A small economy has only two consumers, Charlie and Doreen.Charlie's utility function is U(x, y)= x + 154y^1/2.Doreen's utility function is U(x, y)= x + 7y.At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Charlie consume? A)121 B)9 C)22 D)18 E)We can't tell without knowing the initial endowments.

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Quizplus · Accepted Answer

Charlie's marginal utility of y is 154y^-1/2, and Doreen's marginal utility of y is 7. At a Pareto optimal allocation, the marginal utilities of y must be equal for both consumers. Therefore, we have:154y^-1/2 = 7Solving for y, we get:y = 121

A Small Economy Has Only Two Consumers, Charlie and Doreen