Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 4x + y, 5y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a
A) vertical line segment and a horizontal line segment which meet in a kink along the line y = 4x.
B) vertical line segment and a horizontal line segment which meet in a kink along the line x = 4y.
C) horizontal line segment and a negatively sloped line segment which meet in a kink along the line x = y.
D) positively sloped line segment and a negatively sloped line segment which meet along the line x = y.
E) horizontal line segment and a positively sloped line segment which meet in a kink along the line x = 4y.

Question

Quizplus · Accepted Answer

The indifference curves of Ethel's utility function U(x, y) = min{ 4x + y, 5y} will be composed of two line segments meeting at a kink. 
Since the minimum function is involved, the curve will move parallel to the x-axis, until it hits the line 4x + y = 5y. From that point, the curve will move parallel to the y-axis. 
This line has a slope of -4, meaning that for every one unit increase in x, y decreases by 4 units. Therefore, the two line segments meet along the line x = y. Hence, option C is correct.

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