Do non-compete clauses undermine minimum wages?

Many low-wage workers in the United States are subject to non-compete clauses, which forbid them to work for competitors. Empirical research has found a link between the prevalence of non-compete clauses and minimum wage legislation. To explain this link, we propose a moral hazard model with minimum wages. Non-compete clauses can be used to punish failure. We characterize the optimal contracts with and without the possibility to use a non-compete clause. We find that the principal only uses a non-compete clause if minimum wages are sufficiently high. Non-compete clauses transfer utility from the agent to the principal because they increase the equilibrium effort without increasing the wages. If non-compete clauses can be arbitrarily severe, there is no minimum wage for which the agent gets a rent. If non-compete clauses are bounded, both the principal and the agent might be made better off than without non-compete clauses.