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 19 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:

Answer 1

Answer: Cathy should therefore purchase less than 20 units of good X and more than 25 units of good Y to reach the optimal bundle.

Step-by-step explanation:

By the rational spending rule, the optimal bundle will be at a quantity where the following is satisfied:

MUx/ MUy = Px / Py

Marginal utility of X / Marginal Utility of Y = Price of X / Price of Y

MUx/ MUy = 9 / 19 = 0.47368

Px / Py = 0.5/1 = 0.5

There is a mismatch as Px/Py is greater than MUx/ MUy.

Marginal utility of X would have to increase and Marginal Utility of Y would have to decrease to get to the optimal bundle.

Marginal utility increases when consumption decreases and vice versa.

Cathy should therefore purchase less than 20 units of good X and more than 25 units of good Y to reach the optimal bundle.