# The inhabitants of an island are equally divided between two tribes: the Quasi-Linears

The inhabitants of an island are equally divided between two tribes: the Quasi-Linears(QL) and the Cobb-Douglas (CD). The sole source of nourishment on the island is orange. Each tribe member lives for two periods. The endowment of a QL is 50 oranges in eachperiod, while the endowment of a CD is 100 oranges in each period. The preferences of aQL tribe member are given by the utility function U(c1, c2) = 100lnc1 + c2, whilepreferences of a CD tribe member are described by the utility function U(c1, c2) = c1c2,where c1 is a consumption of oranges in period 1 and c2 is consumption of oranges inperiod 2. Despite their limited diet, the islanders are quite sophisticated. There is a centralclearing house where each tribe can post offers of how many period 2 oranges they willgive up for a period 1 oranges. a) How are the posted offers related to the interest rate? What is the budgetconstraint of a member of the QL tribe? What is the budget constraint of amember of the CD tribe?b) What is the gross demand for consumption by a QL tribe member for orangesin period 1? What is the gross demand for consumption by a QL tribe memberfor oranges in period 2?c) What are the net demands for consumption in period 1 for a member of QLtribe? What are the net demands for consumption in period 1 for a member ofCD tribe?d) What is the equilibrium interest rate or the price of period 1 oranges in term ofperiod 2 oranges? What tribe consists of lenders? How much do they lend?How much do they consume in period 2? Which tribe consists of borrowersand what is the period consumption of the borrowers?