I study the labor market implications of limited information inherent in the job search pro- cess. I build an equilibrium search model where workers have partial information regarding the payoffs of jobs. Workers pay a cost to direct job search that is proportional to the divergence between the chosen search strategy and a benchmark random search strategy. With this cost, workers apply to every job with a positive probability, but apply to high-payoff jobs with higher probabilities. I embed this partially directed search behavior into an equilibrium wage posting model where firms and workers match bilaterally. Partially directed search leads to monopsony power: firms extract a markdown due to the cost of directing search. Efficiency of the market equilibrium depends on whether the markdowns are equally distributed across firms. The dispersion of markdowns arises endogenously when the cost is high enough. In these cases, the unproductive firms are bounded by workers outside options and extract lower markdowns than the productive firms. Workers apply to unproductive firms too often compared with the efficient allocation. A minimum wage redistributes from the unproductive firms to workers, but worsens the inefficiency by further increasing the markdown dispersion; progressive corporate income taxation redistributes from the productive firms to workers, and restores efficiency by decreasing the markdown dispersion. I provide a micro-foundation for the baseline model based on information acquisition with rational inattention.