Let X = R2, let u: X→ R be given by u(x) = x²r3, and let be the preference relation on X given by utility representation u. Show that: (a) The function u is not concave. [Hint: Take a second partial derivative with respect to one of the coordinates.] 1/2 1/2 (b) The preference relation is convex. [Hint: You may use the fact that the function f : X → R given by f(x) = x/²² is concave. If you feel like doing some math, try to show that f is concave, but you don't need to do this.]

Let X = R2, let u: X→ R be given by u(x) = x²r3, and let be the preference relation on X given by utility representation u. Show that: (a) The function u is not concave. [Hint: Take a second partial derivative with respect to one of the coordinates.] 1/2 1/2 (b) The preference relation is convex. [Hint: You may use the fact that the function f : X → R given by f(x) = x/²² is concave. If you feel like doing some math, try to show that f is concave, but you don't need to do this.]

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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