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.

Pareto Improving Taxation in Incomplete Markets

“…These primitives for the Generic Sensitivity of dP and the Logic of Pareto Improvement yield Next we illustrate how to check whether a tax policy passes this test via demand theory in incomplete markets, as developed by Turner (2003a). We show that the four tax policies in the introduction pass this test, and therefore generically admit Pareto improving taxes, owing to the unifying logic of a sensitive price adjustment.…”

“…Conversely, we prove that if the price adjustment is sufficiently sensitive to risk aversion, then for almost all risk aversions and endowments, Pareto improving taxes exist. We show how to verify this sensitivity test with standard demand theory, which Turner (2003a) extends from complete to incomplete markets.…”

“…We must check whether each policy meets the Full Reaction of Demand to Policy and the Sufficient Independence of Reactions. For this we report the theory of demand in incomplete markets as developed by Turner (2003a). The basic idea is to use decompositions of ∆, ∇ in terms of Slutsky matrices, and then to perturb these Slutsky matrices by perturbing risk aversion, while preserving neoclassical demand at the budget variables under consideration.…”

“…In turn, to decide whether a tax policy meets primitives (1), (2), we invoke an extension of Slutsky theory from complete to incomplete markets. Turner (2003a) develops the Slutsky theory of demand for commodities and assets in incomplete markets.…”

Pareto Improving Monetary Policy in Incomplete Markets

“…Conversely, if the price adjustment is sufficiently sensitive to risk aversion, then for almost all risk aversions and endowments, Pareto improving monetary policy exists, as we show. We then verify this sensitivity test with standard demand theory, which Turner (2003a) extends from complete to incomplete markets. Turner (2003a) develops the Slutsky theory of demand for commodities and assets in incomplete markets.…”