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HW_06_Solutions

# HW_06_Solutions - HW 6 suggested solutions Question 1 In...

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HW 6 - suggested solutions February 12, 2010 Question 1 In figure 1 we see the two indifference curves through the endowment point. Question 2 In figure 2 we see the two indifference curves through the endowment point. All bundles to the northeast of IC 1 are preferred by agent 1. All bundles to the southwest of IC 2 are preferred by agent 2. All bundles between the indifference curves are preferred by both and hence allow mutual gains from trade. Question 3 In figure 3 we see the set of efficient allocations (red line). In particular it is the set of bundles for which MRS 1 = MRS 2 , or x 1 y 2 = 2 y 2 x 2 y 2 2 = 2 x 2 y 2 = 2 10 - x 1 10 - y 1 . We can solve this for y 1 to get y 1 = 10 x 1 20 - x 1 and hence the set of efficient allocations is [( x , y ) , ( 10 - x , 10 - y )] : y = 10 x 20 - x , x [ 0, 10 ] . The set of efficient allocations that make each consumer better off relative to his/her endowment is the piece of the red line between the indifference curves, or [( x , y ) , ( 10 - x , 10 - y )] : y = 10 x 20 - x , x [ 0, 10 ] , u 1 ( x , y ) 18, u 2 ( 10 - x , 10 - y ) 7 · 16 .

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