Selling to a continuum of buyers with private values and entry costs

Abstract This paper studies the revenue‐maximizing selling mechanism with a continuum of buyers who have two‐dimensional private information: valuation and entry cost. Using optimal control methods, we solve this two‐dimensional screening problem with endogenous entry and derive sufficient conditions under which the optimal mechanism is a posted price. These conditions reduce the original problem to a one‐dimensional one in which a buyer's type is net valuation, and the optimal posted price matches that of the transformed environment. Finally, under mild conditions, revenue maximization implies underselling relative to the efficient allocation.