income distribution ,pls show the step consider an economy consisting of three p
ID: 1099325 • Letter: I
Question
income distribution ,pls show the step
consider an economy consisting of three people: Tom, Dick and Harry. Their utility functions are Here, ct, cd and ch are the quantities of a single good consumed by Tom, Dick and Harry. Tom and Dick are each endowed with 600 units of this good, and Harry is endowed with no units of the good. An allocation in this economy is a way of dividing up the existing goods between the three people. "The allocate ion in which Tom and Dick each consume 3-50 units of the good, and Harry consumes 500 units of the good, is Pareto optimal." "The allocation in which Tom and Dick each consume 500 units of the good, and Harry consumes 200 units of the good, is Pareto optimal." Assume that Tom and Dick each choose to donate some of their endowed goods to Harry. If Tom donates 150 units. Dick's utility is maximized by donating A Nash equilibrium consists of a pair of donations, one from Tom and one from Dick, such that neither person can alter his donation so as to make himself better off. In the Nash equilibrium, how many units of goods does each person contribute?Explanation / Answer
19. (a) it is true because neither tom nor dick can increase their utility without reducing harry's utility. this can be checked by increaing harry's consumption from 500 goods. the utility of both tom and dick reduces
20. (b) it is false because tom and dick can increase their utility without reducing harry's utility. this can be checked by increaing harry's consumption from 200 goods. the utility of both tom and dick increases.
utility at 500, 500, 200: t = d = 50000000, h= 200
utility at 450, 450, 300: t = d = 60750000, h = 300
21. (b) this can be checked by trial and error. you calculate dick's utility at various values of donation and you will find that it reduces as we move away from 150 on either side.
22. (c) this can be solved in a similar way as 21
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