French camp The French POW camp is very large. It consists of I* identical Antoines that each has preferences represented by the following utility function: UX = (CA) (TA) : . Each French POW receives endowments: C; = T; =1. This implies that p* ED* ED* We consider the limiting case in which I* - co, and the inverse excess demand function becomes the horizontal line of height Pa 10 1 09English camp 5 Recall that the English camp consists of Alex and Bobby. Utility functions and demand functions are as specified in the previous question: UA = (CA) (TA); UB = (CB) (TB) 2 . CA = Ap (TA + PCA) ; C' = = (TB + PCB) ; Td = I CO (TA + PCA) ; T'S = = (TB + PCB ) . Case 1 Endowments are TA = 1; CA = 1; TB = 1; CB = 1. 1. 10 points. Show that the English inverse excess supply function is: PES 3 - ES 2. 10 points. Assume the transport cost function is X(A) = -A. With free trade with the French, what is the equilibrium English free-trade price (PFT) and quantity of coffee (A) exported? Show your work.Case 2 Suppose upon receipt of the Red Cross packages, the camp commandant for the English camp re-arranged the contents and gave Alex and Bobby the following endowments: TA ; EA: ! IBU'IO'! T3 = 53: \"IRWIN g; 1. 10 points. Show that the inverse excess supply function is: 1 ES 10 p = g_gs 2. 10 points. What is the freetrade English price and the quantity of ex ported coee? Show your work. 3. 10 points. Show that in this case both Alex and Bobby are better off with free trade that they were with autarky