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11BM2rev

# 11BM2rev - econ/ams 11b winter 2010 Midterm 2 Review 1 FInd...

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econ/ams 11b winter 2010 Midterm 2 Review 1. FInd the critical point(s) of the functions below subject to the given constraint. a. h ( u, v ) = 5 u + 8 v ; 2 u 2 + 3 v 2 = 30. b. k ( x, y, z ) = xy 2 z 3 ; 5 x + 8 y + 12 z = 300. 2. A household’s utility function is given by U ( q A , q B , q C ) = 5 ln q A +12 ln q B +18 ln q C , where q A , q B and q C are the quantities of goods of type A , B and C that the household consumes per year. The average prices per unit of these goods are p A = 10, p B = 15 and p C = 25, respectively, and the household’s disposable income is Y d = \$60 , 000. a. Assuming that the household spends all of its disposable income on these three goods, how many units of each type should the household consume to maximize its utility ? b. By how much will the household need to increase its disposable income to increase its maximum utility by 5 units? Justify your answer. c. What proportion of its income does the household spend on each type of good when utility is maximized? Do these proportions depend on the income level? Justify your answer.

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11BM2rev - econ/ams 11b winter 2010 Midterm 2 Review 1 FInd...

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