Isabella's utility function is U(x, y) = 4min{x, y} + y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are
A) L-shaped with kinks where x = y.
B) made up of two line segments that meet where x = y. One of these line segments is horizontal and the other has slope -4.
C) L-shaped with kinks where x = 5y.
D) made up of two line segments that meet where x = 5y. One of these line segments is vertical and the other has slope -1.
E) V-shaped with kinks where x = 4y.

Question

Quizplus · Accepted Answer

The utility function is linear in y, which means that the marginal rate of substitution between x and y is either constant or undefined. To find the shape of the indifference curves, we can start by setting U(x,y) equal to a constant level of utility, say C. Then we have:

4min{x,y} + y = C

For any fixed value of C, this equation describes a straight line in the x-y plane. To see this, we can consider two cases:

- If x < y, then the equation becomes 4x + y = C. Solving for y, we get y = C - 4x, which is a line with slope -4 and y-intercept at (0,C).
- If x >= y, then the equation becomes 4y + y = C. Simplifying, we get y = C/5, which is a horizontal line at y = C/5.

Thus, each indifference curve is made up of two line segments that meet where x = y. One of these line segments is horizontal and the other has slope -4. This corresponds to answer choice B.

Isabella's Utility Function Is U(x, Y) = 4min{x, Y}