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 22.Whenever she has more avocados than grapefruits, the slope is 21/2.Mary would be indifferent between a bundle with 22 avocados and 37 grapefruits and another bundle that has 37 avocados and
A)27 grapefruits.
B)32 grapefruits.
C)17 grapefruits.
D)22 grapefruits.
E)24.5 grapefruits.

Question

Quizplus · Accepted Answer

We know that Mary's MRS is constant along an indifference curve. Therefore, we can use the information given to set up the following equation:
22 = -dG/dA    when G > A
21/2 = -dG/dA    when A > G
Where G is the quantity of grapefruits and A is the quantity of avocados.
Rearranging each equation, we get:
dG/dA = -22    when G > A
dG/dA = -2/21    when A > G
The negative signs indicate that Mary is willing to give up some avocados in order to get more grapefruits, and vice versa.
Now we can use this information to find the bundle that Mary would be indifferent to the bundle 22 avocados and 37 grapefruits. This bundle has a slope of -22/37. Since the slope of an indifference curve is also the MRS, we can equate this to -dG/dA and solve for the bundle that has the same MRS:
-22/37 = -dG/dA    when G > A
dG/dA = 37/22    when G > A
So Mary would be indifferent to a bundle that has 37 avocados and 37/2 = 18.5 grapefruits (since (37/22) * 22 = 37). She would also be indifferent to a bundle that has 22/2 = 11 avocados and 22 grapefruits (since -(2/21) * 21/2 = -1). However, neither of these bundles are among the answer choices.
To narrow it down further, we need to look at the slope of the indifference curve for each answer choice:
(A) dG/dA = -27/22
(B) dG/dA = -16/21
(C) dG/dA = -17/2
(D) dG/dA = -22/37
(E) dG/dA = -49/44
By comparing the slopes to the slopes of the indifference curves associated with the bundles that Mary is indifferent between, we can see that (D) is the answer.

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