Editing General equilibrium theory (section)

===Determinacy===
Given that equilibria may not be unique, it is of some interest to ask whether any particular equilibrium is at least locally unique. If so, then [[comparative statics]] can be applied as long as the shocks to the system are not too large. As stated above, in a [[regular economy]] equilibria will be finite, hence locally unique. One reassuring result, due to Debreu, is that "most" economies are regular.

Work by Michael Mandler (1999) has challenged this claim.<ref name="Mandler 1999">{{cite book |last=Mandler |first=Michael |year=1999 |title=Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics |location=Oxford |publisher=Oxford University Press |isbn=978-0-19-510087-7 |url-access=registration |url=https://archive.org/details/dilemmasineconom0000mand }}</ref> The Arrow–Debreu–McKenzie model is neutral between models of production functions as continuously differentiable and as formed from (linear combinations of) fixed coefficient processes. Mandler accepts that, under either model of production, the initial endowments will not be consistent with a continuum of equilibria, except for a set of [[Lebesgue measure]] zero. However, endowments change with time in the model and this evolution of endowments is determined by the decisions of agents (e.g., firms) in the model. Agents in the model have an interest in equilibria being indeterminate:

<blockquote>
Indeterminacy, moreover, is not just a technical nuisance; it undermines the price-taking assumption of competitive models. Since arbitrary small manipulations of factor supplies can dramatically increase a factor's price, factor owners will not take prices to be parametric.<ref name="Mandler 1999" />{{rp|17}}
</blockquote>

When technology is modeled by (linear combinations) of fixed coefficient processes, optimizing agents will drive endowments to be such that a continuum of equilibria exist:

<blockquote>
The endowments where indeterminacy occurs systematically arise through time and therefore cannot be dismissed; the Arrow-Debreu-McKenzie model is thus fully subject to the dilemmas of factor price theory.<ref name="Mandler 1999" />{{rp|19}}
</blockquote>

Some have questioned the practical applicability of the general equilibrium approach based on the possibility of non-uniqueness of equilibria.