Optimal contract with private information on cost expectation and variability

A multidimensional-and-sequential screening problem arises in a framework where the agent is privately informed about expected cost and cost variability and, subsequently, learns the realized cost as well. As the principal's marginal surplus function becomes less concave/more convex, the optimal mechanism reflects progressively stronger incentives to mimic less inefficient types, and to misrepresent the cost variability relative to the expected cost. When the principal's knowledge imperfection about the cost variability is sufficiently less important than that about the expected cost, quantities are pooled with respect to the former for a high-expected-cost agent. A low-expected-cost agent is not assigned the first-best output at least in some state of nature.