A Sparsity-Based Model of Bounded Rationality

This article defines and analyzes a “sparse max” operator, which is a less than fully attentive and rational version of the traditional max operator. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of first-order importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the sparse max remains tractable to compute. Moreover, the induced outcomes reflect basic psychological forces governing limited attention. The sparse max yields a behavioral version of basic chapters of the microeconomics textbook: consumer demand and competitive equilibrium. I obtain a behavioral version of Marshallian and Hicksian demand, Arrow-Debreu competitive equilibrium, the Slutsky matrix, the Edgeworth box, Roy’s identity, and so on. The Slutsky matrix is no longer symmetric: nonsalient prices are associated with anomalously small demand elasticities. Because the consumer exhibits nominal illusion, in the Edgeworth box, the offer curve is a two-dimensional surface rather than a one-dimensional curve. As a result, different aggregate price levels correspond to materially distinct competitive equilibria, in a similar spirit to a Phillips curve. The Arrow-Debreu welfare theorems typically do not hold. This framework provides a way to assess which parts of basic microeconomics are robust, and which are not, to the assumption of perfect maximization. JEL Codes: D01, D03, D11, D51.