Both Mary and Anne love chocolate (x) and roses (y). Suppose Mary's preferences can be represented by U Mary ( x, y) = x + y2 and Anne's preferences can be represented by U Anne ( x, y) = x2 + y.
a) What is the equation of an indifference curve for Mary? For Anne?
b) What is the MRS of these functions? Note, for Mary, MUx = 1 and MUy = 2y.For Anne, MUx = 2x and MUy = 1. What is the geometric equivalent of theMRS? What is the interpretation of the MRS?
c) Do these tastes have diminishing marginal rates of substitution? Are they convex?
d) Assume that on Valentine's Day Tom would like to give both girls chocolate and roses. All he has are 5 chocolates and 5 roses. Assume that Mary got 4chocolates and 2 roses, the bundle M: (4,2) and Anne got the rest, the bundleA: (1,3). On two separate graphs (one for each girl) with chocolate on the horizontal axis and roses on the vertical, draw Mary's indifference curve andAnne's indifference curve that satisfies our assumptions and pass through the bundles they have. Calculate utility along those indifference curves.
e) Assuming Mary has the bundle M and Anne has a bundle A, could they trade with each other so that both would be better off? If yes, who is willing to give up chocolate? For how many roses? Show that indeed with trade, both girls are better off. (Calculate utilities at new baskets and compare it with the original utilities)
f) Repeat part d) assuming that their initial bundles were switched so that Mary has the bundle (1,3) and Anne has the bundle (4,2).
g) Is it possible in this case (continue with part f) for Mary and Anne to trade with each other so that both will be better off?