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Sorry this might be a little too rudimentary for you, but I'm not an Econ background. When I was doing exercises for MGW chapter 17 "Positive Existence of Equilibrium" I came across the following statement

The consumers preferences are strictly convex, this implies that there is no equilibrium in the overall economy generated by replication.

What doe equilibrium generated by replication mean? I couldn't find it in the text.

Thanks in advance.

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For each agent in the economy, create n agents with the same endowment and preferences. The result is the replication economy. Sometimes n is taken to infinity in proofs. Chapter 17.I in Mas-Colell explains in detail. Related material is the regularizing effects of aggregation, appendix of Chapter 4.

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  • $\begingroup$ Thanks a lot for your reply. If that's the definition, can I also ask you why when consumers preferences are strictly convex, this implies that there is no equilibrium in the overall economy generated by replication? It seems to me in this case the equilibrium is unique but at the same time is symmetric to every consumers and thus seems to be a replication? $\endgroup$ – Kenneth Chen Nov 10 '15 at 18:23
  • $\begingroup$ Preferences convex or utility functions convex? Because convex preferences are a good thing for equilibrium existence. $\endgroup$ – Sander Heinsalu Nov 10 '15 at 18:27
  • $\begingroup$ Preferences convex $\endgroup$ – Kenneth Chen Nov 10 '15 at 20:34
  • $\begingroup$ @Kenneth Chen I don't think this statement holds without additional assumptions/context. $\endgroup$ – Giskard Nov 10 '15 at 21:31
  • $\begingroup$ @denesp If so what would that possibly be? Right now I'm still confused what does no equilibrium with replication mean. $\endgroup$ – Kenneth Chen Nov 10 '15 at 21:32

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