Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by DA, UB R30 →R where UA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). O Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient.
Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by DA, UB R30 →R where UA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). O Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient.
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.5P
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Transcribed Image Text:Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB:
RR where uA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2-
Which 2 of the following 8 options are true:
There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0).
O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10).
Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources.
We cannot apply the First Welfare Theorem because preferences violate local non-satiation.
The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient.
For all price vectors PER3 we have p1z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}.
O Preferences of both players satisfy strict convexity.
At initial endowment eA= (5, 5), eg = (5, 5), there is a Walrasian Equilibrium with prices p = (1, 2).
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