FIGURE 6- 2
-Refer to Figure 6- 2. Suppose the price of Y is $1, the consumer's income is $10, and the consumer is currently buying 3 units of good X and 4 units of good Y. If this consumer is maximizing her utility, then the price of X must be
A) $1.
B) $2.
C) $3.
D) $4.
E) impossible to tell with the given information.

Question

FIGURE 6- 2
-Refer to Figure 6- 2. Suppose the price of Y is $1, the consumer's income is $10, and the consumer is currently buying 3 units of good X and 4 units of good Y. If this consumer is maximizing her utility, then the price of X must be
A) $1. 
B) $2. 
C) $3. 
D) $4. 
E) impossible to tell with the given information.

Quizplus · Accepted Answer

If the consumer is maximizing her utility, then the marginal utility per dollar spent on both goods must be equal. At the current bundle, the marginal utility per dollar spent on X is 4/3 and the marginal utility per dollar spent on Y is 1. Thus, the price of X must be such that its marginal utility per dollar spent equals 1. Solving for the price of X, we get: 
MUx/Px = MUy/Py
4/3Px = 1/1
Px = 3/4
Since the consumer is currently buying 3 units of good X, the total amount spent on X is Px*3 = 9/4. This means that the consumer has $10 - 4 = $6 left to spend on Y. Since the price of Y is $1, the consumer can buy 6 units of Y. Thus, the consumer's optimal bundle is (3,6), which is on the budget line with a price ratio of 2 (i.e., Px/Py = 2/1). Therefore, the price of X must be $2.

FIGURE 6- 2 -Refer to Figure 6- 2. Suppose the Price of Y