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practicefinal2-key

# 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 . Is the 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 : Solution 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 = ln 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 y s.t. U 0 = x 1 / 3 y 2 / 3 where U 0 is equivalent to the maximum utility (a) (4 marks) Find the values of x and y that solve this minimization problem.

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

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