The table below shows the total utility associated with various units of goods X and Y. Table 6.5

- Refer to Table 6.5.Given that the price of good X is $2 per unit,the price of good Y is $5 per unit,and that the consumer spends a total of $14 on both goods,what is the total utility associated with the utility-maximizing combination?
A)84
B)154
C)172
D)Indeterminate
E)215

Question

The table below shows the total utility associated with various units of goods X and Y. Table 6.5

- Refer to Table 6.5.Given that the price of good X is $2 per unit,the price of good Y is $5 per unit,and that the consumer spends a total of $14 on both goods,what is the total utility associated with the utility-maximizing combination?
A)84 
B)154 
C)172 
D)Indeterminate 
E)215

Quizplus · Accepted Answer

To maximize total utility while spending a total of $14, the consumer should allocate their budget between the two goods so that the marginal utility per dollar spent is equal for both goods. We can find the marginal utility per dollar spent for each good by dividing the marginal utility by the price.

For Good X, the marginal utility per dollar spent is: 
MUx/Px = 18/2 = 9

For Good Y, the marginal utility per dollar spent is: 
MUy/Py = 64/5 = 12.8

Since the marginal utility per dollar spent is higher for Good Y, the consumer should allocate more of their budget towards Good Y. In this case, they should spend 2*$5 = $10 on Good Y, and $14 - $10 = $4 on Good X.

The total utility associated with this utility-maximizing combination is the sum of the marginal utilities of each good at these consumption levels, which is:

MUx + MUy = 18 + 80 = 98

Therefore, the answer is (C) 172.

The Table Below Shows the Total Utility Associated with Various