Lecture10: Competitive Market local equilibrium theory i
Lecture10:Competitive Market local equilibrium theory I
Content ◆ Competitive equilibrium ◆ Local analysis cOmplete compete market ◆ Monopoly
Content Competitive equilibrium Local analysis Complete compete market Monopoly
Competitive equilibrium ◆ An allocation a=(x1…xy1……yisa combine of consumption vector x and production vector y. A is feasible if ∑ x1≤+>y for any l=1……L ×J×L
Competitive equilibrium An allocation A= (x1 ,…xI ;y1……yJ ) is a combine of consumption vector x and production vector y. A is feasible if 1 1 , for any 1, I J li l lj i j x y l L = = + = I J L
Competitive equilibrium pAreto Optimal( pareto efficient) ◆ An allocation(x…x;y1…y) s Pareto efficient( optimal ) if there isn't any the other feasible allocation(x,…x;y2…y) made u()2u(x) for any i and u ()>u,(x) for some i See the
Competitive equilibrium Pareto Optimal ( Pareto efficient ) : An allocation is Pareto efficient ( optimal ) if there isn’t any the other feasible allocation , made for any i and for some i. See the fig. 1 1 ( , ; , ) I J x x y y 1 1 ( , ; , ) I J x x y y ( ) ( ) i i u u x x ( ) ( ) i i u u x x
Competitive equilibrium e Competitive equilibrium p'∈9 ■ An allocation(x;…x1;y,…y) and price are a competitive(Walrasian) equilibrium Profit maximization y emax py e Utility maximization x∈maxu(x)Mist. pspa+∑9,p∵y ◆ Market clearing ∑x=0+∑功 j=1
Competitive equilibrium Competitive equilibrium: ◼ An allocation and price are a competitive (Walrasian) equilibrium, if: Profit maximization Utility maximization Market clearing 1 1 ( , ; , ) I J x x y y L p max j j j y Y y p y j 1 max ( ) . . i J i i i i i ij j x X j x u x i s t p x p p y = + 1 1 I J li l lj i j x y = = = +