shrinkingcore

shrinkingcore - Shrinking Core Example Consider two...

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Shrinking Core Example Consider two individuals, A and B , who have identical utility functions x 1 x 2 . A starts off with e A 1 = 10 and e A 2 = 0 while B starts off with e B 1 = 0 and e B 2 = 10. Note that both A and B get zero utility from their current endowments. Since both are getting zero utility from their endowments, all Pareto efficient points that give utility greater than or equal to zero for both A and B will be in the core. Therefore, x A 1 = 0, x A 2 = 0, x B 1 = 10, and x B 2 = 10 is a point in the core: A gets zero utility and this a PE point as there is no way of making A or B better off without making the other worse off. Suppose now that there are two A ’s and two B ’s. If we give both A’s zero of each good and both B’s 10 of each good will this allocation be in the core? The answer is no, as the core requires both Pareto efficiency and that no coalition of individuals could be made better off by trading among themselves. The only coalition when there is one
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