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An important result due to Debreu (1970) states that almost any economy, defined by an initial distribution of consumer's endowments, is regular. In technical terms, the set of nonregular economies is of Lebesgue Measure zero.

Combined with the Index Theorem this result implies that a given economy will have a finite (and odd) number of equilibria.


REFERENCES

Debreu, G. (1970) "Economies with a finite set of equilibria", ''Econometrica'', 38.

Mas-Colell, A., Whinston, M. and Green, J. (1995). "Microeconomic Theory", ''Oxford University Press''