1999/11/01 by P.-A. Chiappori, Ivar Ekeland · 49 citations
Economics, Econometrics and Finance · Social Sciences · Mathematics · #Economic theories and models #Gender, Labor, and Family Dynamics #Income, Poverty, and Inequality #Differential calculus #Differential (mechanical device) #Decomposition #Aggregate (composite) #Aggregate demand #Distribution (mathematics) #Characterization (materials science) #Mathematical economics #Mathematics #Field (mathematics) #Economics #Mathematical optimization #Mathematical analysis #Pure mathematics #Physics
paper · doi:10.1111/1468-0262.00085
published in Econometrica 67(6), 1435-1457 (Wiley)
openalex publication_date 1999/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior differential calculus provides very useful tools to address these problems. In particular, we show, using these techniques, that any analytic mapping in Rn satisfying Walras Law can be locally decomposed as the sum of n individual, utility-maximizing market demand functions. In addition, we show that the result holds for arbitrary (price-dependent) income distributions, and that the decomposition can be chosen such that it varies continuously with the mapping. Finally, when income distribution can be freely chosen, then decomposition requires only n/2 agents.