This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: T. Mitra Fall, 2008 Economics 6170 Problem Set 7 [Due on Wednesday, November 12] 1. [Converse of Eulers Theorem] (a) Let f : R n ++ R ++ be a continuously differentiable function on its domain, which satisfies x f ( x ) = f ( x ) for all x R n ++ . Show that f is homogeneous of degree one on its domain. (b) Generalize the result in (a) to provide an appropriate converse of Eulers theorem. 2. [Homothetic Functions] A function F : R n + R + is called a homothetic function on R n + if there exists a function f : R n + R + which is homogeneous of degree one on R n + , and there exists a function g : R + R + which is an increasing function on R + , such that F ( x ) = g ( f ( x )) for all x R n + . (a) Let F : R n + R + be a function which is homogeneous of degree r > on R n + . Show that F is a homothetic function on R n + . (b) Let F : R 2 + R + be defined by: F ( x 1 ,x 2 ) = x 1 x 1 2 1 + x 1 x 1 2 for all ( x 1 ,x 2 ) R 2 + where...
View
Full
Document
 Fall '08
 MITRA

Click to edit the document details