A model of price discrimination under loss aversion and state-contingent reference points

We study optimal price discrimination when a monopolist faces a continuum of consumers with reference-dependent preferences. A consumer's valuation for product quality consists of an intrinsic valuation affected by a private state signal (type) and a gain-loss valuation that depends on deviations of purchased quality from a reference point. Following [Koszegi and Rabin, 2006], we consider loss-averse buyers who evaluate gains and losses in terms of changes in the consumption valuation, but in our model each buyer evaluates consumption outcomes relative to his own state-contingent reference quality level. We capture the process by which reference qualities are formed via a reference consumption plan, and use a generalization of the Mirrlees representation of the indirect utility to fully characterize optimal contracts for loss-averse consumers. We find that, depending on the reference plan, optimal price discrimination may exhibit (i) downward distortions beyond the standard downward distortions due to screening, (ii) efficiency gains relative to second-best contracts without loss aversion, and (iii) upward distortions above first-best quality levels without loss aversion. We consider ex ante and ex post consistent contracts in which quality offers by the firm coincide, in expectations or at every state realization, respectively, with the reference quality levels. We find the firm's unique preferred ex ante and ex post consistent contract menu and specify conditions under which, for the second case, it also constitutes the consumers' preferred menu.