2. Properties of cost function Proposition: Shephards lemma)if x(w, q) is single point, then x(w,g=Vc(w,g Proposition6: D, X(w, q)=Dw c(w, q)is symmetric negative semi-definite, and D x(w, a)w=0 e the. Proposition: if f(?) is HD1, co and x(.is HD1 too, if f() is concave, co is convex in 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 =