consider a pure exchange economy of two individual and two goods x and y individual A is endowed with 1 unit of good X and none of good Y,while individual B with 1 unit of good Y and none of good X.Assuming utility function of individual A and B to be Ua=XA
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Consider a pure exchange economy with two consumers (A and B), two goods (1 and
2), and endowment point E = (Ae,
Be) (so that Ae is the initial endowment of consumer A
and Be is the initial endowment of consumer B). Suppose the two consumers have identical
preferences represented by the utility function u. You may assume that u is smooth, strictly
increasing in each of its arguments, and strictly concave.
1. Show that X = ( Ae+ Be
2
,
Ae+ Be
2
) is a Pareto efficient allocation.
2. Can the allocation X be supported as a market equilibrium? If so, what prices would
support this allocation as a market equilibrium?
3. Are there other Pareto efficient allocations in this economy?
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