In end-of-chapter exercise 4.1, I described my dislike for grits and my fondness for Coco Puffs Cereal.
A. In part A of exercise 4.1, you were asked to assume that my tastes satisfy convexity and continuity and then to illustrate indifference curves on a graph with grits on the horizontal axis and cereal on the vertical.
(a) Now add a budget constraint (with some positive prices for grits and cereal and some exogenous income I for me). Illustrate my optimal choice given my tastes.
(b) Does your answer change if my tastes are non-convex (as in part (b) of exercise 4.1A)?
(c) In part (c) of exercise 4.1A, you were asked to imagine that I hate cereal as well and that my tastes are again convex. Illustrate my optimal choice under this assumption.
(d) Does your answer change when my tastes are not convex (as in part (d) of exercise 4.1A)?
B. In part B of exercise 4.1 you derived a utility function that was consistent with my dislike for grits.
(a) Can you explain why the Lagrange method will not work if you used it to try to solve the optimization problem using this utility functions?