practicefinal2-key - Partial Solutions to Practice Final #2...

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Partial Solutions to Practice Final #2 1. Minimize z =3 x 2 xy +2 y 2 4 x 7 y +12 subject to the inequality constraint x + y 15 .I st h e constraint binding or non-binding?ANSWER L =3 x 2 xy +2 y 2 4 x 7 y +12+ λ ( x + y 15) kuhn-tucker L x =6 x y 4+ λ 0 x 0 L y = x +4 y 7 0 y 0 L λ = x + y 15 0 λ 0 Try non-binding λ =0 :So lu t ion x =1 and y =2 . Violates constraint 2. Given the utility function u = x a y b , show that both u and the monotonic transformation, v =ln( x a y b ) have the same MRS. ANSWER dU = ax a 1 y b dx + bx a y b 1 dy =0 dy dx = ay bx then v =l n u = a ln x + b ln y dv = a μ 1 x dx + b μ 1 y dy =0 dy dx = ay bx Question 8 (second part only) 1. Myrtle’s utility maximization problem could be recast as the following: Minimize p x x + p y ys . t .U 0 = x 1 / 3 y 2 / 3 where U 0 is equivalent to the maximum utility (a)
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This note was uploaded on 09/13/2009 for the course EOCNOMICS Econ 331 taught by Professor Kelvinkwainger during the Spring '09 term at Simon Fraser.

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practicefinal2-key - Partial Solutions to Practice Final #2...

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