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. 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.  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

Before the price change, the consumer maximizes utility by consuming X and Y up to the point where the ratio of their marginal utilities equals their prices:
MUx/Px = MUy/Py
3/$4 = 2/$2
The consumer purchases 3 units of X and 6 units of Y for a total expenditure of $18.

If the price of X decreases to $2, the ratio of marginal utilities changes to:
MUx/Px = MUy/Py
3/$2 = 2/$2
The consumer will now purchase more X and less Y, without reducing total utility. The new utility-maximizing combination can be found by setting up a new ratio of marginal utilities and solving for the new quantities: 
MUx/Px = MUy/Py
4/$2 = 1/$2
The consumer will purchase 4 units of X and 5 units of Y, for a total expenditure of $18. This is the option D.

Answer the Question on the Basis of the Following Marginal