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 fixed. Each food worker produces 6t 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 preferences over food and clothing represented by the utility function: U(Dc;Df ) = (Dc)^(1/3) (Df )^(2/3) 1. What is the autarky trade price (the relative price of food and clothing) in this economy? Hint: recall the property of Cobb-Douglas utility functions relating expenditure shares on both goods. 2. In autarky, how many units of food and clothing will be 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 600 food workers and 300 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. 4. Compare the consumption levels of workers in both countries. What explains the differences between the two consumption levels? 5. Now assume that these two countries open to trade with one another. (a) What will be the free trade relative price of food and clothing? (b) 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. (d) For each type of worker in both countries, assess whether they are better-off in the new trade equilibrium. How might you have predicted this pattern before calculating the new consumption levels and the free trade price equilibrium? For the following questions, assume that all workers belong to a representative ’family’ – each containing 2 food workers and 1 clothing worker. 6. 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? What is the intuition for this result?