Question

True or False

Answer each of the following statements True/False. Give a full explanation of your answer. Include clearly labelled graphs where appropriate. (9 points)

a. Consider the following consumption bundles of two goods: (x1,x2) = (27,10), (x1, x2) = (40, 18), and (x1, x2) = (200, 7). Monotonicity implies that (40, 18) is preferred to (27, 10), but does not imply that (200, 7) is preferred to (27, 10).

b. If the marginal rate of substitution between two goods x1 and x2 is not equal to 1, then it is possible for these two goods to be perfect substitutes.

c. When the consumer maximizes his utility over two goods, x1 and x2, the marginal utilities of each good are always equal.

Answer 1

a. Monotonicity implies that the preferred consumption bundle must contain more of all the goods. Thus, (40,18) is preferred over (27,10) but (200,7) is not preferred over (27,18). Hence, the given statement is correct.

b. Two goods can be perfect substitutes if MRS between two goods at different consumption bundles (of those goods) is constant even if it is not equal to 1. Hence, the given statement is correct.

c. When consumer maximizes his utility over two goods, the marginal utilities of each good may not be equal to one. The given statement is false.