2. Properties of cost function Propositions: Shephard's lemma)if x(w, q) is single point, then x(w,q=c(w, q Proposition6: Dx(w, q)=Dc(w, q)is symmetric negative semi-definite, and Dx(w,q)·W=0 Proposition: if f( )is HD1, c( and x(.is HD1 too, if f( )is concave, c( is convex in q lecture 3 for Chu Kechen Honors Collegelecture3 for Chu Kechen Honors College 2.Properties of cost function ▪ Proposition5: (Shephard’s lemma) if x(w,q) is single point, then ▪ Proposition6: is symmetric negative semi-definite, and see the fig. ▪ Proposition7: if f(.) is HD1, c(.) and x(.) is HD1 too, if f(.) is concave, c(.) is convex in q. ( , ) ( , ) w x w w q c q = 2 ( , ) ( , ) D q D c q w w x w w = ( , ) 0 D q w x w w =