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How was the convexity of preferences assumption important for making the argument that competitive equilibria are efficient? Does this mean convexity is necessary for the

  1. How was the convexity of preferences assumption important for making the argument that competitive equilibria are efficient? Does this mean convexity is necessary for the FWT to hold? A short response will do.
  2. Is convexity of the production set a necessary assumption for the SWT to hold?

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