711hw105 - E CON 711 A NSWER K EY TO HW4 Chang-Koo(CK Chi...

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Unformatted text preview: E CON 711 A NSWER K EY TO HW4 Chang-Koo(CK) Chi October 8, 2009 Problem 6 Each person i ∈ { 1, 2, 3 } faces two problems; choosing x A i how much he has for dinner when plan A is selected and x B i . In case of plan A, his(say, person 1) budget constraint is depicted by 6 x A 1 + m A 1 ≤ w , (0.1) where m A 1 represents the amount of money he spends for consuming the other stuffs. In case of plan B, however, note that the expenditure for dinner depends on his order amount as well as the others’ because it is equally shared. So his budget constraint is given by 1 3 ( 6 x B 1 + 6 x B 2 + 6 x B 3 ) + m B 1 ≤ w . (0.2) To answer (b), suppose that their preference is quasilinear with respect to m by regrading it as numeraire. Observing its first-order condition MU x ( x A 1 ) = 6 MU x ( x B 1 ) = 2, x B 1 > x A 1 follows by the diminishing law of marginal utility. ¥ Problem 7 (a) Yes, he will. Note that he makes 200 calls under the original plan, which means that the utility increment he could enjoy from the 201th call is not as valuable as 10 cents, its additional cost. Definitely, it is not worth 15 cents, its additional cost for the new plan. Hence he will make some calls(less than 200) but he can still make 200 calls(it costs 30 bucks) even when he changed the plan, which demonstrates that he will be better off by choosing the new plan.(Recall the Weak Axiom.) ¥ 1 (b) No, it does not necessarily imply that he will stick to the original plan. His deci- sion hinges upon what his utility function of making calls looks like. One proper counter-example is as follows: Suppose that his marginal utility is given by u ( x ) = .17 if 0 ≤ x ≤ 100 u ( x ) = .10 if 101 ≤ x ≤ 200 u ( x ) = .8 if 200 ≤ x ....
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711hw105 - E CON 711 A NSWER K EY TO HW4 Chang-Koo(CK Chi...

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