Uniqueness, stability, and local comparative statics for competitive equilibrium

Donald Keenan and Taewon Kim

International Journal of Economic Theory, 2015, vol. 11, issue 2, 169-176

Abstract: type="main" xml:lang="en">

The aggregate law of demand for an exchange economy can be weakened while still obtaining uniqueness, global stability, and good local comparative static properties for equilibrium. Classically, this is done by assuming that the Jacobian of excess demand is negative definite in the dimensions of compensated price changes, this being the weak axiom for aggregate demand. Similarly, though, one obtains the very same properties of equilibrium by only assuming that this Jacobian acts negatively in the one remaining complementary dimension. We refer to this dimension as the direction of the income effect, in analogy to a representative consumer. It is further argued that stability under this complementary condition is less sensitive than is the weak axiom to breakdowns in the condition far from the region under consideration.

Date: 2015
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