Screening and the Cost of a Prescribed Quantity Schedule

An institution assigns task actions to privately informed agents subject to a prescribed quantity schedule and the requirement of reproducing a stationary type distribution. Actions determine current output and shape successor types, so stationarity constrains the aggregate action distribution while incentive compatibility governs its allocation across private types. Incentives order the effective allocation: the prescribed quantity scaled by the action multiplier. Under a nonincreasing schedule, an action marginal is implementable if and only if it dominates in the convex order the distribution that holds this effective allocation constant. A stationary target is implementable if and only if some marginal above this bound reproduces it; we characterize when finitely many unconditional action statistics suffice for this test. For interval actions, the bound implies a sharp variance floor determined by the relative dispersion of prescribed quantities. Variance above the floor enables sorting until output attains its mean-constrained maximum, beyond which within-type lotteries absorb residual variance costlessly. Strict incentive compatibility preserves target moments at interior points and approaches the weak output maximum arbitrarily closely. Additional moment restrictions can lower output and preclude strict incentives at boundary targets. These losses stem from the quantity commitment. For nonnegative types and interval actions, freely chosen quantities allow monotone sorting to preserve any technologically feasible action marginal.