🤖 AI Summary
This study investigates how an upstream monopolist selects the distribution of buyer valuations to optimally trade off consumer surplus against seller profit. Employing mechanism design theory, variational analysis, and optimal control methods, the paper characterizes—for the first time—the efficiency frontier between these two objectives and uncovers a phase transition in market structure as the relative weight on profit varies. When the profit weight is at least as large as that on consumer surplus, the optimal valuation distribution collapses to a degenerate point mass at the highest type. Conversely, when consumer surplus receives greater weight, no types are excluded or clustered at interior points; higher emphasis on consumer surplus yields greater market heterogeneity but lower total surplus. Under mild curvature conditions, this solution is unique.
📝 Abstract
Economic institutions often influence market outcomes not by directly controlling sellers'menus, but by shaping the market composition sellers face. We study this problem in the canonical monopoly screening model. An upstream actor chooses the distribution of buyer valuations, after which a monopolist offers the optimal quality-price menu. We characterize the optimal market composition and the efficient frontier of consumer surplus and profit. If the upstream actor places at least as much weight on profits as on consumer surplus, the optimal market collapses to the top type. If the weight on consumer surplus is larger than the weight on profits, the optimal market exhibits no exclusion, no interior bunching, and a positive mass at the highest valuation. Under a mild curvature condition, the optimum is unique. As the weight on consumer surplus rises, the optimal market becomes more heterogeneous and less concentrated at the top: the interior expands while the top segment shrinks. Consumer surplus rises, profit falls, and total surplus declines.