fin-401-07fa

Fin-401-07fa - 1 7th December 2007 Instructions Answer 6 of the following 8 questions All questions are of equal weight Indicate clearly on the rst

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1 7th December 2007 Instructions : Answer 6 of the following 8 questions. All questions are of equal weight. Indicate clearly on the f rst page which questions you want marked. 1. A job candidate from a big US university is presenting his work which empha- sizes a “wonderful” new functional form for estimating ordinary demand equations, based on the utility maximizing approach. Two of the observations on one of his households are that the household bought: (a) (1 , 1) at prices (1 , 2) and (b) (3 / 2 , 1 / 2) at prices (2 , 2) . What question would you ask him? ANSWER Cost of these bundles at these prices 1 2 Deductions 1 35 / 21 " 2 2 44 2 " 1 These data are inconsistent with WARP so it is nonsensical to f t demand equa- tions based on utility-maxmizing approach to the data. The natural question is “Why areyoudo ingth is–itmakesnosense?” 2. Consider a risk-averse individual with initial wealth w 0 and VNM utility func- tion u ( · ) who must decide whether and for how much to insure his car. Assume the probability that he will not have an accident is π . In the event of an accident, he incurs a loss of $ L in damages. Suppose that insurance is available at an actuarially fair price, that is, one that yields insurance companies zero expected pro f ts; denote the price of $1 worth of insurance coverage by p. If the loss ( L ) increased would this individual buy more or less insurance at the point where insurance is fair? Justify your answer carefully. The individual’s expected utility will be f ( x,p, π ,w 0 ,L )= π u ( w 0 px )+(1 π ) u ( w 0 px L + x ) If the insurance is priced “fairly” the f rm’s expected pro f tonea chdo l la ro f insuranceiszero ,so
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2 π p +(1 π )( p 1) = 0 or p =1 π . To f ndtheopt ima lva lueo f x given the parameters of the problem set f ( x, p, π ,w 0 ,L ) x =0 and solve for x at p π .Thu s ( p ) π u ± ( w 0 px )+(1 π )(1 p ) u ± ( w 0 px L + x )=0 or u ± ( w 0 px )= u ± ( w 0 px L + x ) and thus w 0 px = w 0 px L + x or x = L. The question asks for the sign of dx/dL at the point where insurance is fair. Since we have just proved that, with fair insurance, x = L , dx dL > 0 . In words, if the person’s loss in the event of an accident increases he or she will buy one more dollar of insurance for each dollar loss increases. 3. Consider the two-state world of Andy and Brian. In the good state each has a wealth of 100 ; in the bad state each has a wealth of 50 , assuming they do not trade with each other. Let the probability of the good state be 2 / 3 . The only way in which they di f er is Andy is risk averse and Brian is risk neutral. Describe as precisely as you can the Pareto e cient allocations for these two people. Now suppose there are many Andys and an equal number Brians. Describe as precisely as you can the
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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Fin-401-07fa - 1 7th December 2007 Instructions Answer 6 of the following 8 questions All questions are of equal weight Indicate clearly on the rst

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