（精）lecture 2 production theory II(高级微观-武大高研,叶建亮).ppt

lecture 2 for Chu Kechen Honors College ch.1 Advanced Microeconomics(lecture 2: production theory II) Ye Jianliang profit maximization Contain: Some definition Isoprofit curve Demand function and it’s properties supply function and it’s properties Profit function and it’s properties 1.Some definition Basic assumption: Y is changeless, no technical improvement. The firm is the price taking. Profit function: When it is one production: 2. Isoprofit curve The profit : We then got the isoprpfit curve . Then and is negative semidifinite. 2.Isoprofit curve Weak Axiom of Profit Maximization (WAPM) if ys, yt are in Y, and choice by firm under price ps and pt. then . we can get: or 2. Isoprofit curve 2. Isoprofit curve 3.Demand function factor demand function (set): proposition5: it’s homogenous of degree zero. 3.Demand function One production: regular p as 1. let x(,w) be the profit maximization choice (function means x is single point under w) of input factor vector under factor price w. then must hold: 3.Demand function When , differentiate with respect to w, we get: or Substitution matrix is a symmetric negative matrix. 1. 2. 3.Demand function Are the profit maximization give us the sufficient information about the production behavior? Such as (1) factor demand function; and (2)yeild (supply) function? Proposition6:demand for factor i is: or 4.supply function Supply set: Proposition7: y(.) is homogenous of degree 1. Proposition8: If Y is convex for any p, then is y(p), if Y is strictly convex, y(p) is a single point. 4.Supply function Proposition9: (Hotelling’s lemma) y(p) is single point, then (recall prop.6) The supply substitution matrix is symmetric positive matrix. And (why?) see the fig. 5.Profit function Proposition10: is homogenous of degree 1