Question

Charlie's brother, Alexander, also consumes apples (A) and bananas (B). Alexander's utility function happens to be U(A, B) = 5A + 2B.

(a) Alexander has 40 apples and 5 bananas. The indifference curve through (40, 5) also include bundle ( _____ , 2).
(b) Alexander has 40 apples and 5 bananas. With this bundle, Alexander would like to give up _____ apple(s) for a banana.

Answer 1

`U(A, B) = 5A + 2B`

a). Bundles
`(40, 5)` = U ( _____ , 2), lie on the same indifference curve. Suppose missing numbers is x.

So,
`U(40, 5) = U(x, 2)`

(40 x 5) + (2 x 5) = 50x + (2 x 2)

210 - 4 = 5x

`x = 41.2`

So Alexander has
`40` apples and
`5` bananas. The indifference curve though
`(40, 5)` also include bundle.

Therefore, (41.2, 2)

b).
`$MRS_(BA) = (MU_B)/(MU_A)$`

`$=(\delta U/\delta B)/(\delta U/\delta A)$`

`$=(2)/(5)$`

= 0.4

So Alexander has
`40` apples and
`5` bananas with this bundle. Alexander would like to give up
`0.4` unit apples for a banana.