Question

In Problem 9, if we graph Mary Granola’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 -2. Whenever she has more avocados than grapefruits, the slope is -1/2. Mary would be indifferent between a bundle with 21 avocados and 33 grapefruits and another bundle with 33 avocados and x grapefruits?

Answer 1

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

dG/dA = -2 => G = -2A = C => G + 2A = 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 21 avocados and 33 grapefruits. For the Bundle U = B*min{2*33 + 21, 33 + 2*21 } = B*min{87 , 75} = 75B

Consider a bundle with 33 avocados and x grapefruits. For the Bundle U = B*min{2*x + 33, x + 2*33 } = B min{2x + 33 , x + 66}. Hence x = 21, in order for her to be indifferent between these 2 bundles

Note when x = 21

U = B*min{2*21 + 33, 21 + 2*33 } = B*min{75 , 87} = 75B

Hence x = 21 grapefruits