The table below shows the total utility associated with various units of goods X and Y.Table 7.5

-Refer to Table 7.5. 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 7.5
 
-Refer to Table 7.5. 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 utility given the budget of $14, the consumer should choose the combination of goods X and Y that gives the highest marginal utility per dollar spent. This means the consumer should keep consuming each good until the marginal utility per dollar spent is equal for both goods. 
For good X, the marginal utility per dollar is highest at the 3rd unit, where it is 18/2 = 9. For good Y, the marginal utility per dollar is also highest at the 3rd unit, where it is 40/15 = 8/3. 
So, the consumer should consume 3 units of good X and 3 units of good Y, which costs 3x2 + 3x5 = $21. Since this is over the budget of $14, the consumer should decrease consumption of good Y by 1 unit, giving a total expenditure of 3x2 + 2x5 = $16. The total utility associated with this combination is TU(X=3, Y=2) = 42 + 40 = 82. 
Repeating this process, we find that consuming 2 units of good Y and 4 units of good X also gives a total expenditure of $14 and a total utility of TU(X=4, Y=2) = 84. Since this is the highest total utility we can achieve given our budget, the best choice is to consume 4 units of good X and 2 units of good Y, with a total utility of 84.

The Table Below Shows the Total Utility Associated with Various