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Unformatted text preview: Fall 2004 ARE211 FINAL EXAM MONDAY DEC 14, ’04 This is the final exam for ARE211. As announced earlier, this is an openbook exam. However, use of computers, calculators, Palm Pilots, cell phones, Blackberries and other comparable objects is forbidden. If a question says “prove formally” then we mean it: a purely verbal answer is unlikely to be given full marks. However, if there’s a step in your answer that involves a theorem that’s given in the lecture notes, then you may state the theorem and reference the notes. Allocate your 180 minutes in this exam wisely. The exam has 175 points, so aim for 1 minute per point. Make sure that you first do all the easy parts, before you move onto the hard parts. Always bear in mind that if you leave a partquestion completely blank, you cannot conceivably get any marks for that part. The questions are designed so that, to some extent, even if you cannot answer some parts, you can still be able to answer later parts. So don’t hesitate to leave a part out. You don’t have to answer questions and parts of questions in the order that they appear on the exam, provided that you clearly indicate the question/part question you are answering. 2 Problem 1 (25 points). Let f : R 2 → R and g : R 2 → R be two concave functions and fix α ∈ R 2 . Let Y = { ( y 1 , y 2 ) ∈ R 2 : 5 x 1 , x 2 ∈ R 2 s.t. y 1 ≤ f ( x 1 ) , y 2 ≤ g ( x 2 ) and x 1 + x 2 ≤ α } . To give you some intuition, functions f and g might be interpreted as production functions, x 1 and x 2 as input vectors and Y as a production set....
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This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Simon

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