Abstract
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 is not necessarily implementable because it might not be interim individually rational. The set of implementable interim optimal mechanisms is characterised by solving a parametric linear maximisation program. These mechanisms might differ from simple price-posting. If the seller offers the mechanism, then mechanisms that are not interim optimal can be supported as equilibrium mechanisms. However, this sub-optimality result seems not to be robust if there are at least two buyers who can make counter-offers of mechanisms after the seller's offer. In that case, a mechanism offered by the seller is an equilibrium mechanism if and only if it is interim optimal.
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