Question 4.

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 innitely divisible.) Sheila is originally en- dowed with 8 shrimp and 4 Fosters. They both have the utility function U (x1, x2) = 1511523. Let shrimp be the numeraire, so that p1 = l. (a) What is the equation describing the Pareto efcient 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 satised 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? ((1) Determine the equilibrium price of Fosters. (e) Draw an Edgeworth box to illustrate the your answers above