Should refusal to sell be illegal?

We analyse a private firm's decision of whether to refuse to sell to a particular group of consumers whose interaction with other consumers generates negative externalities. The literature has rarely incorporated this motive directly into the firm's profit-maximisation problem. Discriminatory refusal-to-sell policies can increase profits and consumer utility among those affected by the negative externality. Of course it also reduces utility among consumers who are refused, raising the possibility of an indeterminate effect on social welfare. We obtain a stark and rather surprising result: The refusal-to-sell policy is socially optimal whenever it is individually optimal for a profit-maximising firm to adopt such a policy. No legislation or regulation is required from a social-welfare perspective (under the assumptions used in the specification of the social welfare function). We prove this result analytically for the case of linear demand functions. Numerical simulations show that the result also holds for constant-price-elasticity demand functions.