Q. 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 in the short run.) Each food worker produces 6 units of food and each clothing worker produces 3 units of clothing. Workers own output which they produce and can trade with another. All workers share the same preferences over food and clothing represented by the utility function: U(DC,DF) = DCD2F.
a) What is the autarky trade price (the relative price of food and clothing) in this economy?
b) In autarky, how many units of food and clothing will be consumed by a clothing worker also with a food worker?
c) 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 only produce 2 units of clothing. Workers in overseas allocate the same preferences as those in their Home.
d) Compare the consumption levels of workers in both countries. Explains the diversity between the countries?