5. 20 points total. Autarky versus free trade. Consider the following situation: Alex and Bobby's endowment economy (the "English" POW camp) is described by the following specifications of representations of preferences and endowments: UA = (CA) (TA) ; UB = (CB) ? (TB) . The solution to this model includes the following demand functions: CA = ( TA+ PCA) ; C' = 2 (TB + PCB) ; rd = "(TA + PCA) ; TB = = (TB +PCB) . Red-cross packages delivered each month give to Alex and Bobby the following endowments: TA = 1; CA = 1; TB = 1; CB = 1. In autarkic equilibrium, Alex's and Bobby's equilibrium is described as: Pa = = COIN T = UA = 1.036 3 3 = 4 3' TB = UB = 1.2136. The sum of Alex and Bobby's utilities in autarky is thus 1.036 + 1.2136 = 2.2496. The English camp is "small" relative to a French camp with which it can trade, and if Alex and Bobby are allowed to trade with the CESM's (a\"Simpsons\" reference, fy'i), i.e., the Bench, they can trade as much or as little as they desire without affecting the freetrade price pFT = 1. In a free trade equilibrium in which Alex and Bobby continue to receive their red-cross package endowments of one unit of tea and one unit of coffee, respectively, their equilibrium is described by: l. a 1_ d__ _ l ' '_ 5' TA 2, U, _ (2) (2) _ 1.1398 1; T3 = 1; U3 = (1)3 (1)3 = 1.0 0:1 a; = The sum of Alex and Bobby's utilities in this freetrade equilibrium is thus 1.1398 + 1.0 = 2.1398. True or false with short explanation (a) 10 points. _____ Alex is better off in free trade than in autarky, and Bobby is worse off in free trade than in autarky. (b) 10 points. _____ Because the sum of Alex and Bobby's utilities is less under free trade than in autarky, we can say that free trade would be worse for the English camp than would be autarky