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f981a - ECON 331 Final Exam Spring 1998(a Name...

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ECON 331 Final Exam Spring 1998 (a) Name: Instructions: The exam is worth 60 marks. All ques- tions are equally weighted. You are to do all questions. Answer all questions in the exam booklets provided. Time allowed is 3 hours. You must hand in the exam with your booklets. 1. A competitive frim has the following production function, q = 60 K +34 L 4 KL 6 K 2 3 L 2 . If p is the market price, w is the wage, and r is the rental rate of captital, then: (a) Write down the fi rm’s pro fi t function. (b) solve for the optimal K and L (c) Use the Hessian to check the second order con- ditions 2. A consumer with the following utility function u = xy 2 faces two constraints. The fi rst is the normal budget constraint where he has \$100 and the price of x and y are both \$1. Also, the consumer has been issued 120 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require \$3 and 6 coupons.
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