Gains from trade and their distribution. A country (\"Home\") is populated with workers who produce either food (F) or clothing (0). There are 200 workers producing food and 100 producing clothingthese numbers are xed in the short run. Each food worker produces 6 units of food and each clothing worker produces 3 units of clothing. Workers own the output they produce and can trade with other workers. All workers share the same preferences over food and clothing represented by the utility function: U(DC: DF) = DC(DF)2 Hint: Recall the property of CobbDouglas utility functions relating expenditure shares on both goods. (a) What are the aggregate endowments of food and clothing in this economy? (b) What is the autarky relative price of clothing to food? C III [113 51, 110W man llIlltS of food and clothing Will be consumed by a ClOthlIl a 31k Y g worker? By a fOOd WOI'kEI'? ((1) There also exists another country (\"Foreign\") that looks surprisingly like the Home country except that there are 600 food workers and 300 clothing workers in this country. These workers have di'erent (lower) productivity levels: a food worker can produce only 1 unit of food while a clothing worker can only produce 2 units of clothing. The workers in Foreign share the same preferences as those in Home. Answer questions (a), (b) and (c) for the Foreign economy in autarky. (e) Compare the autarky consumption levels of workers in both countries. What explains the differences between countries? (f) Now assume that these 2 countries open to trade with each other. (i) What will be the free trade relative price of clothing to food? (ii) Describe the pattern of trade (which country exports what and how much). Verify that the export supply matches the import demand for both goods. (iii) Calculate the new consumption levels of both types of workers in both countries. (iv) For each type of worker in both countries, assess whether they are better off in the new trade equilibrium. Could you have predicted this pattern before calculating the new consumption levels and the free trade price equilibrium? How? (v) Now assume that all workers belong to representative \"families\" each containing 2 food workers and 1 clothing worker. Describe how the consumption patterns (the number of units of food and clothing consumed) of the \"families" change between autarky and the trade equilibrium. Are the \"families\" in both countries unambiguously better off? Why should you not be surprised by this result? (g) Without redoing the calculations in (1'), describe how your answers would change if the productivity of both types of Foreign workers were multiplied by 10. In partic- ular, what will happen to: (i) The pattern of trade (what good is exported by each country) (ii) The distribution of the gains from trade 0 Which workers will gain from trade? a What will happen to the \"families\" of workers in each country? (h) Return to the trade equilibrium described in (f) If workers can switch occupations in the long run, what will happen to the number of workers in each industry (only describe the directionnot the magnitude0f the change)