Question

Suppose that Cathy spends all of her income on 20 units of good X and 25 units of good Y. Cathy's marginal utility from the 20th unit of good X is 9 utils, and her marginal utility from the 25th unit of good Y is 17 utils. If the price of good X is $0.50 per unit and the price of good Y is $1.00 per unit, then to comply with the rational spending rule, Cathy should:
(A) purchase more than 20 units of good X and less than 25 units of Y.
(B) purchase less than 20 units of good X and more than 25 units of good Y.
(C) purchase more than 20 units of good X and more than 25 units of good Y.
(D) continue to purchase 20 units of good X and 25 units of good Y.

Answer 1

Answer:

The correct answer is option B.

Explanation:

Cathy spends all of her income on 20 units of good X and 25 units of good Y.

Cathy's marginal utility from the 20th unit of good X is 9 utils, and her marginal utility from the 25th unit of good Y is 17 utils.

The price of good X is $0.50 per unit and the price of good Y is $1.00 per unit.

The total utility from consumption of both the goods will be maximized when the ratio of the marginal utility derived and price of the good is equal for both the goods.

The ratio for good X

= $\frac{9}{0.5}$

= 18

The ratio for good Y

= $\frac{17}{1}$

= 17

Since the ratio is greater for good X, it means that Cathy should consume less of good X and more of good Y to increase total utility.