Convex Functions

Convex and concave functions have many important properties that are useful in Economics and Optimization. In this Chapter the basic properties of convex and concave functions are explained, including some fundamental results involving these functions. In particular, the role of convexity and concavity in Optimization is stressed. Since a function ƒ is concave if and only if − ƒ is convex, any result related to a convex function can easily be translated for a concave function. For this reason only the proofs related to convex functions are presented. For the sake of completeness, the corresponding results for the concave case are summarized in Appendix B.