Recall that Tommy Twit's mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences.Her favorite bundle for Tommy is (2, 7), that is, 2 cookies and 7 glasses of milk.Tommy's mother's indifference curve that passes through the point (c, m) = (4, 5)also passes through
A)the point (6, 3).
B)the points (2, 3), (6, 7), and (4, 9).
C)the point (2, 7).
D)the points (4, 7), (2, 5), and (2, 9).
E)None of the above.

Question

Quizplus · Accepted Answer

Since the indifference curve is defined as the set of bundles that have the same level of utility as the favorite bundle (2,7), it follows that any bundle on the same indifference curve as (c,m) must have the same departure from the favorite bundle as (c,m).

Let us denote the departure of the bundle (x,y) from the favorite bundle (2,7) by D(x,y), where D(x,y) = |x-2| + |y-7|. Then, if the indifference curve that passes through (c,m) also passes through (x,y), we must have:

D(c,m) = D(x,y)

Expanding the absolute values, we get:

|c-2| + |m-7| = |x-2| + |y-7|

Now, we can use the information that the indifference curve passes through (4,5) to solve for one of the variables. Specifically, if we substitute c=4 and m=5, we get:

|4-2| + |5-7| = |x-2| + |y-7|

2 + 2 = |x-2| + |y-7|

4 = |x-2| + |y-7|

Next, we use the fact that (2,7) is on the indifference curve. Substituting x=2 and y=7, we get:

|2-2| + |7-7| = |2-2| + |7-7|

0 = 0

This implies that any bundle on the indifference curve can be obtained from (2,7) by making equal and opposite changes to the number of cookies and the number of glasses of milk. More precisely, if (x,y) is on the indifference curve, then:

x - 2 = 7 - y

or equivalently:

x + y = 9

Therefore, any point that satisfies both equations |x-2| + |y-7| = 4 and x + y = 9 must be on the indifference curve that passes through (4,5).

It is easy to check that the points (2,3), (6,7), and (4,9) satisfy both equations, while (6,3), (4,7), (2,5), and (2,9) do not. Therefore, the answer is B.

Recall That Tommy Twit's Mother Measures the Departure of Any