3. Demand function When vf(x( w)=w, differentiate with respect to w we get: Df(x w). DX w)=Ior Dx(W)=[Df(x( w))I Substitution matrix Dx( w) is a symmetric negative matrix 1. Ox, /w,=ax, /aw 2.dwdx=wDx(,w)dw≤0 lecture 2 for Chu Kechen Honors Collegelecture 2 for Chu Kechen Honors College 3.Demand function • When , differentiate with respect to w, we get: or • Substitution matrix is a symmetric negative matrix. – 1. – 2.  = f ( (, )) x w w 2 D f D I ( ) x(,w) x(,w)  = 2 1 D D f [ ( )]− x(,w) x(,w) = Dx(,w) 0 T d d d D d w x w x(,w) w =  / / i j j i   =   x w x w