We provide a theory of wage dispersion and involuntary unemployment based on optimal monopsony pricing. A wage schedule that includes a wage exceeding the market-clearing wage is optimal whenever the cost of procurement under a market-clearing wage is not convex at the optimal level of employment. Introducing a minimum wage between the lowest wage offered in equilibrium and the market-clearing wage decreases involuntary unemployment and increases employment. More generally, whenever there is wage dispersion and involuntary unemployment at a given minimum wage, a sufficiently small increase in that wage increases employment and decreases involuntary unemployment. If there is no involuntary unemployment at a given minimum wage, a sufficiently small increase in that wage increases employment. Introducing a model of quantity competition in which the aggregate quantity is procured at minimal cost, we show that setting a minimum wage above—but sufficiently close to—the lowest wage offered in equilibrium absent wage regulation still increases employment.
