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Stability Theorems with Economic Applications

Paul Champsaur
Jacques Dreze
Claude Henry

Abstract

In recent years, stability analysis has been extended in two directions, which are useful for economic applications. The first direction concerns differential equations with discontinuous right-hand sides. The second direction concerns difference equations with multivalued right-hand sides. The present paper reviews some of these contributions (in Section 5, 6, and the Appendix), brings out their similarities, and illustrates their applications to economic problems. The illustration concerns an economy with both private and public goods (Section 2). It is shown (Section 3) how an efficient allocation for that economy can be reached through a globally stable process, combining a price-guided market allocation of private goods and a quantitative planning procedure for public goods. A discrete version of the planning procedure, using an internally defined variable speed of adjustment, is also shown (Section 4) to be quasi-stable.