Dynamic contracting under permanent and transitory private information

I examine a model of long-term contracting in which the buyer is privately informed about the discrete probability distribution for his future value for a divisible product, and fully characterize the optimal long term contract that will be offered by a monopolistic seller in a simple case where two types of buyers can have two types of utility in any period. In such a case, the buyer more likely to have a high utility type will receive the first-best allocations indifferent of his value report, while the lower type will receive the first best only if he makes a high utility report. The paper also supplements the current literature on infinite dynamic games with continuous buyer types, which relies on the use of a distribution of types with full support and an envelope theorem. With discrete types, the number of compatibility constraints considered can be greatly reduced by sandwiching the border of the space of solutions allowed by constraints: formulate the maximization problem in a wider space with fewer constraints and prove that the solution obeys a simpler set of stronger constraints that places it in the allowed region.