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3. Japan and China produce two goods each, cars (C) and rice (R) and use three factors of production. Cars (C) are produced using only machinery (K) and skilled labor (S) and rice (R) is produced using only machinery (K) and unskilled labor (U). Machinery is completely mobile between the two sectors (KR+Kc=K) while unskilled labor is only used in sector R and skilled labor is only used in sector C. Assume that the relative world price for rice is given and constant at (PR / Pc). a) Draw a diagram that shows the demand for machinery, the nominal return to machinery (r), and the allocation of machinery between the two sectors in Japan. Please carefully label all axes, origins and (equations and names of the) curves. b) Suppose sometime in the future, Japan tries to offset a declining population growth rate by allowing more open immigration. Some predict that this would lead to a migration of unskilled workers from China to Japan. If this is true, what will happen to the allocation of machinery in Japan between sector R and sector C? Please depict your answer in the above graph and discuss your result clearly