We analyse how public health insurance affects private insurance markets in mixed public-private systems. Extending the standard selection framework to incorporate heterogeneous risk aversion, quality preferences, income constraints, and administrative costs, we characterise equilibrium outcomes under both adverse and advantageous selection, and identify a double-margin mechanism that arises under the latter. Under adverse selection, public coverage attracts low-risk types away from the private market, worsening the private risk pool, raising premiums, and generating further exit; a self-reinforcing deterioration of private contract terms operating solely at the intensive margin. Under advantageous selection the direction reverses and public coverage now attracts high-risk, low quality-preference types, endogenously improving private contract terms through the zero-profit condition. Under institutional structures where public insurance is means-tested and private insurance is priced above actuarial value due to administrative costs, this resultant improvement in the private insurance pool crowds-in previously excluded marginal types at the extensive margin. We show that the two margins, (intensive and extensive) are causally linked. This feedback loop is absent from existing models. For the extensive margin effect the mechanism requires exactly three conditions to hold: advantageous selection, administrative costs, and income-based eligibility for public insurance. Institutional setting is shown to be important. The double-margin operates fully under means-tested public insurance, and takes a modified form under mandatory basic insurance with voluntary supplementary coverage. Only the intensive margin operates under NHS-type universal coverage. Standard crowd-out measures, which capture only the intensive margin under either selection regime systematically misstate the consequences of public insurance expansion.
