The table shows the total utility data for products X and Y. Assume that the prices of X and Y are $3 and $4, respectively, and that consumer income is $18. How many units of the two products will the consumer buy to get maximum utility?
A) 1 of X and 4 of Y
B) 2 of X and 2 of Y
C) 2 of X and 3 of Y
D) 3 of X and 4 of Y

Question

The table shows the total utility data for products X and Y. Assume that the prices of X and Y are $3 and $4, respectively, and that consumer income is $18.  How many units of the two products will the consumer buy to get maximum utility?
A) 1 of X and 4 of Y 
B) 2 of X and 2 of Y 
C) 2 of X and 3 of Y 
D) 3 of X and 4 of Y

Quizplus · Accepted Answer

To find the optimal consumption bundle, we need to calculate the marginal utilities per dollar spent on each product:

For X, MU/Price = 10/3 = 3.33

For Y, MU/Price = 16/4 = 4

The consumer should purchase more of product Y, as its marginal utility per dollar spent is higher. To find the optimal quantity of each, we need to set the marginal utility per dollar spent equal to each other, and solve for the quantities:

10/3 = 16/4(Y/X)
40 = 48(Y/X)
Y/X = 40/48 = 5/6

Now we can use the budget constraint to find the quantity demanded for each:

3X + 4Y = 18

Substitute Y/X = 5/6:

3X + 4(5/6)X = 18
X = 2

Therefore, the optimal consumption bundle is 2 units of X and 3 units of Y.

The Table Shows the Total Utility Data for Products X