Question

Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA = (ω1A, ω2A) and person B is initially endowed with ωB = (ω1B, ω2B), where ω1A + ω1B = ω1 and ω2A + ω2B = ω2. Person A’s preferences are given by UA(x1, x2) = ln(x1) + x2 and Person B’s preferences are given by UB(x1, x2)=x1 + ln(x2).You are informed that p2 = 1, that ω1A = 0, and that ω2A > 1. With this extra information you can say that:

A.there will be no trade

B. x2A =ω2A + 1

C.p1 = ω2B + 1

D.x2B= 1/(ω2B +1)

E. x2A =ω1B + 1

Answer #1

Consider an exchange economy consisting of two people, A and B,
endowed with two goods, 1 and 2. Person A is initially endowed with
Wa = (0,9) and person B is initially endowed with Wb = (10,0). They
have identical preferences, which are given by Ua,b (X1, X2) =
(X1)^2 x X2 . Suppose that P2 = 1 . Under the competitive
equilibrium, what is P1?

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utility functions over goods x and y (6)
ua=ua(xa,ya)=xaya
ub=ub(xb,yb)=xbyb
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an Edgeworth box that would show this two-person two-goods
situation.
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