Econ313Prelim2SolSpring08

Econ313Prelim2SolSpring08 - Econ313-1 Spring 2008 Talia Bar...

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Econ313-1 Spring 2008 Talia Bar Prelim 2 suggested solution Part I - Questions 1 and 2. Question 1 (20 minutes) (Consumer theory) People on Gull island consume two goods x 1 and x 2 . Each consumers°preferences are rational, well behaved and homothetic*. These preferences are represented by a utility function u ( x 1 ; x 2 ) (same utility for all consumers rich or poor). Initially, prices of the goods are p 1 = 1 and p 2 = 1 : There are rich and poor people in the island. Rich islanders have an income m R = 120 : Poor islanders (poor or low income) have income m L = 100 : Assume interior solutions throughout this question. (a) It is known that the optimal choice of rich islanders is ( x 1 ; x 2 ) R = (60 ; 60) : What is the optimal choice of poor islanders? (b) Provide one graph in the 2 goods space x 1 ° x 2 showing the budget and the optimal choice of a rich consumer and of a poor consumer. Show each consumer°s indi/erence curve though his optimal point. Recall that the income o/er curves of homothetic preferences are all straight lines through the origin. When income is scaled up or down by any amount t > 0 , the demanded 1
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bundle scales up or down by the same amount. In this question, since a poor consumer has the same homothetic utility as a rich consumer and only a lower income, demand is scaled down by the same proportion, hence ( x 1 ; x 2 ) L = (50 ; 50) : (c) A new king came to power. The king decides to promote equality for all islanders. He imposes a tax of t
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