A regular economy is an economy characterized by an
excess demand function which has the property that its slope at any equilibrium price vector is non-zero. In other words, if we graph the excess demand function against prices, then the excess demand function "cuts" the x-axis assuring that each equilibrium is locally unique. Local uniqueness in turn permits the use of
comparative statics
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter.
As a type of ''static analysis'' it compares two different equilibrium states, after the ...
- an analysis of how the economy responds to external
shocks - as long as these shocks are not too large.
An important result due to
Debreu (1970) states that almost any economy, defined by an initial distribution of consumers' endowments, is regular. In technical terms, the set of nonregular economies is of
Lebesgue measure zero.
Combined with the
index theorem
Index (or its plural form indices) may refer to:
Arts, entertainment, and media Fictional entities
* Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index''
* The Index, an item on a Halo megastru ...
this result implies that almost any economy will have a finite (and odd) number of equilibria.
References
*Debreu, G. (1970). Economies with a finite set of equilibria. ''Econometrica'', 38 (3), 387–392.
*Dierker, E. (1972). Two Remarks on the Number of Equilibria of an Economy. ''Econometrica'', 40 (5), 951–953.
*
Mas-Colell, A., Whinston, M. and Green, J. (1995). Microeconomic Theory. ''Oxford University Press''.
General equilibrium theory