HW1_Solutions

# HW1_Solutions - 6 a)MRS=y b)Convex indifference curve...

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Solutions to HW1 1) a)0.5*LA+1.25*NY 200 b) For NY<20 the previous budget set For NY 20 the budget set is 0.5*LA+NY 200 c) For NY<20 0.5*LA+1.25NY 200 For NY 20 the budget set is 0.25*LA+NY 200 2) a)Bag End: 3H+F 3000 Bree: 2H+4F 3000 b)Bag End is Cheaper if 3H+F<2H+4F implying H<3F Bree is Cheaper if 3H+F>2H+4F implying H>3F c)Please see Appendix 3) a)1.5*C+2*M 65 b) 1.5*C+2*M 65 and C 4 c) 1.5*C+2*M 65 and C 4 and M 30 d) 1.5*C+2*M+S 65

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4) a)MRS=3 Yes 2 4 6 8 10 6 4 2 2 b)MRS=(y/x)Yes 2 4 6 8 10 4 6 8 10 c)(1/(2 x)) Yes 2 4 6 8 10 0.5 1.0 1.5 2.0 2.5 3.0
d)((-x)/y) If y>0 then the indifference curve is convex. 2 4 6 8 10 10 5 5 10 e)((y²)/(x²)) Convex 2 4 6 8 10 10 10 20 5) a)MUx=y MUy=x MRS=(y/x) diminishing MRS b)MUx=2xy² MUy=2x²y MRS=(y/x)diminishing MRS c)MUx=(1/x) MUy=(1/y) MRS=(y/x)diminishing MRS These three functions are monotone transformations of each other. The analysis shows that the MRS will still be diminishing even though the marginal utilities may change.

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Unformatted text preview: 6) a)MRS=y b)Convex indifference curve indicating that the function is quasiconcave. c)x+lny=K d) Here x good can be interpreted as a numeraire (or corresponding monetary value) MUx=1 and MUy=1/y. Here the marginal utility for an additional unit of x is constant whereas it is decreasing for the good y. The indifference curves are parallel to each other with respect to numeraire good x. Accordingly if there is an increase in income without any change in prices, the consumer will choose to buy more of good x and will buy the same amount of y good that was chosen before. e)Since the function is linear in x, then the utility increases with the same amount of increase in x. For good y, utility increases less than the amount that is consumed. This function might be useful in the aggregation of utilities in welfare analysis. APPENDIX...
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HW1_Solutions - 6 a)MRS=y b)Convex indifference curve...

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