Answer the question on the basis of the following marginal utility data for products X and Y.Assume that the prices of X and Y are $4 and $2 respectively and that the consumer's income is $18. $\begin{array}{c}
\begin{array}{c}
\text {Units}\
\underline{\text {of X }}\
1\
2\
3\
4\
5\
6
\end{array}
\begin{array}{c}
\text {Marginal}\
\underline{\text {Utility, X}}\
20\
16\
12\
8\
6\
4
\end{array}
\begin{array}{c}
\text {Units}\
\underline{\text {of Y }}\
1\
2\
3\
4\
5\
6
\end{array}
\begin{array}{c}
\text {Marginal}\
\underline{\text {Utility, Y}}\
16\
14\
12\
10\
8\
6
\end{array}
\end{array}$
Refer to the data.If the price of X decreases to $2,then the utility-maximizing combination of the two products is:
A) 2 of X and 5 of Y.
B) 4 of X and 6 of Y.
C) 6 of X and 3 of Y.
D) 4 of X and 5 of Y.

Question

Answer the question on the basis of the following marginal utility data for products X and Y.Assume that the prices of X and Y are $4 and $2 respectively and that the consumer's income is $18. $\begin{array}{c}
\begin{array}{c}
\text {Units}\
\underline{\text {of  X }}\
1\
2\
3\
4\
5\
6
\end{array}
\begin{array}{c}
\text {Marginal}\
\underline{\text {Utility, X}}\
20\
16\
12\
8\
6\
4
\end{array}
\begin{array}{c}
\text {Units}\
\underline{\text {of  Y }}\
1\
2\
3\
4\
5\
6
\end{array}
\begin{array}{c}
\text {Marginal}\
\underline{\text {Utility, Y}}\
16\
14\
12\
10\
8\
6
\end{array}
\end{array}$
 Refer to the data.If the price of X decreases to $2,then the utility-maximizing combination of the two products is:
A) 2 of X and 5 of Y.
B) 4 of X and 6 of Y.
C) 6 of X and 3 of Y.
D) 4 of X and 5 of Y.

Quizplus · Accepted Answer

To find the utility-maximizing combination of X and Y, we need to calculate the marginal utility per dollar for both goods.

Initially:

MUx/Px = 20/4 = 5 
MUy/Py = 16/2 = 8

After the price of X decreases to $2:

MUx/Px = 16/2 = 8 
MUy/Py = 16/2 = 8

Now, we need to compare the marginal utility per dollar of both goods and choose the combination that gives us the highest ratio.

Option A: 2 of X and 5 of Y 
MUx/Px = 16/2 = 8 
MUy/Py = 8/2 = 4 
Total Utility = (2*16) + (5*8) = 72

Option B: 4 of X and 6 of Y 
MUx/Px = 16/2 = 8 
MUy/Py = 6/2 = 3 
Total Utility = (4*16) + (6*6) = 80

Option C: 6 of X and 3 of Y 
MUx/Px = 12/2 = 6 
MUy/Py = 12/2 = 6 
Total Utility = (6*12) + (3*12) = 108

Option D: 4 of X and 5 of Y 
MUx/Px = 12/2 = 6 
MUy/Py = 8/2 = 4 
Total Utility = (4*12) + (5*8) = 76

Therefore, the utility-maximizing combination of the two products is 6 units of X and 3 units of Y.

Answer the Question on the Basis of the Following Marginal