浙江大学：《高级微观经济学》课程PPT教学课件（英文版）Lecture 2 Advanced Microeconomic

Advanced icroeconomic (lecture 2: production theory II Ye Jianliang

Advanced Microeconomics (lecture 2: production theory II) Ye Jianliang

profit maximization o Content, 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 • Content: – 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 taker. 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 taker. • 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 o The profit p·f(x) 丌(p,W)=p·f(x)-W.X=元 slope=w/ We then got the q=f(x) isoprofit curve Then Vf(x)=wlp and D2f(x')is negative semi-definite 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 semi-definite.   ( , ) ( ) 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 pys>py.we can get:(p3-p2)(y-y)≥0Or△p△y≥0 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

2. Isoprofit curve q q 1 lecture 2 for Chu Kechen Honors College

lecture 2 for Chu Kechen Honors College 2. Isoprofit curve y 1 y 2 x q y 1 y 2 x q

2. Isoprofit curve YI q YO q X lecture 2 for Chu Kechen Honors College

lecture 2 for Chu Kechen Honors College 2. Isoprofit curve y 1 y 2 x q y 1 y 2 x YI q YO

3. Demand function factor demand function(set): x=x(p, w) X=XEV(q: wx=pg-I(p, w)) propositions: it's homogenous of degree zero lecture 2 for Chu Kechen Honors College

lecture 2 for Chu Kechen Honors College 3.Demand function • factor demand function (set): • proposition5: it’s homogenous of degree zero. X { ( ) : ( , )} =  = − x wx w V q pq p  x = x w ( , ) p

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 n(=0→Vf(x)=w Ox( w) D f(x) is symmetric negative definite lecture 2 for Chu Kechen Honors College

lecture 2 for Chu Kechen Honors College 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: (.) 0 ( ) (, ) f  = →  =  x w x w 2 2 (.) 0 ( ) is symmetric negative definite. D f    →  2 x x

3. Demand function When Vf(x( w))=w, differentiate with respect to w we get D f(x( w). Dx(w)= or Dx( w)=Df(x( wI- Substitution matrix Dx(w) is a symmetric negative matrIx 1. Ox, /Ow=ax, /Ow -2.dwdk= dwDX( w)lw≤0 lecture 2 for Chu Kechen Honors College

lecture 2 for Chu Kechen Honors College 3.Demand function • When , differentiate with respect to w, we get: or • Substitution matrix is a symmetric negative matrix. – 1. – 2.  = f ( (, )) x w w 2 D f D I ( ) x(,w) x(,w)  = 2 1 D D f [ ( )]− x(,w) x(,w) = Dx(,w) 0 T d d d D d w x w x(,w) w =  / / i j j i   =   x w x w