Question

Suppose that the utility function for two

commodities is given by U = x² y³ and the budget constraint is 10x + 15y = 250. Find the values of x and y that maximize utility 

Answer 1

The utility is maximized, when:

MUx/Px = MUy/Py and 10x + 15y = 250.

$MUx = U'(x) = 2xy^3,$

$MUy = U'(y) = 3x^2 y^2.$

$2xy^3/10 = 3x^2 y^2/15,$

y/5 = x/5,

y = x,

10x + 15x = 250,

x = y = 10 units.