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# hw2_3070sol - Suggested solutions for HW2 Econ 3070...

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Suggested solutions for HW2 Econ 3070 February 5, 2009 Carefully show how you derive you answer and be sure to interpret your answer where necessary. 1. (a) The utility function is U ( H )=10 H H 2 0 5 10 15 20 25 U(H) 24681 0 H Marginal utility is: U 0 ( H 2 H -10 -8 -6 -4 -2 0 2 4 6 8 10 U'(H) 0 H (b) Jimmy will stop consuming hot dogs when an additional hot dog diminishes his utility, i.e., at a point where his marginal utility turns 1

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negative. We can solve for this quantity using utility maximization problem: max H 0 U ( H )=10 H H 2 The F.O.C. for this problem are U 0 ( H )=0 , so 10 2 H =0 , H =5 . S.O.C. U 00 ( H ) 0 are satis f ed, 2 < 0 . (c) Are Jimmy’s preferences monotone? Why? No, the utility is increasing in H from 0 to 5 and decreasing there- after, so the preferences represented by this utility function are not monotone. 2. (a) U ( F,C )= FC. To draw the indi f erence curves, express C = u/F and plot the curves for u =12 , 18 , 24 . 24 = FC 0 2 4 6 8 10 12 14 16 18 20 C 24681 01 2 1 41 6 1 82 0 F (b) Yes, the MRS is decreasing, as the IC become F atter as we move along the curve (letting Julie to consume more food and less clothing keeping the utility at the same level): this indicates that food, when becoming more abundant in the bundle, becomes less valuable rela- tive to clothing. Indeed, in this case MRS f,c ( MU f MUc = C F ,
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hw2_3070sol - Suggested solutions for HW2 Econ 3070...

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