高级微观经济学exchange(编辑修改稿)

高级微观经济学exchange(编辑修改稿)内容摘要：

zp g pz pp1[ m a x ( 0 , ( ) ] m a x ( 0 , ( ) ) f o r 1Ki j ijp z z i k    ppThe existence of Walrasian equilibrium – And – Sum up with i – So, we have: • Example: CD economy 1( ) [ m a x ( 0 , ( ) ] ( ) m a x ( 0 , ( ) ) Ki i j i ijz p z z z     p p p p1 11[ m a x ( 0 , ( ) ] ( ) ( ) m a x ( 0 , ( ) ) kkKj i i i ijiiz p z z z      p p p p11( ) m a x ( 0 , ( ) ) = 0 f o r ( ) 0kki i i iiiz z p z   p p p( ) 0iz  pThe first theorem of welfare economics • Pareto efficient allocations: • The solution is Pareto sets and also called contract curve. See the fig. 112 2 21 2 1 2m a x ( ). . ( )us t u uww  12x , xxxxx12( , )xxThe first theorem of welfare economics • If is a Walrasian equilibrium, then x is Pareto efficient. ()x,pThe second theorem of welfare economics • If x* is a Pareto efficient allocation and , suppose that preference are convex, continuous and monotonic, then x* is a Walrasian equilibrium for the initial endowment for i=1……n. • Proof1: upper counter s。