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?

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?

Quizplus · Accepted Answer

To determine the utility-maximizing combination, we need to find the Marginal Utility per Dollar (MUD) for both goods. To do this, we divide the marginal utility of each good by its price.

For good X:
The MUD for X = MUx/Px = (29-22)/(2) = 3.5

For good Y:
The MUD for Y = MUy/Py = (24-20)/(5) = 0.8

Since the MUD for X is greater than the MUD for Y, the consumer should allocate more of their budget towards good X. Let x be the number of units of good X purchased and y be the number of units of good Y purchased.

We know that PxX + PyY = $14, which can be rewritten as:
2x + 5y = 14
Solving for y, we get y = (14-2x)/5

The total utility associated with the optimal combination can be calculated as:
TU = MUx(x) + MUy(y)
TU = [(22 + 21 + 20 + 18 + 15) + (18 + 20 + 21 + 22)] + [(18 + 20 + 21 + 23)] = 172

Therefore, the best choice is C, with a total utility of 172.

The Table Below Shows the Total Utility Associated with Various