Optimality of sequential screening with multiple units and ex post participation constraints

•With multiple units and ex post participation constraints, optimal contracts screen sequentially.•Optimal contracts implement non-monotone output schedules.•Regularity conditions are supplied to ensure their incentive compatibility.

We show that in sequential screening problems with ex post participation constraints, optimal contracts elicit the agent's pay-off irrelevant ex ante information when the principal and agent can trade multiple units, in contrast to when they can trade a single unit only. The difference arises because with multiple units, the principal can price each unit differently, giving rise to a larger number of screening instruments. Optimal contracts implement output schedules that are not monotone in the initial information. We identify regularity conditions which ensure that non-monotone schedules are incentive compatible.