An Analysis of Portion Cap Rules with a Multiproduct Seller

Abstract

I study the impacts of limiting the quantity of one product in a two‐goods market with privately informed buyers. The goal is to explore effects on consumer surplus and consumption of both products. The main finding is that following moderate enough caps, a standard nonlinear pricing model predicts an increase in surplus for the buyer with low preference for the regulated good and high valuation for the unregulated product. Specific changes in allocation depend on the model's parameters. Consumption of the limited good is reduced, whereas consumption of the unregulated item often falls. Changes in screening are also interesting. Severe enough caps cause the seller to move from full separation to bunching some types. These results are applicable to food retail and other industries, where portion cap rules are a regulatory alternative and the impact on consumer surplus is an important consideration.