2. Gains from trade and their distribution. A country ("Home") is populated with workers who produce either food (F) or clothing (C). There are 200 workers producing food and 100 producing clothing - these 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: U095, BF) = DC(DF)2 Hint: Recall the property of Cobb-Douglas utility functions relating expenditure shareson both goods. (3) What are the aggregate endowments of food and clothing in this economy? (b) What is the autarky relative price of clothing to food? (c) In autarky, how many units of food and clothing will be consumed by a clothing worker? By a food worker? (d) There also exists another country ("Foreign") that looks surprisingly like the Home country except that there are 600 food workers and goo clothing workers in this country. These workers have different (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