The consumer's utility function for goods X and Y is U = 3X + 15Y. Good X is placed on the x-axis and good Y is placed on the y-axis. Which of the following statements is TRUE?
I. The marginal utility of good Y is 15.
II. The MRS_XY = 5.
III. The consumer is always willing to trade away 5 units of good X for 1 unit of good Y.

Question

Quizplus · Accepted Answer

I. The marginal utility of good Y is 15, which is true because the coefficient of Y in the utility function represents the marginal utility of Y. III. The statement about the consumer always willing to trade away 5 units of good X for 1 unit of good Y is true because the marginal rate of substitution (MRS), which is the ratio of the marginal utility of X to the marginal utility of Y, is 3/15 = 1/5, meaning the consumer is indifferent to trading 5 units of X for 1 unit of Y to maintain the same level of utility.

The Consumer's Utility Function for Goods X and Y Is