3. Suppose' u¹(x¹) − − (2 − ¹;)² – (2 − ¹;)² for each agent i, and w} = w = 2 andw} = w} = 0.(a) Argue that no allocation z with r¦ ‡ r, can be Pareto optimal.(b) Argue that any allocation z with r = ris Pareto optimal.r(c) What are all of the competitive equilibria?

Utility function : ui =-(2 -x1i )2 -(2 - x2i)2 There are two economic agents , 1 & 2 w11 = w22…

3. Suppose¹ u¹(rª) = −(2 − x{ )² – (2 — £½)² for each agent i, and w=w = 2 and w₁ =w₂ = 0. (a) Argue that no allocation r with x ‡ ½ can be Pareto optimal. (b) Argue that any allocation with x = x is Pareto optimal. (c) What are all of the competitive equilibria?

3. Suppose¹ u¹(rª) = −(2 − x{ )² – (2 — £½)² for each agent i, and w=w = 2 and w₁ =w₂ = 0. (a) Argue that no allocation r with x ‡ ½ can be Pareto optimal. (b) Argue that any allocation with x = x is Pareto optimal. (c) What are all of the competitive equilibria?

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

3. Suppose' u¹(x¹) − − (2 − ¹;)² – (2 − ¹;)² for each agent i, and w} = w = 2 and
w} = w} = 0.
(a) Argue that no allocation z with r¦ ‡ r, can be Pareto optimal.
(b) Argue that any allocation z with r = ris Pareto optimal.
r
(c) What are all of the competitive equilibria?

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