A country L\"Home\"J is populated with workers who produce either tood {b'} or clothing (C). There are workers producing food and IUD producing clothing - thme numbers are xed. Each food worker produces (it unites of food and each clothing worker produces 3 units of clothing. Workers own the output they produce and can trade with one another. All workers share the same preferencm over food and clothing represented by the utility function: Urns. Dal = DEED? 1. What is the autarky trade price [the relative price of food and clothing) in this economy? Hint: recall the property of ISolih-Ilouglas utility functions relating expenditure shares on both goods. 2. In autarkyI how many units of food and clothing will he consumed by a clothing worker? By a food worker? There also exists another country (\"Foreign\") that looks surprisingly like the Home country except that there are EDD food workers and 30D 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 produce 2 units of clothing. The workers in Foreign share the same preferences as those in Home. 3. Answer questions 1 and 2 for the Foreign economy in autarky. 1. ICompare the consumption levels of workers in both countries. What explains the differences between the two consumption levels? 5. Now assume that these two countrim open to trade with one another. (a) What will be the free trade relative price of food and clothing? (h) Describe the pattern of trade (who exports what, and how much]. Verify that the export supply matches the import demand for both goods. {c} Calculate the new consumption levels of both types of workers in both countries