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We estimate the price sensitivity in health care among adolescents and young adults, and assess how it varies across income groups and gender, using a regression discontinuity design. We use the age differential cost-sharing in Swedish primary care as our identification strategy. At the 20th birthday, the copayment increases from €0 to approx. €10 per primary care physician visit and close to this threshold the copayment faced by each person is distributed almost as good as if randomized. The analysis is performed using high-quality health care and economic register data of 73,000 individuals aged 18–22. Our results show that the copayment decreases the average number of visits by 7%. Among women visits are reduced by 9%, for low-income individuals by 11%, and for low-income women by 14%. In conclusion, modest copayments have significant utilization effects, and even in a policy context with relatively low income inequalities, the effect is substantially larger in low-income groups and among women.