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final-old2 - ECON 331 Final Exam Saturday K Wainwright...

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ECON 331 Final Exam Saturday, April 12, 1997 K. Wainwright Name Instructions. — Put you name on the EXAM and the Booklets you use for your answers. — The Exam Sheet must also be handed in as proof you wrote the test. Time allowed is 2.5 HOURS. Total marks = 100 Part One: Shorter problems, 10 marks each 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? 2. Given the utility function u = x a y b , show that both u and the monotonic transforma- tion, v = ln( x a y b ) have the same MRS. 3. Given y = 4 xe 3 x (a) Find the critical point. (b) Check to see if the function is at a maximum or minimum. 4. A $100 bar of gold is appreciating in value according to the formula V = 100 e t How long should the gold bar be kept to maximize the present value if under continuous compounding (a) r = 0 . 08? (b) r = 0 . 12? 5. Suppose an industry has two fi rms which have identical cost functions of the form C ( q i ) = K + cq i (where i = 1 , 2 and 0 < c < 1 ). The market demand function is
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