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We develop a framework for modelling choice in the presence of framing effects. An extended choice function assigns a chosen element to every pair (A, f) where A is a set of alternatives, and f is a frame. A frame includes observable information that is irrelevant in the rational assessment of the alternatives, but nonetheless affects choice. We relate the new framework to the classical model of choice correspondence. Conditions are identified under which there exists either a transitive or a transitive and complete binary relation R such that an alternative x is chosen in some (A, f) iff x is R‐maximal in the set A. We then demonstrate that the framework of choice correspondence misses information, which is essential to economic modelling, and which is incorporated in the extended choice function.

Panel and experimental data are used to analyse the economic outcomes in the extended warranty market. We establish that the strong demand and high profits in this market are driven by consumers distorting the failure probability of the insured product, rather than standard risk aversion or sellers’ market power. Providing information to consumers about failure probabilities significantly reduces their willingness to pay for warranties, indicating the important role of information, or lack of, in driving consumers’ purchase behaviour. Such information provision is shown to be more effective in enhancing consumer welfare than additional market competition.