Unformatted text preview: f is concave, g is convex, and Slater’s constraint qualiﬁcation holds, then the Saddlepoint condition holds. Note that facts 1. and 3. give properties so that the Kuhn-Tucker conditions are necessary for a solution; 2. and 4. give properties for the Kuhn-Tucker conditions to be suﬃcient for a solution. I used fact 2. in the proof I gave for the First Welfare Theorem for the 2-good quasilinear economy (under convexity assumptions on preferences and technologies). 1 You will ﬁnd a proof of facts 1. and 2. in R. Sundaram’s A First Course in Optimization , pages 194-198. The two facts are summarized in his Theorem 7.16 on page 187. Note however that he subsumes nonnegativity constraints into his “h” function, whereas I list them separately. 1...
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- Spring '10
- Microeconomics, Convex function, Slater, lagrange multipliers, Kuhn-Tucker conditions