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exam_micro1_2006b

# exam_micro1_2006b - Microeconomics 1 Master 1 APE Exam 2 22...

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Microeconomics 1, Master 1 APE Exam 2 22 January 2007 Please write legibly and show your work clearly. Brie°y answer the following questions: (You should not write more than 10 lines per answer) 1. Explain the °rst theorem of welfare economics. 2. Write down and comment Slutsky equation. 3. Under which conditions a preference relation is said to be rational? 4. State Shepard’s lemma. Exercise 1 Fred is an expected utility-maximizing driver who likes to speed. He can either exert self-restraint (at a high effort) and therefore drive safely, or self-indulgence (with low effort) and drive recklessly. Let high effort be represented by e = 1 and low effort by e = 0 : Suppose further that Fred’s preferences over effort and wealth are represented by the utility function u ( w ; e ) = p w ° 5 e : Suppose Fred has an initial wealth of 1000 euros . If Fred gets in an accident, he incurs a 500-euro loss . The probability that Fred gets in an accident depends on his effort level: if e = 0 ; Pr f accident g = 2 3 ; if e = 1 ; Pr f accident g = 1 4 : Assume there are no other costs associated with the accident besides the 500 euros. 1. Will Fred drive safely or recklessly? From now on, it is assumed that Fred drives recklessly, i.e. e = 0 and Pr f accident g = 2 3 : An insurance

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