Advanced microeconomics (LECTURE 3: production theory I) Ye Jianliang
Advanced Microeconomics (LECTURE 3:production theory III) Ye Jianliang
Cost Minimization Content Definitions Properties of cost function WACM Some forms of cost functions lecture 3 for Chu Kechen Honors College
lecture3 for Chu Kechen Honors College Cost Minimization ▪ Content: • Definitions • Properties of cost function • WACM • Some forms of cost functions
1. Definitions One production, cost function is c(w, q=min WX x≥0 St.f(x)≥q The optimal solution x(w, q), is the conditional factor demand function Question1: calculate the conditional factor demand function of c-d tech and ces tech lecture 3 for Chu Kechen Honors College
lecture3 for Chu Kechen Honors College 1.Definitions ▪ One production, cost function is ▪ The optimal solution x(w,q), is the conditional factor demand function. ▪ Question1:calculate the conditional factor demand function of C-D tech. and CES tech. 0 ( , ) min . . ( ) x c q s t f x q = w w x
1. Definitions Recall the cost minimization condition let x>0, then set Lagrangian (2x)=wx-4(f(x)-q) We got w=nVf(X) he What a is? lecture 3 for Chu Kechen Honors College
lecture3 for Chu Kechen Honors College 1.Definitions ▪ Recall the cost minimization condition, let x>0, then set Lagrangian: ▪ We got: see the fig. ▪ What is? L ( , ) ( ( ) ) x wx x = − − f q f ( ) w x =
2. Properties of cost function Proposition: c(w, q) is homogeneous of degree 1 in w, and non-decreasing in q Proposition 2: c(w, q) is concave function of Proposition3: x(w, g) is homogeneous of degree 0 in w Proposition4: if v(q) is convex, then is x( if v(g is strictly convex, x(. is single point lecture 3 for Chu Kechen Honors College
lecture3 for Chu Kechen Honors College 2.Properties of cost function ▪ Proposition1: c(w,q) is homogeneous of degree 1 in w, and non-decreasing in q. ▪ Proposition2: c(w,q) is concave function of w. ▪ Proposition3: x(w,q) is homogeneous of degree 0 in w. ▪ Proposition4:if V(q) is convex, then is x(.) if V(q) is strictly convex, x(.) is single point