We had a question on this site for Fundamental equations in economics. What I'd like to know is what are the most important proofs needed in economics?
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$\begingroup$ I think a fundamental series of proofs are the separating hyperplane theorem, the supporting hyperplane theorem, and then using them (and fixed-pointe theorems) to prove the first and second welfare theorems. Also, proving the existence of equilibria. $\endgroup$– 123Apr 13, 2017 at 16:35
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$\begingroup$ How is this different from asking for the fundamental theorems in economics? Is the emphasis on proofs supposed to mean something, like conceptually sophisticated or technically challenging? $\endgroup$– Herr K.Apr 13, 2017 at 17:57
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I would say the following four:
Nash Equilibrium via Fixed Point (either Kakutani, Brouwer or Tarski, depending on the problem);
Welfare theorems via Hanh-Banach theory (mainly the separating hyperplane theorem);
Utility and Profit Optimization via Weierstrass Theorem, Kuhn-Tucker conditions, and existence of a Lagrangian;
Minimization of Least Squares;