How does comparative advantage work with actual numbers, and why does it lead to trade even when one country is better at everything?

Comparative advantage is one of the most powerful (and counterintuitive) results in economics. The key insight: it's about relative efficiency, not absolute efficiency. Even if one country is better at everything, both benefit from specialization.

Setup — Two Countries, Two Goods

Consider Alveria and Brentford, each with 100 labor hours available:

Country	Hours to Produce 1 Unit of Wine	Hours to Produce 1 Unit of Textiles
Alveria	2 hours	5 hours
Brentford	6 hours	10 hours

Alveria has absolute advantage in BOTH goods — it's faster at producing wine (2 vs 6 hours) AND textiles (5 vs 10 hours).

Step 1: Calculate Opportunity Costs

Country	Opportunity Cost of 1 Wine	Opportunity Cost of 1 Textile
Alveria	2/5 = 0.40 textiles	5/2 = 2.50 wine
Brentford	6/10 = 0.60 textiles	10/6 = 1.67 wine

• Alveria's opportunity cost of wine (0.40 textiles) < Brentford's (0.60) --> Alveria has comparative advantage in wine
• Brentford's opportunity cost of textiles (1.67 wine) < Alveria's (2.50) --> Brentford has comparative advantage in textiles

Step 2: Production Without Trade (Autarky)

Assume each splits labor 50/50:

Country	Wine Produced	Textiles Produced
Alveria (50 hrs each)	25 wine	10 textiles
Brentford (50 hrs each)	8.33 wine	5 textiles
World Total	33.33 wine	15 textiles

Step 3: Production With Specialization

Each country fully specializes in its comparative advantage good:

Country	Wine Produced	Textiles Produced
Alveria (100 hrs on wine)	50 wine	0 textiles
Brentford (100 hrs on textiles)	0 wine	10 textiles
World Total	50 wine	10 textiles

Hmm — wine rose from 33.33 to 50, but textiles fell from 15 to 10. Let's do partial specialization instead.

Alveria: 80 hrs wine, 20 hrs textiles = 40 wine + 4 textiles Brentford: 100 hrs textiles = 10 textiles World: 40 wine + 14 textiles

Still more wine (40 > 33.33) with nearly the same textiles (14 vs 15). Now they trade.

Step 4: Trade at Mutually Beneficial Terms

The trade price must be between the two opportunity costs:

• 1 wine trades for between 0.40 and 0.60 textiles
• Say they agree on 1 wine = 0.50 textiles

Alveria trades 12 wine for 6 textiles from Brentford:

• Alveria ends with: 28 wine + 10 textiles (vs 25 + 10 in autarky) --> gains 3 wine
• Brentford ends with: 12 wine + 4 textiles (vs 8.33 + 5 in autarky) --> gains 3.67 wine, loses 1 textile but net better off

Both countries are better off after trade, even though Alveria was more efficient at both goods.

Exam Tip: CFA Level I will give you production data and ask you to determine comparative advantage, calculate opportunity costs, or identify mutually beneficial terms of trade. The terms of trade must fall between the two countries' opportunity costs.

Explore international trade theory in our CFA Level I Economics course.