Phil Rupp, from Problem 4, has a sister Ethel who 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) vertical line segment and a horizontal line segment that meet in a kink along the line y = 5x.
B) positively sloped line segment and a negatively sloped line segment that meet along the line x = y.
C) horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.
D) vertical line segment and a horizontal line segment that meet in a kink along the line x = 5y.
E) horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 5y.

Question

Quizplus · Accepted Answer

The utility function U(x,y) = min{5x+y,6y} suggests that Ethel values her y (vertical axis) less than she values her x (horizontal axis). Her indifference curves will therefore be L-shaped.

To find the kink point of the indifference curve, we set 5x+y = 6y, which simplifies to 5x = 5y or x = y.

Thus, Ethel's indifference curves consist of a horizontal line segment (corresponding to the region where 5x+y ≤ 6y, or 5x ≤ y) and a negatively sloped line segment (corresponding to the region where 5x+y > 6y, or 5x > y) that meet in a kink along the line x = y.

Therefore, the correct answer is C, horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.

Phil Rupp, from Problem 4, Has a Sister Ethel Who