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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.

Respuesta :

Solution :

[tex]U(A, B) = 5A + 2B[/tex]

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

So, [tex]U(40, 5) = U(x, 2)[/tex]

   (40 x 5) + (2 x 5) = 50x + (2 x 2)

     210 - 4  = 5x

       [tex]x = 41.2[/tex]

So Alexander has [tex]40[/tex] apples and [tex]5[/tex] bananas. The indifference curve though [tex](40, 5)[/tex] also include bundle.

Therefore, (41.2, 2)

b). [tex]$MRS_{BA} = \frac{MU_B}{MU_A}$[/tex]

                  [tex]$=\frac{\delta U/\delta B}{\delta U/\delta A}$[/tex]

                  [tex]$=\frac{2}{5}$[/tex]

                 = 0.4

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

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