Buyer Optimal Demand and Monopoly Pricing*
This paper analyzes a bilateral trade model where the buyer can choose any cumulative distribution function (CDF) supported on [0, 1] which then determines her valuation. The seller, after observing the buyer's choice of the CDF but not its realization, gives a takeit or leave it offer to the buyer. We characterize the unique equilibrium outcome of this game and show that in this outcome, the price and the payoffs of both the buyer and the seller are equal to 1/e. The equilibrium CDF of the buyer generates a unit elastic demand on [1/e, 1]