Lecture 12: Exchange General Equilibrium theory
Lecture 12: Exchange General Equilibrium theory I
Content Pure exchange system The existence of Walrasian equilibrium The first theorem of welfare economics The second theorem of welfare economics EXchange with production
Content • Pure exchange system • The existence of Walrasian equilibrium • The first theorem of welfare economics • The second theorem of welfare economics • Exchange with production
Pure exchange system An allocation A=(x, x))is feasible if , for any I=l,…L @, is the endowments of commodity l Edgeworth box:2×2
Pure exchange system • An allocation A= (x1 ,…xI ) is feasible if • is the endowments of commodity l • Edgeworth box: 2×2 1 , for any 1, I li l i x l L = = l
Pure exchange system Walrasian equilibrium An allocation(x2…x) and price p'∈are a Walrasian equilibrium if Utility maximization x∈maxa1(x) x∈X St.px≤pOl Feasible x;≤O see the fig
Pure exchange system • Walrasian equilibrium: – An allocation and price are a Walrasian equilibrium, if: • Utility maximization • Feasible see the fig. 1 ( , )I x x L p max ( ) . . i i i i x X i i x u x s t x p p 1 I li l i x =
The existence of walrasian equilibrium Given an endowment w, is there any Walrasian equilibria? Assumption 1: The demand function is Hdo of price The aggregated extra-demands (p)=∑x(p,p)- Assumption2: Walras law: p=(P)=0
The existence of Walrasian equilibrium • Given an endowment w, is there any walrasian equilibria? • Assumption1:The demand function is HD0 of price. The aggregated extra-demands • Assumption2: Walras’ law: 1 ( ) [ ( , ) ] I i i i i z p x p pw w = = − pz p( ) 0 =