We use a simple framework, adopted from general equilibrium search models, to estimate the extent to which monopsony power (or labor market frictions) can account for gender differences in pay, using data from a chain of regional grocery stores. In this framework, the elasticity of labor supply to the firm can be inferred from estimates of the elasticity of the separation rate with respect to the wage. We identify elasticities of separation from differences in wages and separation rates across job titles and across different years. We estimate elasticities of labor supply to the firm of about 3.5 for men and about 2.7 for women, suggesting significant wage-setting power for the firm. The differences in estimated elasticities of labor supply predict wage differences that are close to the observed male/female wage differences at the firm.