# ps8 - = x α y β where α,β> 0(a Show that f is concave...

This preview shows page 1. Sign up to view the full content.

Atsushi Inoue ECG 765: Mathematical Methods for Economics Fall 2009 Problem Set ] 8 Due in class on Tuesday, October 27 1. Check whether each of the following functions is concave, convex, strictly concave, strictly convex, or neither. (a) f ( x ) = log( x ) on < ++ . (b) f ( x ) = exp( x ) on < . (c) f ( x ) = sin( x ) on < . (d) f ( x ) = x 5 on < ++ . (4 points) 2. Deﬁne f : < 2 ++ → < by f ( x,y
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) = x α y β where α,β > 0. (a) Show that f is concave if α + β ≤ 1. (2 points) (b) Show that f is quasi-concave, but not concave, if α + β > 1. (2 points) 3. Read pages 407–409 of Simon and Blume (1994) and do exercise 17.9 of Simon and Blume (1994, p.410). (2 points) 1...
View Full Document

## This note was uploaded on 10/22/2009 for the course ECG 765 taught by Professor Fackler during the Fall '07 term at N.C. State.

Ask a homework question - tutors are online