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:

In autarky, how many units of food and clothing will be consumed by a clothing worker? By a food worker?

1/32/3 U (Dc, DF) = DD2/3 F