Bruce and Sheila both consume the same goods (shrimp and Fosters) in a pure exchange econ- omy. Bruce is originally endowed with 4 units of good 1 (shrimp) and 6 units of good 2 (Fosters). (As usual, think of both shrimp and Fosters as being infinitely divisible.) Sheila is originally en- dowed with 8 shrimp and 4 Fosters. They both have the utility function U(X1, X2) = x1 x3. Let shrimp be the numeraire, so that pı =1. Required:
a. What is the equation describing the Pareto efficient allocations? Which of these allocations are individually rational?
b. How many shrimp does Bruce wish to buy (or sell) in terms of the price of Fosters? At what price of good 2 is Bruce satisfied with his endowment (i. e., he does not want to buy or sell any shrimp)?
c. How many shrimp does Sheila wish to buy (or sell) in terms of the price of Fosters?
d. Determine the equilibrium price of Fosters.
e. Draw an Edgeworth box to illustrate the your answers above.