Answer to Question #291070 in Calculus for Miera Ali

Question

Suppose that the utility function for two products is given by U = x²y, and the budget constraint is 2x + 3y = 120. Find the values of x and y that maximize utility.

Answer 1

The utility is maximized, when:

MUx/Px = MUy/Py and 2x + 3y = 120.

MUx = U'(x) = 2xy,

$MUy = U'(y) = x^2.$

$2xy/2 = x^2/3,$

y = x/3,

2x + 3×x/3 = 120,

3x = 120,

x = 40 units,

y = 40/3 = 13 1/3 units.