Suppose kent and auburn both produce only food and clothing. they each have the following production possibilities functions:

kent: food = 6-(2/3) clothing
auburn: food = 8- (4/3) clothing

under what situation would trade not occur between these 2 countries?

a. the term of trade is 1 food for 0.8 clothing.
b. the term of trade is 1 food for 0.5 clothing.
c. the term of trade is 1 food for 1.25 clothing.
d. the term of trade is 1 food for 1.33 clothing.

b. The term of trade is 1 Food for 0.5 Clothing.

Explanation:

Change in food = -(2/3)(Change in Clothing) and It change in clothing = 1

=> Change in Food = -2/3

in order to produce 1 more clothing Kent has to sacrifice 2/3 food and hence Opportunity cost of Producing one clothing is 2/3 unit of food for Kent. Similarly, Opportunity cost of Producing one food is 3/2 unit of Clothing for Kent  

Auburn:

Change in food = -(4/3)(Change in Clothing) and It change in clothing = 1

=> Change in Food = -4/3

in order to produce 1 more clothing Kent has to sacrifice 4/3 food and hence Opportunity cost of Producing one clothing is 4/3 unit of food for Auburn. Similarly, Opportunity cost of Producing one food is 3/4 unit of Clothing for Auburn

Opportunity cost of producing Food is less for Auburn and hence it will export Food and Kent will import Food.

Auburn will export Food and benefitial from trade if (3/2)C > 1F and Kent will import Food and benefitial from trade if (3/4)C < 1F.

Trade will be benefitial if (3/4)C < 1F < (3/2)C => 0.75C < 1F < 1.5C

Therefore, Under situation where The term of trade is 1 Food for 0.5 Clothing would trade not occur between these 2 countries.

was my answer wrong?

the third answer is correct.