PS1 problem 3 solution

# PS1 problem 3 solution - Practice Problem 1 Riccardo M...

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Practice Problem 1 Riccardo M. Masolo April 6, 2008 1 Question 3: Pareto Eﬃciency a- The set of feasible alternatives, maintaining the same assumptions as in Question 2 for what concerns nonnegative consumption and possibility of wasting goods, is: X = { (( x 1 ,y 1 ) , ( x 2 ,y 2 )) : x 1 ,x 2 ,y 1 ,y 2 0 and x 1 + x 2 10 . 5 , y 1 + y 2 6 } b- The set of Pareto Eﬃcient alternatives can be characterized noticing how only agent one ”enjoys” good y . So any allocation such that all of good y is consumed by agent 1 and good x is not wasted will be part of the PE set: PE = { (( x 1 ,y 1 ) , ( x 2 ,y 2 )) : x 1 ,x 2 0 y 1 = 6 , y 2 = 0 , and x 1 + x 2 = 10 . 5 } c- Right from the deﬁnition of UPS in your notes one can describe it as: UPS = { ( u 1 ,u 2 ) : u 1 = 1 3 x 1 + y 2 1 , u 2 = 5 x 2 for some

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PS1 problem 3 solution - Practice Problem 1 Riccardo M...

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