Econometrica: Mar, 1980, Volume 48, Issue 2

Commodity Exchanges as Gradient Processes

https://doi.org/0012-9682(198003)48:2<387:CEAGP>2.0.CO;2-U
p. 387-400

Claude D’Aspremont, Henry Tulkens

The purpose here is to make explicit the sense in which two dynamic processes, due to Malinvaud and others (whose solutions determine an efficient allocation for a given economy), are related to the gradient projection method known in the nonlinear optimization literature. The connections we establish derive from simple observations on first order characterizations of efficient allocations; they also lead to the formulation of another process, that applies to a classical welfare maximization problem; finally they provide a common basis for an a priori justification of each of the three processes involved, which supplements the intrinsic properties that they can be shown to have.