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. $Y‾1614121086\begin{array}{c}\begin{array}{c}\text {Units}\\\underline{\text {of X }}\\1\\2\\3\\4\\5\\6\end{array}\begin{array}{c}\text {Marginal}\\\underline{\text {Utility, X}}\\20\\16\\12\\8\\6\\4\end{array}\begin{array}{c}\text {Units}\\\underline{\text {of Y }}\\1\\2\\3\\4\\5\\6\end{array}\begin{array}{c}\text {Marginal}\\\underline{\text {Utility, Y}}\\16\\14\\12\\10\\8\\6\end{array}\end{array}$
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.

Y‾1614121086\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.

Jackson Dulaney · Accepted Answer

Final Answer : D, Explanation :  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 = 5MUy/Py = 16/2 = 8After the price of X decreases to $2:MUx/Px = 16/2 = 8MUy/Py = 16/2 = 8Now, 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 YMUx/Px = 16/2 = 8MUy/Py = 8/2 = 4Total Utility = (2*16) + (5*8) = 72Option B: 4 of X and 6 of YMUx/Px = 16/2 = 8MUy/Py = 6/2 = 3Total Utility = (4*16) + (6*6) = 80Option C: 6 of X and 3 of YMUx/Px = 12/2 = 6MUy/Py = 12/2 = 6Total Utility = (6*12) + (3*12) = 108Option D: 4 of X and 5 of YMUx/Px = 12/2 = 6MUy/Py = 8/2 = 4Total Utility = (4*12) + (5*8) = 76Therefore, the utility-maximizing combination of the two products is 6 units of X and 3 units of Y.

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