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9. AJ has a utility function: u(x,y) = x2y3. The price of x is px =...

9. AJ has a utility function: u(x,y) = x2y3. The price of x is px = 1 and the price of y is py = 2, and AJ has income m = 15 to spend on the goods. To maximize his utility, how many units of y will AJ consume?

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Answer #1

We need to Max subject to the budget constraint PxX+PyY = Income

which is x+2y =15; Unless there is a Corner Solution, the solution will occur where the highest indifference curve is tangent to the budget constraint. Equivalent to that is the statement: The Marginal Rate of Substitution equals the price ratio.

Marginal Utility with respect to x

Marginal Utility with respect to y  

Plug the values:

;   

4y =3x...........................................1

We know the equation of budget constraint

x+2y =15 .....................................2

Solve the eq1 and 2

Eliminate the x to get the value of y

4y = 3(15-2y)

10y =45 ; y =4.5 Units

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