I hate grits so much that the very idea of owning grits makes me sick. I do, on the other hand, enjoy a good breakfast of Coco Puffs Cereal.
A: In each of the following, put boxes of grits on the horizontal axis and boxes of cereal on the vertical.
Then graph three indifference curves and number them.
(a) Assume that my tastes satisfy the convexity and continuity assumptions and otherwise satisfy the description above.
(b) How would your answer change if my tastes were “non-convex”—i.e. if averages were worse than extremes.
(c) How would your answer to (a) change if I hated both Coco Puffs and grits but we again assumed my tastes satisfy the convexity assumption.
(d)What if I hated both goods and my tastes were non-convex?
B: Now suppose you like both grits and Coco Puffs, that your tastes satisfy our five basic assumptions and that they can be represented by the utility function u(x1,x2) = x1x2.
(a) Consider two bundles, A=(1,20) and B=(10,2). Which one do you prefer?
(b) Use bundles A and B to illustrate that these tastes are in fact convex.
(c) What is the MRS at bundle A? What is it at bundle B?
(d)What is the simplest possible transformation of this function that would represent tastes consistent with those described in A(d)?
(e) Now consider tastes that are instead defined by the function u(x1,x2)
(f ) Do these tastes have diminishing marginal rates of substitution? Are they convex?
(g) How could you most easily turn this utility function into one that represents tastes like those described in A(c)?