There are two countries, China (CHN) and India (IND), and two goods, 1 and 2. Households in each country have identical preferences over consumption of the two goods, given by: U (C1, C2) = C 2/3 1 C 1/3 2 Both goods are produced using labor as the sole factor. The production technology available for producing good i {1, 2} in country c {CHN, IND} is given by: Xc i = a c iL c i where Xc i and L c i denote output and labor input in sector i, country c respectively. Country c is also endowed with Lc units of labor that are perfectly mobile across the two sectors. In what follows, assume that the ratio of labor endowments is: LCHN LIND = 5 3 and marginal products of labor are: a CHN 1 = 4 a CHN 2 = 2 a IND 1 = 3 a IND 2 = 5 (a) Let U c aut and U c trade denote the value of household utility in country c under autarky and free trade respectively. Assume that there is complete specialization under free trade, with each country only producing one good. What are the gains from trade in each country (i.e. what are U CHN trade /UCHN aut and U IND trade/UIND aut )? (20 points) (b) Now suppose that there is technological progress in both countries, so that the marginal products of labor in each sector increase and become: a CHN 1 = 8 a CHN 2 = 4 a IND 1 = 6 a IND 2 = 10 How do the gains from trade in each country under these new technologies compare with the gains from trade in part (a)? Explain clearly the reasoning for your answer