Phil Rupp's sister Ethel has the utility function U(x, y)= min{5x + y, 6y}.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a
A)horizontal line segment and a negatively sloped line segment which meet in a kink along the line x = y.
B)vertical line segment and a horizontal line segment which meet in a kink along the line y = 5x.
C)positively sloped line segment and a negatively sloped line segment which meet along the line x = y.
D)vertical line segment and a horizontal line segment which meet in a kink along the line x = 5y.
E)horizontal line segment and a positively sloped line segment which meet in a kink along the line x = 5y.

Question

Quizplus · Accepted Answer

Ethel's utility function is based on the minimum of two expressions: $5x + y$ and $6y$. This creates indifference curves that are piecewise linear, consisting of segments where one part of the utility function dominates until the two expressions equal each other, leading to a kink. The kink occurs where $5x + y = 6y$, simplifying to $x = y$, indicating a negatively sloped line segment (since as x increases, y must decrease to maintain equality) and a horizontal line segment (representing the portion where an increase in x does not affect utility because the utility is determined by the other term, $6y$, which does not depend on x). This matches the description in choice A.

Phil Rupp's Sister Ethel Has the Utility Function U(x, Y)=