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Unformatted text preview: Econ3131 Spring 2008 Talia Bar Prelim 1, suggested solution Question 1 (30 minutes) max A;Y A s & Y 1 & s s:t:A;Y Â¡ and p A A + p Y Y = m Interior solution since CD utility. We solve the system: sY (1 Â¢ s ) A = p A p Y p A A + p Y Y = m b. The solution to the system above is. MRS condition implies p Y Y = (1 Â¢ s ) p A A s Substitution into the budget 1 p A A + (1 & s ) p A A s = m sp A A + (1 & s ) p A A = sm A = sm p A : Y = (1 & s ) m p Y : Given our parameter values: A = 1 4 Â¡ 60 3 4 = 20 Y = 3 4 Â¡ 60 1 = 45 : c. Using the demand for A; we need A = 1 4 & b m 3 4 = 30 ) b m = 90 : The cost of this policy is 90 & 60 = 30 per student. c. 2 A = sm c p A = 1 4 & 60 c p A = 30 ) c p A = 1 2 : Cost of the policy is 30 & ( 3 4 Â¡ 1 2 ) = 7 : 5 d. The price subsidy achieves the A = 30 goal with lower cost to the academy than the increase in cafeteria . Intuitively, the &rst policy increases consumption of apples only through an income e/ect. The second policy lowers the price of good 1, hence, money spent on this subsidy increases demand for apples in two ways, an income e/ect, and a...
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 Spring '06
 MASSON
 Utility, optimal choice

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