Consider a pure exchange economy with two goods k = 1,2 and two households i A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively. Utility functions for households A and B are UA (TA1, A2) = TAITA2 and UB(B1, B2) = XB1³2. (a) Find an expression for the Pareto optimal set. (b) Assume e A = (4, 4) and eg = (5,8) are A and B endowments, respectively. Find the competitive equilibrium. (c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this result should not surprise us?

ENGR.ECONOMIC ANALYSIS
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Consider a pure exchange economy with two goods k = 1,2 and two households
i = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively.
Utility functions for households A and B are
UA (TA1, A2) = TA1TA2 and UB(B1, B2) = XB1T32.
(a) Find an expression for the Pareto optimal set.
(b) Assume e A = (4,4) and eg (5,8) are A and B endowments, respectively. Find
the competitive equilibrium.
(c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this
result should not surprise us?
Transcribed Image Text:Consider a pure exchange economy with two goods k = 1,2 and two households i = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively. Utility functions for households A and B are UA (TA1, A2) = TA1TA2 and UB(B1, B2) = XB1T32. (a) Find an expression for the Pareto optimal set. (b) Assume e A = (4,4) and eg (5,8) are A and B endowments, respectively. Find the competitive equilibrium. (c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this result should not surprise us?
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