Question

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:

Answer 1

Sol:

Autarky trade price (PF/PC) = 1/2
In autarky, how many units of food and clothing will be consumed by a clothing worker? By a food worker?

Ans – total production of food = 1200 units

Total production of cloth = 300 units

Budget constraint

DF + DC = 1500 --(1)

MRS = (2)*[(DF)-1/3]/[DC]-2/3
MRS = 2[DC2/3/DF1/3] = ½

DC/DF = ¼

4(DC) =DF

Substituting in 1, DC = 300, DF = 1200

There also exists another country (ìForeignî) that looks surprisingly like the Home coun- try except that there are 600 food workers and 300 clothing workers in this country. These workers have di§erent (lower) productivity levels: a food worker can produce only 1 unit of food while a clothing worker can only produce 2 units of clothing. The workers in Foreign share the same preferences as those in Home.