Variations on the Theme of Scarf’s Counter-Example

Alok Kumar and Martin Shubik

01-12-074

In this paper we study the relationship between the stability of a competitive equilibrium (CE) and the price adjustment mechanism used to attain that equilibrium point. Using two specific examples, a three-commodity exchange economy with a unique competitive equilibrium (Scarf's global instability example) and a two-commodity, two-trader-type exchange economy with multiple competitive equilibria, we show that the stability of a CE depends critically upon the dynamics of the price adjustment mechanism. A particular CE may be unstable under one price adjustment mechanism but stable under another. The joint dynamics of the chosen price adjustment mechanism and the given economy determines the overall stability of its competitive equilibrium. Our results suggest that context-rich studies of economic systems which focus on a specific price adjustment mechanism may provide insights into the dynamics and stability of economic systems that are often not revealed through a context-independent analysis.