Consider an exchange economy with the two consumers. Consumer 1 has utility function u1 (x1,x2)=x2...

Question

Consider an exchange economy with the two consumers. Consumer 1 has utility function u1 (x1,x2)=x2 and endowment e1=(1,1) and consumer 2 has utility function u2 (x1,x2)=x1+x2 and endowment e2=(1,0).

(a) Which of the hypotheses of Theorem 5.4 fail in this example?

(b) Show that there does not exist a Walrasian equilibrium in this exchange economy.

Robert · Accepted Answer

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Answer (a) 
If each consumer’s utility function is continuous, strongly increasing, and strictly quasiconcave, 
and if the aggregate endowment of each good is strictly positive (i.e., Ii=1 ei ≫ 0), then 
aggregate excess demand satisfies certain conditions.

Consider an exchange economy with the two consumers. Consumer 1 has utility function u1 (x1,x2)=x2 and endowment e1=(1,1) and consumer 2 has utility function u2 (x1,x2)=x1+x2 and endowment e2=(1,0)....

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