Adopting a mechanism design approach to optimal monopsony pricing, we show that market power can cause involuntary unemployment and that introducing an appropriate minimum wage can eliminate it. Specifically, we characterize when using a procurement mechanism involving wage dispersion and involuntary unemployment is optimal for a monopsony. Setting a minimum wage equal to the equilibrium wage under price-taking behavior then maximizes total employment and social surplus, and eliminates involuntary unemployment. Even setting a minimum wage equal to the highest wage offered under the laissez-faire equilibrium increases total employment and workers' pay, and decreases and possibly eliminates involuntary unemployment. If a minimum wage does not induce involuntary unemployment or induces both involuntary unemployment and wage dispersion, then a marginal increase in the minimum wage generically increases employment and decreases involuntary unemployment and wage dispersion. Extensions show that our key insights generalize to quantity competition and horizontally differentiated workers and jobs.