Lecture10: Competitive Market local equilibrium theory I
Lecture10:Competitive Market local equilibrium theory I
Content Competitive equilibrium ◆ Local analysis o Complete compete market ◆ Monopoly
Content Competitive equilibrium Local analysis Complete compete market Monopoly
Competitive equilibrium ◆ An allocation a=(x1…xy1……y)isa combine of consumption vector x and production vector y. A is feasible if ∑ x1≤O,+ ∑y, for any l=1,…L I×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 o Pareto Optimal( pareto efficient ◆ An allocation(x;…x:…y) is Pareto efficient( optimal if there isn't any the other feasible allocation (xi,. yi, yn) made u (x,)2u,(x) for any i and u, (x)>(x) for some i See the fig
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 o Competitive equilibrium ∈汎 An allocation(x,…xy,…y) and price are a competitive(Walrasian) equilibrium Profit maximization y E max p y Vj Utility maximization x∈maxu1(x)ⅵist.p'x≤p+ x.∈X ∑Qp·y Market clearing >x=O,+2y
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 = = = +