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aps2x313_f08 - Econ 3130.1 Wissink Fall 2008 PS#2 XtraQ...

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1. Central High School (CHS) gets utility from spending money on computers and sports: u = u(C, S) where C = $spent on computers and S = $spent on sports. Central High School has $60,000 to spend on computers and sports, so its budget equation is C + S = $60,000. CHS has preferences that can be represented by the utility function U(C, S) = CS 2 . NOTE: so preferences are Cobb Douglas with α =1/3. So demands are: C = I/3Pc and S = 2I/3Ps. Note that Pc and Ps are both $1. I = 60K originally or 70K if you get the government money. a) Draw the original budget line and the budget lines for Plan A and for Plan B. Ans: See next page. b) Find the “no-plan status quo” expenditures on computers and sports that maximizes CHS’s utility subject to its budget constraint. Show the utility maximizing choice on your graph. Ans: Use what you know about Cobb Douglas to get: C=20K and S=40K (see graph). c) If Plan A is adopted, find the expenditures on computers and sports that maximizes CHS's utility subject to its budget constraint. Show the utility maximizing choice on your graph.
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