29.2 (0) Consider a small exchange economy with two consumers, Astrid and Birger, and two commodities, herring and cheese. Astrid's initial endowment is 4 units of herring and 1 unit of cheese. Birger's initial en- dowment has no herring and 7 units of cheese. Astrid's utility function is U(HA, CA) = HACA. Birger is a more inflexible person. His utility func- tion is U(HB, CB) = min{ HB, CB}. (Here HA and CA are the amounts of herring and cheese for Astrid, and HB and C's are amounts of herring and cheese for Birger.) (a) Draw an Edgeworth box, showing the initial allocation and sketching in a few indifference curves. Measure Astrid's consumption from the lower left and Birger's from the upper right. In your Edgeworth box, draw two different indifference curves for each person, using blue ink for Astrid's and red ink for Birger's. Herring Birger 4 e Blue curves 2 Black line Red curves 0 4 6 8 Astrid Cheese (b) Use black ink to show the locus of Pareto optimal allocations. (Hint: Since Birger is kinky, calculus won't help much here. But notice that because of the rigidity of the proportions in which he demands the two goods, it would be inefficient to give Birger a positive amount of either good if he had less than that amount of the other good. What does that tell you about where the Pareto efficient locus has to be?) Pareto efficient allocations lie on the line with slope 1 extending from Birger's corner of the box