Comparative Advantage with Opportunity Costs
Two countries, North and South, each produce only two goods: wheat and cloth. In one year, North can produce either 100 units of wheat or 50 units of cloth (or any linear combination). South can produce either 60 units of wheat or 60 units of cloth (or any linear combination). Both countries have identical preferences and currently split their resources equally between the two goods, producing and consuming 50 wheat and 25 cloth (North) and 30 wheat and 30 cloth (South). They are considering specialization and trade.
1. Calculate each country's opportunity cost of producing one unit of cloth in terms of wheat, determine comparative advantage, and identify the range of terms of trade that would benefit both.
Read the worked answer
North: 100 wheat or 50 cloth → 1 cloth costs 100/50 = 2 wheat. Equivalently 1 wheat costs 0.5 cloth. South: 60 wheat or 60 cloth → 1 cloth costs 60/60 = 1 wheat. Equivalently 1 wheat costs 1 cloth.
Comparative advantage: South has the lower opportunity cost of cloth (1 wheat < 2 wheat), so South should specialize in cloth. North has the lower opportunity cost of wheat (0.5 cloth < 1 cloth), so North should specialize in wheat.
Terms of trade: 1 cloth must trade for between 1 and 2 wheat. If 1 cloth trades for more than 1 wheat, South gains; if it trades for less than 2 wheat, North gains. So the acceptable range is 1 wheat < price of cloth < 2 wheat per unit of cloth.
2. Show that full specialization and trade at a terms of trade of 1.5 wheat per cloth makes both countries better off than their current split-production outcome.
Read the worked answer
Current (no trade): North produces/consumes 50W + 25C; South 30W + 30C. Total = 80W + 55C.
Full specialization: North produces 100W, South produces 60C. Total = 100W + 60C - more of both goods, so trade can make both better off.
Trade at 1.5W per C. Suppose North trades 30W to South for 20C (30/1.5 = 20). North ends with 100 − 30 = 70W and 20C. Compare to 50W + 25C: North gains 20W but loses 5C. Is that better? At North's own opportunity cost, 5C = 10W, so 20W gained > 10W equivalent lost - yes, North gains. South ends with 60 − 20 = 40C and 30W. Compare to 30W + 30C: South gains 10C at the cost of 0W - clearly better (South gave up no wheat in consumption; it received 30W for 20C).
Both are better off. The exact split depends on the bargained price, but any price strictly between 1 and 2 wheat per cloth yields gains from trade.
3. Suppose South discovers a new technology that doubles its cloth productivity (now 120 cloth or 60 wheat). Recompute comparative advantage and explain whether North still gains from trade.
Read the worked answer
New South: 60 wheat or 120 cloth → 1 cloth costs 60/120 = 0.5 wheat; 1 wheat costs 2 cloth. North: 1 cloth costs 2 wheat; 1 wheat costs 0.5 cloth.
South now has comparative advantage in cloth (0.5 < 2), and North still has comparative advantage in wheat (0.5 < 2). So the pattern is unchanged: South specializes in cloth, North in wheat.
North still gains: it can buy cloth for less than its own opportunity cost of 2 wheat. The terms of trade range is now 0.5 wheat < price of cloth < 2 wheat. Even though South became more productive, North's comparative advantage in wheat persists because comparative advantage depends on relative, not absolute, costs. The judgment: absolute productivity gains do not eliminate gains from trade as long as relative opportunity costs differ.