420KSpring10HW4answer

420KSpring10HW4answer - Homework 4 Spring 08(Total 20...

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Homework 4, Spring 08 (Total 20 points), Due on Mar. 11, Thu. Q1 (7pt.): Consider an exchange economy with two goods and n individuals, in which consumer i ’s preference is represented by u i ( x i 1 , x i 2 ) = a i x i 1 + b i x i 2 and her initial holding is given by ( ω i 1 , ω i 2 ), where i = 1 , ··· , n . Establish the equation which determines the competitive equilibrium relative price p * 1 p * 2 . —- You don’t have to solve it. Answer : For each i , her MRS is a i 2 x i 1 b i 2 x i 2 = a i x i 2 b i x i 1 Hence the tangency condition MRS = p 1 p 2 yields x i 2 = b 2 i p 2 1 a 2 i p 2 2 · x i 1 Plug this into the budget equation p 1 x i 1 + p 2 x i 2 = p 1 ω i 1 + p 2 ω i 2 , we have x i 1 = p 1 p 2 ω i 1 + ω i 2 p 1 p 2 + a 2 i b 2 i · p 2 1 p 2 2 , x i 2 = b 2 i p 2 1 a 2 i p 2 2 · p 1 p 2 ω i 1 + ω i 2 p 1 p 2 + a 2 i b 2 i · p 2 1 p 2 2 The equation for the equilibrium price boils down to i x i 1 = i ω i 1 , hence it is ± i
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420KSpring10HW4answer - Homework 4 Spring 08(Total 20...

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