We study labor market competition with heterogeneous firms and consumers. Worker types are continuously distributed within the population and a finite number of firms have specific skill requirements. Specific human capital investment is the cost of training a worker to be able to work for a particular firm and depends on the difference between the worker’s skill type and the firm’s skill requirement. A firm’s profit equals its output minus wages, its share of training costs, and a fixed cost. We solve for symmetric free-entry Nash equilibria of the wage offer game under two different information structures. When firms can identify worker types before employment, firms can pay different net wages to workers with different training costs. When firms cannot identify worker training costs in advance, firms pay workers equal wages, but workers absorb training costs. The level of fixed costs, the size of the labor market, and the cost of investment in human capital all affect the equilibrium settings. We also consider different tax instruments to increase allocative efficiency and to finance investment in general human capital.