N=7

5. Consider a planet populated by two people, Willis (W) and Jeriba (J), who care about two goods, food (F) and clothing (C), produced by two firms called FACME and CACME. These firms use labour (L) to produce food and clothing respectively. Willis only cares about food and his utility function is Uw(Fw) = Fw where Fw is how much food Willis consumes. Jeriba only cares about clothing and her utility function is UJ(CJ) = CJ. Willis is the sole owner of FACME, whose technology is described by the function f(LF) = JLF where LF is how much labour FACME uses. Jeriba is the sole owner of CACME, whose technology is given by the function f(Lc) = (N+2)Lc where Lc is how much labour CACME uses. Willis and Jeriba are endowed with 2N+1 hours each. a) Find the mathematical expression for the PPF and draw it with clothing on the horizontal axis. What is the MRPT? b) Find FACME's and CACME's demand for labour input. Then find their supply and profit functions. C) Find Willis' and Jeriba's demands for food and clothing. d) Normalizing the wage, find the prices of food and clothing that clear all markets. Find the resulting equilibrium allocation. Is it true that at that equilibrium allocation the MRPT is equal (in absolute value) to the ratio of equilibrium prices and to Willis' and Jeriba's MRSs'? Why