Instructions. You need to provide a detailed justication of your claims to get credits. You should label all axes and important points in the graphs to get full credits. Round to one decimal places if necessary. 1. (30 points) Home and Foreign produce two goods, Food (F } and Housing (H) using a single factor of production, labor (L). All consumers share identical homothetic preferences. Production exhibits constant returns to scale, with the following unit labor requirements: our = 3, out; = 12, aEF = 6, (LEE = 12. Labor endowments are L = 120 in Home and L\" = 96 in Foreign. (a) Both countries are initially closed to international trade. 1. (5 points) Draw the production possibilities frontier (PPF) for Home, with QF production on the horizontal axis and Q H production on the vertical axis. Indicate the production and consumption points in the autarky equilibrium in Home on the graph. What is the autarky equilibrium relative price of clothing (PF/PEP in Horne? ii. (5 points) Draw the production possibilities frontier (PPF) for Foreign, with Q} production on the horizontal axis and QIBH production on the vertical axis. Indicate the production and consumption points in the autarky equilibrium in Foreign on the graph. What is the autarky equilibrium relative price of clothing (Pg/PEI)A in Foreign? iii. (5 points) Which product does Home have camparative advantage in production? What about Foreign? (b) The two countries are now open to international trade. 1. (5 points) Calculate the relative supply in the world market (QFXQH)W when two countries perfectly specialize in producing goods which they have comparative advantage on. ii (5 points) The relative world demand is given as follows: 2 PF/PH' Dp/DH = What is the equilibrium relative price and relative quantityr in the world economy? iii. (5 points) Suppose Home experienced a population growth so that the labor endowment changes to L = 150. What is the new equilibrium relative price and new equilibrium relative quantity in the world economy