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?
(3) 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.
Answer questions 1 and 2 for the Foreign economy in autarky.