Diana consumes commodities x and y and her utility function is U(x, y)=xy².Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 3 units of x and 6 units of y, how many units of good y will she consume? A)11 B)3 C)8 D)14 E)None of the above.

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Quizplus · Accepted Answer

The marginal utility of x is MUx = y, while the marginal utility of y is MUy = x. The ratio of the marginal utilities is MUx/MUy = y/x. Therefore, to maximize utility subject to the budget constraint, Diana should consume good x until its marginal utility per dollar is equal to that of good y. MUx/Px = MUy/Py, or y/2 = x. Rearranging, we get y = 2x. 
The budget constraint is 2x + y = 12, or x + y/2 = 6. Substituting y = 2x, we get x + x = 6, or x = 3. Therefore, Diana will consume 3 units of x and 2x = 6 units of y.

Diana Consumes Commodities X and Y and Her Utility Function