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fin-401-06wa

# fin-401-06wa - 1 10th April 2006 Instructions Answer 7 of...

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1 10th April 2006 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. Let X be a choice set and ( B ,C ( · )) be a choice structure on X . (a) Using mathematics, de f ne the weak axiom of revealed preference (WARP). Assume B 1 B , B 2 B , { a, b } B 1 , { a, b } B 2 .ThenWARPsay s a C ( B 1 ) , b C ( B 2 ) a C ( B 2 ) . (b) Assume a two-good model and a price-taking consumer whose behaviour is consistent with WARP. Prove that the substitution e f ect (Slutsky method) of a reduc t ioninthep r iceo fgood1canno tleadtoareduc t ioninthecon sump t iono f good 1. Diagram from Econ 201. Note: no indi f erence curves or other references to the preference-based approach are permitted here. 2. Consider a price-taking agent who likes consumption c and leisure l .Anyt ime notspentatleisureisspentworkingandthetimeendowmentis T . Denotethepriceof consumption by p , the price of leisure by w and the value of the person’s endowment of money by m .L e t c ( p, w, m, T ) and l ( p, w, m, T ) be Marshallian demands, and h c ( p, w, u, T ) and h l ( p, w, u, T ) be Hicksian demands. Fill in the following tables for u = c +2 l 1 / 2 , 0 l T. Thebudgetconstra intis pc + wl = wT + m. c ( p, w, m, T ) l ( p, w, m, T ) Range wT + m p p w p

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2 h c ( p, w, u, T ) h l ( p, w, u, T ) Range u 2 p w p 2 w 2 p w min ± u 2 ,T 1 / 2 ² 0 u 2 4 u 2 p w and u 2 T 1 / 2 u 2 T 1 / 2 TT 1 / 2 p w and u 2 >T 1 / 2 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 3 / 4 . 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 competitive equilibrium of this economy. Draw an Edgeworth rectangle with wealth in the good state along the horizontal axis and wealth in the bad state along the vertical axis. The dimensions of the rectangle are 200 by 100 and the endowment point is right in the middle. Put Andy’s origin in the lower left corner and Brian’s origin in the upper right corner. Andy is risk averse so his indi f erence curves are convex to his origin. Brian is risk neutral so his indi f erence curves are straight lines; in fact, they have a numerical slope equal to the probability of the good state over the probability of the bad state, which is 3 / 4 over 1 / 4 or 3 . The tangencies trapped between the Andy and Brian indi f erence curves through their endowment points form the core – that is, the Pareto e cient allocations where neither person is worse o f
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fin-401-06wa - 1 10th April 2006 Instructions Answer 7 of...

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