Sesión Aplicaciones de la Matemática y Física MatemáticaEfficient intertemporal allocations with variational utility
Luis Alcalá
Instituto de Matemática Aplicada San Luis, CONICET-UNSL, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
We study Pareto optimal allocations for an infinite-horizon economy with many consumers in a deterministic environment. The direct or primal approach with recursive utilities developed in [1,5] sometimes faces technical difficulties or requires unsatisfactory assumptions. Then, we propose a dual approach based on a variational representation of recursive utilities introduced by [2,3], allowing for Pareto weights to vary over time. As a result, we are able to characterize intertemporal efficient allocations, the path followed by Pareto weights, and obtain an aggregate or social discount factor as a by-product of the optimization problem. We also develop analytical results when consumers have Kreps-Porteus [4] recursive utilities and discuss some implications for consistent aggregation and updating of a social welfare function.
Referencias
[1] R.-A. Dana and C. Le Van (1990) Pareto optima in an infinite-horizon economy where agents have recursive preferences, Journal of Optimization Theory and Applications, 64, no. 2, 269-292.
[2] B. Dumas, R. Uppal, and T. Wang (2000) Efficient intertemporal allocations with recursive utility, Journal of Economic Theory, 93, 240-259.
[3] P.-Y. Geoffard (1996) Discounting and optimizing: Capital accumulation as a variational minmax problem, Journal of Economic Theory, 69, 53-70.
[4] D. Kreps and E. Porteus (1978) Temporal resolution of uncertainty and dynamic choice theory, Econometrica, 46, no. 1, 185-200.
[5] R. Lucas and N. Stokey (1984) Optimal growth with many consumers, Journal of Economic Theory, 32, 139-171.