Which of the following utility functions is an example of preferences for perfect complements?
A) $U ( x , y ) = y \sqrt { x }$
B) $U ( x , y ) = \min \{ 2 x , y \}$
C) $U ( x , y ) = 3 x + 5 y$
D) $U ( x , y ) = 2 x ^ { 2 } + 4 y$

Question

Which of the following utility functions is an example of preferences for perfect complements? 
A) $U ( x , y ) = y \sqrt { x }$
B) $U ( x , y ) = \min \{ 2 x , y \}$
C) $U ( x , y ) = 3 x + 5 y$
D) $U ( x , y ) = 2 x ^ { 2 } + 4 y$

Quizplus · Accepted Answer

In the utility function U(x, y) = min{2x, y}, the consumer's utility depends only on the minimum amount of x and y that they consume. This is a characteristic of preferences for perfect complements, where the consumer always wants to consume a fixed ratio of two goods, regardless of their prices. The other utility functions do not demonstrate this characteristic. The utility function U(x,y) = min{2x,y} represents preferences for perfect complements, where x and y are consumed in fixed proportions, just like the left and right shoes of a pair. The marginal utility of one good is always zero unless consumed in conjunction with the other good. This means that the consumer is indifferent to any combination of goods where their quantities do not match. For example, if the consumer has 3 units of good x and 5 units of good y, the utility will be 6 because the consumer has only 3 units of x that can be consumed with 3 units of y, which gives the minimum value equal to the utility. Therefore, option B is the correct answer.

Which of the Following Utility Functions Is an Example of Preferences