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Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 a...

First, there is no such thing as the competitive equilibrium price vector. If $(p_1,p_2,p_3)$ is a competitive equilibrium price vector, so is every positive multiple of this vector. Second, to find t …
Michael Greinecker's user avatar
2 votes
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How to find the competitive equilibrium?

Here is a lazy tricks-based approach that requires almost no calculations: First, we know that every equilibrium allocation must be Pareto efficient by the first welfare theorem. If $B$ consumes diffe …
Michael Greinecker's user avatar
2 votes
Accepted

Competitive equilibrium in an exchange economy with lexicographic preferences

The preferences of agent $A$ cannot be represented by any utility function and the prefeences of $B$ not by a differentiable utility function, so forget calculus approaches. Since $A$ has strictly mo …
Michael Greinecker's user avatar
7 votes
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Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Yes. The Debreu version of the Sonnenschein-Mantel-Debreu theorem guarantees that excess demand has to satisfy very little restrictions if there are as many consumers as commodities. An explicit exam …
Michael Greinecker's user avatar