Abby's utility function is given by U = X²Y². For this utility function, MU_x = 2XY² and MU_y = 2X²Y. If good X costs $10 and good Y costs $5, then Abby will consume ____ times as many units of good Y as she does units of good X.

Question

Quizplus · Accepted Answer

The marginal utility per dollar spent on each good should be equal at the optimum. Given the marginal utilities (MU) for X and Y, we have MUx/PriceX = MUy/PriceY. Substituting the given values, we get (2XY)/10 = (2XY)/5, simplifying to 1/10 = 1/5, which implies that for every unit of X, 2 units of Y are consumed to equalize the marginal utility per dollar spent.

Abby's Utility Function Is Given by U = X2Y2

Abby's Utility Function Is Given by U = X²Y²