高级微观经济学Cost Minimization推荐.pptVIP

lecture3 for Chu Kechen Honors College Advanced Microeconomics(LECTURE 3:production theory III) Ye Jianliang Cost Minimization Content: Definitions Properties of cost function WACM Some forms of cost functions 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. 1.Definitions Recall the cost minimization condition, let x0, then set Lagrangian: We got: see the fig. What is? 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. 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. 3.WACM Weak Axiom of Cost Minimization (WACM): if xs, xt are in Y, and choice by firm under price ws and wt. then . we can get: 3.WACM 3.WACM 4.Some forms of cost functions If , corresponding price , and is the limited factor (fixed assets), while is the variable factor. The total cost is 4.Some forms of cost functions Envelope theorem: an objective function depend on some parameter. Then: see the prove. 4.Some forms of cost functions LAC and SAC: So See the fig. 4. Duality Given the technology, we can obtain the cost function, are the cos