. In a quantitative model calibrated to this mechanism, replacing score-based assignment with a capacity-preserving lottery raises completed fertility by 0.24 children per couple. Pronatal transfers deliver one eighth of that increase. Education taxes deliver almost none. Preference shifts, not a fiercer race, explain the decline across cohorts.