Working Paper: NBER ID: w25025
Authors: Thibault Fally
Abstract: This paper examines demand systems where the demand for a good depends only on its own price, consumer income, and a single aggregator synthesizing information on all other prices. This generalizes directly-separable preferences where the Lagrange multiplier provides such an aggregator. As indicated by Gorman (1972), symmetry of the Slutsky substitution terms implies that such demand can take only one of two simple forms. Conversely, here we show that only weak conditions ensure that such demand systems are integrable, i.e. can be derived from the maximization of a well-behaved utility function. This paper further studies useful properties and applications of these demand systems.
Keywords: Demand Systems; Integrability; Utility Functions; Economic Theory
JEL Codes: D11; D40; L13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Demand systems characterized by generalized separability (D10) | Integrability of demand systems (D10) |
| If demand function is of the form q_i = d_i(f(p_i, w)) (J23) | Integrability is guaranteed (D52) |
| d_i is monotonically decreasing in p_i (C69) | Demand q_i decreases with price (D41) |
| Slutsky substitution matrix must be symmetric and negative semidefinite (C69) | Demand to be integrable (C69) |
| Generalized Gorman-Pollak demand system (D11) | Direct additivity with flexible income effects (H31) |
| Generalized non-homothetic CES demand system (D11) | Flexible price effects but restricted income effects (H31) |