Quoting from MWG p.519, Chapter 10: Pure Exchange, The Edgeworth Box

..., any intersection of the consumers' offer curves at an allocation different from the endowment point $\omega$ corresponds to an equilibrium..."

Does this mean that the endowment point can never be an equilibrium or that the crossing of offer curves there is not enough to guarantee that?

  • $\begingroup$ Which page is that from? Context? $\endgroup$ – Michael Greinecker Nov 17 '18 at 22:57
  • $\begingroup$ @MichaelGreinecker Added references in the text $\endgroup$ – PhDing Nov 17 '18 at 22:59

The endowment can be an equilibrium allocation. But as is written on page 518, if indifference curves are smooth, which we will assume in the following, they must be tangent to the offer curve at the endowment. So if the offer curves cross at the endowment, the indifference curves must cross too. But if the indifference curves at the endowment cross each other, the endowment cannot be Pareto efficient. But every equilibrium allocation is efficient, so the initial endowment will not be an equilibrium allocation if the offer curves cross each other there (they would need to be tangent.)

  • $\begingroup$ By "smooth" we mean indifference curves with no kinks? $\endgroup$ – PhDing Nov 17 '18 at 23:39
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    $\begingroup$ I'm not sure what's the exact condition is, but it is a differentiability assumption. $\endgroup$ – Michael Greinecker Nov 17 '18 at 23:42

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