if we graph Mary Granola's indifference curves with avocados on the horizontal axis and grapefruits on the vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is -2.Whenever she has more avocados than grapefruits, the slope is -1/2.Mary would be indifferent between a bundle with 23 avocados and 29 grapefruits and another bundle with 31 avocados and
A)25 grapefruits.
B)27 grapefruits.
C)19 grapefruits.
D)22 grapefruits.
E)23.50 grapefruits.

Question

Quizplus · Accepted Answer

We need to compare the slope of the indifference curve at two different points to find out which bundle Mary would prefer. The slope of the indifference curve at a point represents the rate at which Mary is willing to trade one good for another while maintaining the same level of utility.

Comparing the two bundles:
- Bundle 1: 23 avocados and 29 grapefruits
- Bundle 2: 31 avocados and X grapefruits (unknown)

Whenever Mary has more grapefruits than avocados, the slope of her indifference curve is F1F1F1S1F1F1F102. Whenever she has more avocados than grapefruits, the slope is F1F1F1S1F1F1F101/2.

For bundle 1, Mary has more grapefruits than avocados. So, the slope of the indifference curve at bundle 1 is:

slope = F1F1F1S1F1F1F102 = (29/2)/(23) = 29/46

For bundle 2, Mary has more avocados than grapefruits. So, the slope of the indifference curve at bundle 2 is:

slope = F1F1F1S1F1F1F101/2 = (31)/(2X) = 31/2X

To find out which bundle Mary would prefer, we need to compare the slopes of the indifference curves at the two bundles. We want to know which bundle gives us the slope that matches 29/46.

Thus, we need to solve for X in the equation:

31/2X = 29/46

Cross-multiplying, we get:

31 * 46 = 2X * 29

X = 31.66

Therefore, Mary would be indifferent between bundle 1 with 23 avocados and 29 grapefruits and bundle 2 with 31 avocados and 22 grapefruits. Because 22 grapefruits is not an option, the closest option to 22 is 23 (choice D), which means that Mary would prefer bundle 1 with 23 avocados and 29 grapefruits over bundle 2 with 31 avocados and 23 grapefruits.

If We Graph Mary Granola's Indifference Curves with Avocados on the Horizontal