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...
View Full Document
This note was uploaded on 11/19/2010 for the course ECON 202 taught by Professor Schlee during the Spring '10 term at ASU.
- Spring '10