Imperfect Price Discrimination and Welfare

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Abstract
We develop a model in which a monopolist uses differences across consumers in their valuation of time to imperfectly price discriminate. Though it is customary to analyse price discrimination problems by the calculus of variations after postulating a continuum of types, we assume a finite number of types and exploit the geometry and duality of the contract set and the structure of the programming specification. We analyse in detail the qualitative properties of the model's solution and show by construction that our results exhaust the implications of the model for equilibrium contract pairs. We show that imperfect discrimination is not bounded in welfare terms between perfect discrimination and single-price monopoly and that the deadweight loss, consumer surplus and output comparisons between single-price monopoly and imperfect discrimination are ambiguous.

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