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2 votes
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Strict preference relation implies weak preference relation

Condition B does not imply condition A. Consider an example of the preference relation defined on $\mathbb{R}$ that is represented by the following utility function: \begin{eqnarray*} u(x)= \begin{...
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3 votes
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Question on the conditions for the existence of a Walrasian equilibrium

When confronted with situations like this its always nice to remember the key statement of the Sonnenschein Matel Debreu Theorem which is: Any function $z(p)$ which satisfies homogeneity, continuity ...
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2 votes
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Find the set of Pareto efficient allocations

We'll consider three cases: For $\alpha \in [\frac{1}{2}, 2]$, there are only two Pareto efficient allocations: $\big\{\big((2,0),(0,2\alpha)\big), \big((0,2\alpha),(2,0)\big) \big\}$ For $\alpha >...
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