I study the incidence and optimal design of unemployment insurance, income and profit taxation in a competitive search economy. In addition to distorting labor supply as in an economy without frictions, taxation also affects labor demand and search behavior. The model highlights a key trade-off between redistribution and (un)employment, both on the intensive (hours) and on the extensive (persons) margin. When profit taxes are optimally set, the expression for the optimal income tax from Diamond (1998) generalizes to a setting with search frictions. I derive a novel expression for the optimal profit tax, and show – both theoretically and numerically – how profit taxes can be used to alleviate distortions from income taxation and unemployment insurance on application decisions and vacancy creation. Preliminary simulations indicate that a positive unemployment benefit, U-shaped marginal taxes and moderate profit subsidies are optimal.