STOR Colloquium: Asen. L. Dontchev (Mathematical Reviews)

Parametric Stability of Solutions in Models of Economic Equilibrium

Recent results about strong metric regularity of solution mappings are applied to  a model of market equilibrium in the exchange of goods. The solution mapping goes from the initial endowments of the agents to the goods they end up with and the supporting prices, and the issue is whether, relative to a particular equilibrium, it has a single-valued, Lipschitz continuous localization. A positive answer is obtained when the chosen goods are not too distant from the endowments. A counterexample demonstrates that, when the distance is too great, such strong metric regularity can fail, with the equilibrium then being unstable with respect to tiny shifts in the endowment parameters, even bifurcating or, on the other hand, vanishing abruptly.

Refreshments will be served at 3:30pm in the 3rd floor lounge of Hanes Hall.