Advanced icroeconomic (lecture 2: production theory II Ye Jianliang
Advanced Microeconomics (lecture 2: production theory II) Ye Jianliang
profit maximization o Contain: Some definition Isoprofit curve Demand function and it's properties supply function and It's properties Profit function and it's properties lecture 2 for Chu Kechen Honors College
lecture 2 for Chu Kechen Honors College 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 o Profit function m(p)=max{py:y∈Y} When it is one production I(p=I(p, w)=max pf(x)-wX lecture 2 for Chu Kechen Honors College
lecture 2 for Chu Kechen Honors College 1.Some definition • Basic assumption: – Y is changeless, no technical improvement. – The firm is the price taking. • Profit function: – When it is one production: ( ) max { : } p p = y y Y ( ) ( , ) max ( ) = = p p f x p w x - wx
2. Isoprofit curve The profit p·f(x) T(D W )=p·f(x)-w·X≡元 Slope=w/p We then got the q=f(x) isoprofit curve Then Vf(x)=wlp and D2f(x')is negative semidifinite lecture 2 for Chu Kechen Honors College
lecture 2 for Chu Kechen Honors College 2. Isoprofit curve • The profit : • We then got the isoprpfit curve . • Then and is negative semidifinite. ( , ) ( ) p p f w x w x = − q x p f − ( ) x w x = / p slope / = w p q f = ( ) x x * f p ( ) = x w/ 2 D f ( ) x
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 p'y' >p'y'. we can get:(p-p)y-y)≥0Or△p△y≥0 价格上升,最优产量也上升 lecture 2 for Chu Kechen Honors College
lecture 2 for Chu Kechen Honors College 2.Isoprofit curve • Weak Axiom of Profit Maximization (WAPM) if y s , y t are in Y, and choice by firm under price p s and p t . then . we can get: or s s s t p y p y ) 0 s t s t (p -p )(y - y p y 0 价格上升，最优产量也上升