fin-401-05faa

# fin-401-05faa - 1 20th December 2005 Instructions: Answer 7...

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1 20th December 2005 Instructions : Answer 7 of the following 9 questions. All questions are of equal weight. Indicate clearly on the f rst page which questions you want marked. 1. Assume some consumer chooses bundle x j at prices p j , j =1 , 2 , 3 , where p 1 =( 1 , 1 , 2) ; x 1 =(5 , 19 , 9) p 2 =( 1 , 1 , 1) ; x 2 =(12 , 12 , 12) p 3 =( 1 , 2 , 1) ; x 3 =(27 , 11 , 1) . Show these data satisfy WARP. Is there an intransitivity in the revealed prefer- ences? Justify your answer. Cost of these bundles at these prices 1 2 3 Deductions 1 42 48 40 1 " 3 2 33 36 39 2 " 1 3 52 48 50 3 " 2 These preferences are consistent with WARP but clearly they violate transitivity. 2. Income and substitution e f ects are an important part of the theory of consumer behaviour. Consider a price-taking consumer in a two-good world. Let m denote money income, ( p 1 ,p 2 ) prices, x j ( p 1 ,p 2 ,m ) Marshallian demands, and h j ( p 1 ,p 2 ,u ) Hicksian demands. Write the Slutsky equation for the e f ect of changing the price of good 2 on the demand for good 1 . Now suppose the person is endowed not with money income m but quantities of goods 1 and 2 ( e 1 ,e 2 ) . Rewrite the Slutsky equation for the e f ect of changing the price of good 2 on the demand for good 1 . x 1 ( p 1 ,p 2 ,m ) p 2 = h 1 ( p 1 ,p 2 ,u ) p 2 x 2 x 1 ( p 1 ,p 2 ,m ) m (1) With endowments x 1 ( p 1 ,p 2 ,p 1 e 1 + p 2 e 2 ) p 2 = x 1 ( p 1 ,p 2 ,m ) p 2 + e 2 x 1 ( p 1 ,p 2 ,m )

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2 x 1 ( p 1 ,p 2 ,p 1 e 1 + p 2 e 2 ) p 2 = h 1 ( p 1 ,p 2 ,u ) p 2 x 2 x 1 ( p 1 ,p 2 ,m ) m + e 2 x 1 ( p 1 ,p 2 ,m ) m = h 1 ( p 1 ,p 2 ,u ) p 2 +( e 2 x 2 ) x 1 ( p 1 ,p 2 ,m ) m 3. Consider the two-state world of Andy and Brian. In the good state each has aw ea l tho f 100 ; in the bad state each has a wealth of 50 , assuming they do not trade with each other. Let the probability of each state be 1 / 2 . The only way in which they di f er is Andy is risk averse and Brian is risk neutral. Both are expected utility maximizers. Describe as precisely as you can the Pareto e
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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-401-05faa - 1 20th December 2005 Instructions: Answer 7...

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