Theory of Demand in Incomplete Markets

Abstract

We develop the theory of demand for commodities and assets facing incompletely insurable uncertainty. First, a Slutsky matrix decomposes into substitution and income effects the derivative of demand with respect to prices and yield structure. Next, we identify the Slutsky matrix's properties. The Slutsky matrix can be perturbed arbitrarily, subject only to preserving these properties, by perturbing the underlying utility's Hessian, while fixing point demand and marginal utility. The key result identifies these Slutsky perturbations. For arguing genericity, it is an alternative to Citanna, Kajii and Villanacci's (1998) first-order conditions approach. The latter results extend to incomplete markets Geanakoplos and Polemarchakis (1980), who introduced Slutsky perturbations.