Remember Tommy Twit from Chapter 3. Tommy is happiest when he has 8 cookies and 4 glasses of milk per day and his indifference curves are concentric circles centered around (8,4). Tommy’s mother, Mrs. Twit, has strong views on nutrition. She believes that too much of anything is as bad as too little. She believes that the perfect diet for Tommy would be 7 glasses of milk and 2 cookies per day. In her view, a diet is healthier the smaller is the sum of the absolute values of the differences between the amounts of each food consumed and the ideal amounts. For example, if Tommy eats 6 cookies and drinks 6 glasses of milk, Mrs. Twit believes that he has 4 too many cookies and 1 too few glasses of milk, so the sum of the absolute values of the differences from her ideal amounts is 5. On the axes below, use blue ink to draw the locus of combinations that Mrs. Twit thinks are exactly as good for Tommy as (6, 6). Also, use red ink to draw the locus of combinations that she thinks is just as good as (8, 4). On the same graph, use red ink to draw an indifference “curve” representing the locus of combinations that Tommy likes just as well as 7 cookies and 8 glasses of milk.
(a) On the graph, shade in the area consisting of combinations of cookies and milk that both Tommy and his mother agree are better than 7 cookies and 8 glasses of milk, where “better” for Mrs. Twit means she thinks it is healthier, and where “better” for Tommy means he likes it better.
(b) Use black ink to sketch the locus of “Pareto optimal” bundles of cookies and milk for Tommy. In this situation, a bundle is Pareto optimal if any bundle that Tommy prefers to this bundle is a bundle that Mrs. Twit thinks is worse for him. The locus of Pareto optimal points that you just drew should consist of two line segments. These run from the point (8,4) to the point 5,7 and from that point to the point 2,7.