The Robust Stability of Every Equilibrium in Economic Models of Exchange Even Under Relaxed Standard Conditions

In an economic model of exchange of goods, the structure can be specified by utility functions. Under utility conditions identified here even more broadly than usual, except for concavity in place of quasi-concavity, every equilibrium will simultaneously be stable with respect to shifts in the associated holdings of the agents and with respect to the Walrasian tâtonnement process of price adjustment. This fact, seemingly contrary to widespread belief, is revealed by paying close attention not only to prices but also to the proximal status of initial holdings.The conditions on the concave utility functions are standard for stability investigations, in that they invoke properties coming from second derivatives, but significantly relaxed in not forcing all goods to be held only in positive amounts. For a given agent, some goods are allowed to have no effect at all on utility, whereas other goods, although insatiably interesting, may anyway end up at zero in equilibrium. Recent advances in variational analysis provide the support needed for working in that context. The stability results also point the way toward further developments in which an equilibrium might evolve in response to exogenous inputs to the agents' holdings, or extractions