This paper develops a technique for studying incentive problems with unidimensional hidden characteristics in a way that is independent of whether the type set is finite, the type distribution has a continuous density, or the type distribution has both mass points and an atomless part. By this technique, the proposition that optimal incentive schemes induce no distortion “at the top” and downward distortions “below the top” is extended to arbitrary type distributions. However, mass points in the interior of the type set require pooling with adjacent higher types and, unless there are other complications, a discontinuous jump in the transition from adjacent lower types.

[The paper analyzes borrowing and lending on uncertain future income, with a positive probability of bankruptcy. Creditor and debtor play a strategic game, in which it is shown that optimal creditor behavior is not generally well defined. The model suggests that under uncertainty the availability of credit may be restricted below that which would be predicted by classical microeconomic theory.]

This paper studies the relation between discrete–time and continuous–time principal–agent models. We derive the continuous–time model as a limit of discrete–time models with ever shorter periods and show that optimal incentive schemes in the discrete–time models approximate the optimal incentive scheme in the continuous model, which is linear in accounts. Under the additional assumption that the principal observes only cumulative total profits at the end and the agent can destroy profits unnoticed, an incentive scheme that is linear in total profits is shown to be approximately optimal in the discrete–time model when the length of the period is small.