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Midterm 1 Answers, Spring 08 Part 1 Q1 : (d) Q2 : (d) Q3 : (c) Q4 : (e) Q5 : (a) Q6 : (c) Q7 : (c) Q8 : (c) Q9 : (b) Q10 : (d) Q11 : (d) Q12 : (a) Q13 : (a) Q14 : (d) Q15 : (b) Part 2 Q1 : By solving 4 x 1 = 3 x 2 and p 1 x 1 + p 2 x 2 = m , we have x 1 ( p 1 ,p 2 ,m ) = 3 m 3 p 1 + 4 p 2 , x 2 ( p 1 ,p 2 ,m ) = 4 m 3 p 1 + 4 p 2 Q2 : MU 1 ( x 1 ,x 2 ) = ∂x 1 (2ln x 1 +3 ln x 2 ) = 2 x 1 , MU 2 ( x 1 ,x 2 ) = ∂x 2 (2ln x 1 +3 ln x 2 ) = 3 x 2 . Hence MRS ( x 1 ,x 2 ) = MU 1 ( x 1 ,x 2 ) MU 2 ( x 1 ,x 2 ) = 2 x 1 3 x 2 = 2 x 2 3 x 1 From the tangency condition MRS ( x 1 ,x 2 ) = p 1 p 2 , we have 2 x 2 3 x 1 = p 1 p 2 , hence x 2 = 3 p 1 2 p 2 · x 1 . Plug this into the budget equation, then p 1 x 1 + p 2 x 2 = p 1 x 1 + p 2 · 3 p 1 2 p 2 · x 1 = 5 p 1 2 · x 1 = m, which yields x 1 = 2 m 5 p 1 . Plug this to the previous formula, then x 2 = 3 m 5 p 1 Summing up, x 1 ( p 1 ,p 2 ,m ) = 2 m 5 p 1 , x 2 ( p 1 ,p 2 ,m ) = 3 m 5 p 1 Q3 : (i) 200 + 300 1 . 1 472 . 73. (ii) 100 +

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