Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min{ 2x + y, 3y}. 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 x = 2y.
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 y = 2x.
E) horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 2y.

Question

Quizplus · Accepted Answer

The indifference curves of Ethel's utility function can be found by setting the two terms in the min{} expression equal to each other. Thus, we have:

2x + y = 3y

and

2x + y < 3y

Simplifying the first equation, we get x = y/2. This is the equation of a line with a negative slope, passing through (0,0) and (2,1). This line represents the portion of the indifference curve where 2x + y = 3y (i.e., where the two terms in the min{} expression are equal).

The second equation is satisfied for all (x,y) such that 2x + y < 3y, which can be rewritten as x < y. This is the equation of a horizontal line passing through (0,0). This line represents the portion of the indifference curve where 2x + y < 3y.

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

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