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Consider an individual with a utility function represented by U(X,Y)=3XY(1/3) where the price of X is...

Consider an individual with a utility function represented by U(X,Y)=3XY(1/3) where the price of X is $2 and the price of $Y is 2 and the individual's total budget is $200. What would be the optimal amount of good X consumed for this individual? (Round to the nearest whole number and report just the number without any units)

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Answer #1

U=3XY^(1/3)

MUx= 3Y^1/3

MUy= 3X(1/3) Y^(-2/3)

MUx/MUy= 3Y/X

Budget constraint= 2X+2Y= 200

At optimal level,MRS= Px/Py

3Y/X= 2/2

3Y=X

2*3Y+2Y=200

8Y=200

Y*= 25

X*= 3*25=75

Optimal amount of Good X= 75

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