Optimization and Economic Equilibrium

In the standard theory of economic equilibrium, various “agents” optimize
what they want to buy and sell in order to adjust their holdings on the
basis of given prices and associated budget constraints. Their decisions
depend on preference relations that are representable nonuniquely by utility
functions on the space of goods vectors. The standard question posed by
economists is whether prices exist under which the resulting total demands
of the agents are matched by total supplies. Equilibrium is a state in
which, at the given prices, no agent wants to buy or sell anything. But
the treatment of equilibrium in the literature is far from satisfactory, in
particular in failing to offer a convincing economic mechanism by which
equilibrium could be achieved and how it might respond to perturbations.

This talk will explain new developments that approach the topic in
different way that takes advantage of simple features of convex
optimization and better knowledge of utility functions.