Question

Mr. Rational has $27 that he plans to spend purchasing 5 units of good X (priced at $3 per unit) and 6 units of good Y (priced at $2 per unit). The marginal utility of the fifth unit of X is 30, and the marginal utility of the sixth unit of Y is 18. If Mr. Rational is a utility maximizer, he should: a. buy less of X and more of Y. b. buy more of X and less of Y. c. buy X and Y in the quantities indicated. d. buy less of X and even lesser than that of Y. e. not buy anything.

Answer 1

Option A, buy less of X and more of Y is correct.

Step-by-step explanation:

The amount that Mr. Rational is going to spend = $27

Quantity of good X = 5 units

Price of good X (Px) = $3 per unit

Marginal utility of 5th unit of X (MUx) = 30

Quantity of good Y = 6 units

Price of good Y (Py) = $2 per unit

Marginal utility of 6th unit of Y (MUy) = 18

`Now \ find \ (MUx)/(Px) = (30)/(3) = 10 \\`

`Now \ (MUy)/(Py) = (18)/(2) = 9`

`Since \ the \ (MUx)/(Px) is \ greater \ than \ (MUy)/(Py).`

So good x will be substituted for y in order to reach the consumer equilibrium.

`(MUx)/(Px) = (MUy)/(Py)`

Thus, Option a. buy less of X and more of Y is correct.