Optimal Trading for an Informed Seller

A seller with perfect monopoly power trades an indivisible object with a buyer. Both the seller's and the buyer's valuations for the object depend on its quality, which is privately known by the seller. Moreover, the seller has perfect information about the buyer's valuation for each quality. Even though posting a fixed price is ex ante optimal, it might not be interim individually rational and hence not necessarily implementable. The set of interim optimal allocations is charac-terised by solving a parametric linear maximisation program. These allocations might differ from simple price-posting. If the seller offers a menu of contracts, then allocations that are not interim optimal can be supported as equilibrium allocations. However, this sub-optimality result seems not to be robust if there are at least two buyers who can counter-offer menus of contracts after the seller's offer. In that case, an allocation is an equilibrium allocation if and only if it is interim optimal