Remark on Rochet and Choné's Square Screening Example

In their study of price discrimination for a monopolist selling heterogeneous products to consumers having private information about their own multidimensional types, J.-C. Rochet and P. Choné [Ironing, sweeping, and multidimensional screening, Econometrica 66 (1998) 783--826] discovered a new form of screening in which consumers with intermediate types are bunched together into isochoice groups of various dimensions incentivized to purchase the same product. They analyzed a particular example involving customer types distributed uniformly over the unit square. For this example, we prove that their proposed solution is not selfconsistent, and we indicate how consistency can be restored.