Question

Intermediate Econ - If anyone has any idea on how to do this problem set, can you show work or explain how you got answer if possible, thanks!

1. Jack has the utility function

u(x, y) = 2x+√y. He is indifferent between two allocations. The first allocation gets Jack 3 of x and 4 of y. The second allocation gets Jack z of x and 9 of y.

(a) What is z?

(b) If Jack is offered the choice between other first allocation and the allocation 0 of x and 49 of y which will he choose?

Answer 1

Solution

Given that : Jack has the utility function, u(x, y) = 2x+√y and that utility values derived out of the 2 different allocations are equal.

Substituting the values in the above given equation according to the allocations.

(a) Allocation 1 - 3 of x and 4 of y

U (x,y) = 2(3) + √(4) i.e., U(x.y) = 8

Allocation 2 -  z of x and 9 of y

Equating the value of 8 to the substituted utility equation

8 = 2(z) + √(9)

This implies z = 2.5

(b) Allocation 0 of x and 49 of y means 2(0) + √(49) i.e., U(x,y) = 7

So,Jack will choose the first allocation i.e., 3 of x and 4 of y

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