Screening and the Price of a Stationary Type Distribution

A stationary mechanism uses a protocol to screen agents and form replacement types. We characterize implementable allocation and distribution pairs and output costs of cohort composition. With three trials, implementation is equivalent to a monotone effective allocation and three moment constraints. Finitely many coordinates suffice exactly when kernel differences are state independent and have finite span; its dimension is the flow rank. At fixed mean, the second moment measures variance. Incentive compatibility requires a minimum; additional variance improves sorting until saturation. The third moment controls its placement. Targets preserving the two-moment value form an interval; departures incur a location tax. Under locally stable IC constraints and independent moment gradients, this tax is locally quadratic. Its coefficient equals the second-moment shadow price per unit of relocation capacity times an IC amplification factor, which exceeds one exactly when IC blocks a first-order change preserving the first two moments.