Stephen Morris Publications

A number of producers of heterogeneous goods with heterogeneous costs compete in prices. When producers know their own production costs and consumers know their values, consumer surplus and total surplus are aligned: the information structure and equilibrium that maximize consumer surplus also maximize total surplus. We report when alignment extends to the case where either consumers are uncertain about their own values or producers are uncertain about their own costs, and we also give examples showing when it does not. Less information for either producers or consumers may intensify competition in a way that benefits consumers but results in inefficient production.

How should a seller offer quantity or quality differentiated products if they have no information about the distribution of demand? We consider a seller who cares about the "profit guarantee" of a pricing rule, that is, the minimum ratio of expected profits to expected social surplus for any distribution of demand.

We show that the profit guarantee is maximized by setting the price markup over cost equal to the elasticity of the cost function. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible demand distributions. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible demand distributions and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.

We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.

We characterize the revenue-maximizing information structure in the second-price auction. The seller faces a trade-off: more information improves the efficiency of the allocation but creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition is high) but to pool high values (where competition is low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising.

We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profits. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level as a by-product of reducing the information rents of the buyer.

We consider a general nonlinear pricing environment with private information. We characterize the information structure that maximizes the sellerís profits. The seller who cannot observe the buyerís willingness to pay can control both the signal that a buyer receives about his value and the selling mechanism. The optimal screening mechanism has finitely many items even with a continuum of types. We identify sufficient conditions under which the optimal mechanism has a single item. Thus, the socially efficient variety of items is decreased drastically at the expense of higher revenue and lower information rents.

We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profit. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level in order to reduce the information rents of the buyers.

We characterize the revenue-maximizing information structure in the second price auction. The seller faces a classic economic trade-o¤: providing more information improves the efficiency of the allocation but also creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition will be high) but to pool high values (where competition will be low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising.

Consider a market with identical firms offering a homogeneous good. For any given ex ante distribution of the price count (the number of firms from which a consumer obtains a quote), we derive a tight upper bound on the equilibrium distribution of sales prices. The bound holds across all models of firms’ common-prior higher-order beliefs about the price count, including the extreme cases of full information and no information. One implication of our results is that a small ex ante probability that the price count is equal to one can lead to a large increase in the expected price. The bound also applies in a large class of models where the price count distribution is endogenously determined.

In digital advertising, a publisher selling impressions faces a trade-off in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches.

In digital advertising, a publisher selling impressions faces a trade-o¤ in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches.