HW_07_Solutions

HW_07_Solutions - Economics 11 HW 7 - Suggested Solutions...

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Economics 11 HW 7 - Suggested Solutions Question 1 (a) All e¢ cient allocations: y A x A = y B x B = 1000 y A 400 x A This becomes y A = 2 : 5 x A : x A y A = 180000 ; x B y B = 40000 : Hence the contract curve is part of the line y A = 2 : 5 x A indi/erence curves. (b) Normalize p y = 1 : Consumer A: ± income = 300 p x + 600 ± demands x A = (1 = 2)(300 p x + 600) p x y A = (1 = 2)(300 p x + 600) 1 Consumer B: ± income = 100 p x + 400 ± demands x B = (1 = 2)(100 p x + 400) p x y B = (1 = 2)(100 p x + 400) 1 1
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Market clearing condition: (1 = 2)(300 p x + 600) 1 + (1 = 2)(100 p x + 400) 1 = 1000 Solve for p x : p x = 2 : 5 By plugging p x = 2 : 5 into the demands we get, x A = 270 ; y A = 675 ; x B = 130 ; y B = 325 : (c) See ±gure 1. Question 2 (a) All e¢ cient allocations: y A x A = ( y B ) 1 = 2 5 = (1200 y A ) 1 = 2 5 This becomes 5 y A = (1200 y A ) 1 = 2 ( x A ) : Squaring both sides and moving all terms to the LHS give us 25( y A ) 2 + ( x A ) 2 y A 1200( x A ) 2 = 0 : Solving for y A using the quadratic formula
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This note was uploaded on 04/01/2010 for the course ECON 180052110 taught by Professor Mcdevitt during the Winter '09 term at UCLA.

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HW_07_Solutions - Economics 11 HW 7 - Suggested Solutions...

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