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1. Consider an international economy consisting of USA and China. There are two factors: capital (K) and labor (L) and two goods: manufacture (M) and food (F). The two countries share the same constant returns to scale production functions. Representative consumers of the two countries share the same homothetic welfare functions with usual properties. At autarky (before trade) and after trade opens, both countries produce both goods. All the prices are in terms of units of food. Thus, the price of food is 1. The USA is capital abundant. Here, L and K are USA endowments of labor and capital and L* and K* are Chinese endowments of labor and capital. Assume that food industry is capital intensive and manufacturing is labor intensive. All markets are competitive. (b) Draw how the relative supply curves of USA and China might look like and explain their relative positions using the Rybczynski theo- rem. Use a on the vertical axis and it on the horizontal axis. (3 points) (c) Now, draw in the common relative demand curve on the graph in (b) . Explain using the graphs, which country has the higher autarky price of manufactures (in terms of food)? (2 points) (d) When the two countries start to trade, which good does China export and which good does it import?. Explain your answer using the above graph. (3 points) (e) Explain how the Heckscher-Ohlin theorem is verified in this case. (3 points) (f) When the trade equilibrium is established, how does the relative price of manufactures in USA change from its autarky value (PR ) to the trade value pp? Put ? How about in China? (2 points) (g) How does the change of the relative price of manufactures in USA affect the relative factor price " in USA? How about in China? (2 (h) How do the changes in the prices of outputs and factors affect the welfare of labor and capital owners in USA? How about in China? (you can use the Stolper-Samuelson theorem in your explanation). (3 points)