How does comparative advantage work with actual numbers, and why does it lead to trade even when one country is better at everything?
CFA Level I Economics covers comparative advantage and I find the concept counterintuitive. If Country A is more efficient at producing both wine and cloth, why would it ever trade with Country B? Can someone show me with numbers how both countries benefit from specializing and trading?
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.
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