Question

If we graph Mary’s indifference curves

with avocados on the horizontal axis and

grapefruits on the vertical axis, then

whenever she has more grapefruits than

avocados, the slope of her indifference

curve is –1/2. Whenever she has more

avocados than grapefruits, the slope is -2.

Mary would be indifferent between a bundle

with 9 avocados and 15 grapefruits and

another bundle with 14 avocados and g

grapefruits. What is g?

Answer 1

ANSWER ;

We can see from the information given in the question that there is kink at A = G, and dG/dA = -2 when G > A and dG/dA = -1/2 when G < A.

Hence,

dG/dA = -2 => G = -2A = C => G + 2A = C

dG/dA = -1/2 => G = -0.5A = C => 2G + A = C

This information implies that this utility function must be of the form :

U = B*min{2G + A , G + 2A} for some constant B

Consider a bundle with 9 avocados and 15 grapefruits.

For the Bundle U = B*min{2*15 + 9, 15 + 2*9 } = B*min{39 , 33} = 33B

Consider a bundle with 14 avocados and G grapefruits.

For the Bundle U = B*min{2*G + 14, G + 2*14 } = B min{2G + 14 , G + 28}. Then, 2G+14=33 OR G+28=33

G=9.5 OR G =5

So, G = 9.5, in order for her to be indifferent between these 2 bundles

Note when x = 9.5

U = B*min{2*9.5 + 14, 9.5 + 2*14 } = B*min{33 , 37.5} = 33B

Hence G = 9.5 grapefruits