Consider a small economy, Home, producing two goods, Food ( F) and Clothes (C), using capital and labour. Suppose production functions of the two goods are F = (KFLF)i C = H(KCLc): where KF = 10 and Kc = 30 are the capital endowment specific to the two sectors, LF and Lc are the number of workers employed in the two sectors subject to the labour constraint LF + Lc = 280. Answer the following questions. All numerical answers must be accurate to two decimal places. a. Assume that the consumer has the following preference: U(F, C) = 3F + 2C, what is the relative price of food in autarky? b. How many workers are employed in the food sector in autarky? c. If price of clothes is Pc = 1, what is the equilibrium wage in autarky? The following information applies to questions (d) to (): Home is open to trade and the world prices of food and clothes are Pp = Pc = 1 d. Which good does Home export? e. When Home is open to trade, the output of its food sector as compared to autarky. f. How many workers are employed in the food sector when Home is open to trade? g. The real wage of a Home worker in terms of clothes is h. Are Home workers better off (in terms of real income) in trade? i. What is the total income to capital owners in the clothes sector when Home is open to trade? j. Are capital owners in the clothes sector better off (in terms of real income) in trade