Tim consumes only apples and bananas. He prefers more apples to fewer, but he gets tired of bananas. If he consumes fewer than 29 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple. But you would have to pay him 1 apple for each banana beyond 29 that he consumes. The indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with A apples and 21 bananas, where A equals
A) 25.
B) 28.
C) 34.
D) 36.
E) None of the above.

Question

Quizplus · Accepted Answer

Let's call the indifference curve that passes through the consumption bundle with 30 apples and 39 bananas "IC1", and the one that passes through the bundle with A apples and 21 bananas "IC2".

Since Tim prefers more apples to fewer, IC1 must be tangent to IC2 at a point where he consumes more apples and fewer bananas. This means that the marginal rate of substitution between apples and bananas is higher on IC2 than on IC1.

On IC1, Tim is willing to give up 1 banana for 1 apple if he consumes fewer than 29 bananas per week. Beyond that, he requires 1 apple for each additional banana. This means that his marginal rate of substitution on IC1 is 1:1 up to 29 bananas, and then it becomes infinite.

On IC2, Tim is willing to give up 1 banana for 1 apple regardless of how many bananas he consumes, since he considers them perfect substitutes if he consumes fewer than 29 bananas per week. Therefore, his marginal rate of substitution on IC2 is 1:1 for all levels of banana consumption.

Since IC2 is steeper than IC1, we know that Tim must be consuming fewer bananas on IC2 than on IC1 to achieve the same level of satisfaction (since he's willing to give up the same amount of bananas for each additional apple).

To find the level of banana consumption on IC2, we need to use the fact that Tim is consuming A apples on this indifference curve. Since he considers 1 banana and 1 apple to be perfect substitutes on IC2, he must be consuming 21+A bananas to achieve the same level of satisfaction as he was on IC1.

Setting these expressions equal to each other and solving for A, we get:

30 + 1*(39-29) = A + 21 + A
A = 28

Therefore, the indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with 28 apples and 21 bananas.

Tim Consumes Only Apples and Bananas