Optimal taxation with directed search and private information

What is left for the income tax when employers’ contracts already insure workers and provide incentives? We study a directed-search economy where firms post output-contingent wage contracts under hidden effort. With observable types and a utilitarian planner, type-specific lump sums, a benefit and a vacancy subsidy implement the constrained optimum. When the planner weights expected utility by the mean of a weight ð ›¾ of realized consumption, differentiable implementing taxes are unique up to a constant and a term that leaves every contract unchanged, and one has ð œ â€²/(1 − ð œ â€²) = −𠜅𠛾′(ð ‘ ) for a single equilibrium scalar 𠜅: no skill distribution or elasticity enters. For nearly constant weights, the slope’s gain over a lump sum is of second order, with leading coefficient proportional to a weighted within-contract variance of a marginal welfare credit. With private productivity, the low type’s wedge splits into a redistributive part, carried by the tax, and a screening part that posting-contingent charges shift to the wage contract; numerically, one anonymous schedule then costs under 10−6 per capita. Without instruments setting each submarket’s level, the tax also redistributes across types, and in our examples its slope is worth far more.