From Quasi- to Competitive Equilibrium
Theorem. Suppose that $(x^*,y^*,p^*)$ is a quasi-equilibrium for the
private ownership economy $\mathcal{E}$. Suppose that for all consumers $n$ and for all $x_n\in
X_n$, the set $\succ_n(x_n)$ is open. If each $w^*_n=p^*x^*_n\geq0$, then $(x^*,y^*,p^*,w^*)$ is
a competitive equilibrium with
transfers.
Proof. This is an immediate consequence of the
definition of a quasi-equilibrium and the cheaper point Lemma.
∎
The cheaper point assumption is automatically satisfied for interior optima, each $x^*_n\gg0$.
what about boundary optima?
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