Goods X and Y

For the following questions, assume that good X is on the horizontal axis and good Y is on the vertical axis in the consumer-choice diagram. PX denotes the price of good X, PY is the price of good Y, and I is the consumer's income. Unless otherwise stated, the consumer's preferences are assumed to satisfy the standard assumptions.

-Refer to Goods X and Y.Suppose the consumer is at an optimum,spending all his income on good X.How are the marginal value of X and the relative price of X related at this corner solution?
A) The marginal value of X and the relative price of X must be equal.
B) The marginal value of X must be less than or equal to the relative price of X.
C) The marginal value of X must be greater than or equal to the relative price of X.
D) There is no definite relationship between the marginal value and the relative price of X.

Question

Goods X and Y

For the following questions, assume that good X is on the horizontal axis and good Y is on the vertical axis in the consumer-choice diagram. PX denotes the price of good X, PY is the price of good Y, and I is the consumer's income. Unless otherwise stated, the consumer's preferences are assumed to satisfy the standard assumptions.

-Refer to Goods X and Y.Suppose the consumer is at an optimum,spending all his income on good X.How are the marginal value of X and the relative price of X related at this corner solution?
A) The marginal value of X and the relative price of X must be equal.
B) The marginal value of X must be less than or equal to the relative price of X.
C) The marginal value of X must be greater than or equal to the relative price of X.
D) There is no definite relationship between the marginal value and the relative price of X.

Quizplus · Accepted Answer

In a corner solution where the consumer spends all their income on good X, the marginal value of X must be greater than or equal to the relative price of X. This is because the consumer sees enough value in good X to spend all their income on it, even at its current price, indicating that the marginal value (the additional satisfaction from consuming one more unit of X) is at least as high as the cost of acquiring it.