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Find the optimum bundle of goods if the utility function is as follow: ?(?, ?) =...

Find the optimum bundle of goods if the utility function is as follow:

?(?, ?) = ?^1/4y^3/4

and ?? = 2 ??? ?? = 1 and income is equal to 100

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Answer #1

Optimal bundle is determined where MRS = Px/Py = 2/1 = 2
MRS = MUx/MUy =

So, MRS = 2 gives,
y/3x = 2
So, y = 2*3x
So, y = 6x

Budget constraint: Px*X + Py*Y = income
So, 2x + 1(6x) = 100
So, 8x = 100
So, x = 100/8
So, x = 12.5

y = 6x = 6*(12.5)
So, y = 75

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