Assume in the market with two consumers, Chloe and Oliver. Chloe’s utility function is U(x, y)...

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Assume in the market with two consumers, Chloe and Oliver. Chloe’s utility function is U(x, y)...

Assume in the market with two consumers, Chloe and Oliver. Chloe’s utility function is U(x, y) = x + 80y^1/2. Oliver’s utility function is U(x, y) = x + 8y. At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Chloe consume?

a. 25

b. 18

c. 121

d. We can’t tell without knowing the initial endowments.

business economics

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Answer 1

Answer #1

a. 25

(At the pareto optimal allocation, MRS for both consumers is equal.
Chloe: MRS = MUx/MUy = (∂U/∂x)/(∂U/∂y) = 1/80(1/2)y^(1/2)-1 = 1/40y^-1/2 = y^1/2/40
Oliver: MRS = MUx/MUy = (∂U/∂x)/(∂U/∂y) = 1/8

So, y^1/2/40 = 1/8
So, y^1/2 = 40/8 = 5
So, y = 5² = 25)

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Answer 2

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