Initial endowments which can result in multiple equilibria in a pure exchange economy are explained here. Given a pure exchange economy, that is given the utility functions (which fulfil the usual properties) and total amounts of each good, what are some properties of the set of 'multiple equilibria endowment points'?
Is this set connected?
If yes, is it convex?
Are there additional properties, does a charaterization (a set of necessary and sufficient properties) exist?
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1$\begingroup$ As a first step, the Index theorem from MWG tells us that generic economies have finite and odd number of equilibria. Perhaps this is the starting point to look at? $\endgroup$– Walrasian AuctioneerCommented May 18, 2021 at 0:06
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1 Answer
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The following article:
TODA, A.A. and WALSH, K.J., 2017. Edgeworth box economies with multiple equilibria. Economic Theory Bulletin, 5(1), pp. 65-80.
though not focusing on the properties of the sets of endowment points that have multiple equilibria, provides a detailed look at the properties of utility functions that give way to the possibility of multiple equilibria.
It examines CRRA, quadratic, quasi-linear, and general additively separable preferences in great detail and could provide some guidance for answering your question.
