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

Solution :

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

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). $MRS_{BA} = \frac{MU_B}{MU_A}$

                  $=\frac{\delta U/\delta B}{\delta U/\delta A}$

                  $=\frac{2}{5}$

                 = 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.