  We study a bilateral trade problem where a principal has private information
that is revealed with delay, such as a seller who does not yet know her
production cost. Postponing the contracting process incurs a costly delay,
while early contracting with limited information can create incentive issues,
as the principal might misrepresent private information that will be revealed
later. We show that the optimal mechanism can effectively address these
challenges by leveraging the sequential nature of the problem. The optimal
mechanism is a menu of two-part tariffs, where the variable part is determined
by the principal's incentives and the fixed part by the agent's incentives. As
two-part tariffs might be impractical in some applications, we also study price
mechanisms. We show that the optimal price mechanism often entails trade at
both the ex-ante and ex-post stages. Dynamic price mechanisms can lower the
cost of delay by transacting with high-type agents early and relax the
incentive constraints by postponing contracts with lower-type agents. We also
generalize our analysis to costly learning and study ex-post efficiency in our
context.
