Adverse selection is an important problem in many markets. Governments respond to it with complex regulations: mandates, community rating, subsidies, risk adjustment, and regulation of contract characteristics. This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero-profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game.
We apply the model to show that mandates can increase efficiency but have unintended consequences. An insurance mandate can increase adverse selection on the intensive margin and lead some consumers to purchase less coverage. Optimal regulation addresses adverse selection on both the extensive and the intensive margins, can be described by a sufficient statistics formula, and includes elements that are commonly used in practice.