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 endowment 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 function is U(HB, CB) = min{HB, CB}. (Here HA and CA are the amounts of herring and cheese for Astrid, and HB and CB 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.
(b) Use black ink to show the locus of Pareto optimal allocations.
(c) Let cheese be the numeraire (with price 1) and let p denote the price of herring. Write an expression for the amount of herring that Birger will demand at these prices. __________
(d) Where the price of cheese is 1 and p is the price of herring, what is the value of Astrid’s initial endoment? __________ How much herring will Astrid demand at price p? _________