Two Coastal Economies Weigh a Trade Agreement
Northport and Southbay are neighboring coastal economies, each with 200 workers, producing only fish and lumber. In Northport one worker can produce either 12 tons of fish or 8 tons of lumber per month. In Southbay one worker can produce either 6 tons of fish or 3 tons of lumber per month. Both have linear production possibility frontiers, so opportunity costs are constant. Today Northport assigns 100 workers to each good (1,200 tons of fish, 800 tons of lumber), and Southbay does the same (600 tons of fish, 300 tons of lumber). No trade occurs. A regional agreement would let each economy specialize and exchange fish for lumber at a negotiated price. Southbay's mill owners oppose the deal, arguing that Northport is more productive in both industries, so Southbay can only lose. Northport's fishing cooperative is enthusiastic but has not done the arithmetic on what price it should accept.
1. Compute each economy's opportunity cost of a ton of lumber and a ton of fish, identify comparative advantage, and explain why the pattern differs from absolute advantage.
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Opportunity costs. Northport: 12 fish or 8 lumber per worker, so 1 ton of lumber costs 12/8 = 1.5 tons of fish, and 1 ton of fish costs 8/12 = 0.67 tons of lumber. Southbay: 6 fish or 3 lumber, so 1 ton of lumber costs 2 tons of fish, and 1 ton of fish costs 0.5 tons of lumber.
Comparative advantage. Lumber: Northport gives up 1.5 fish per ton versus Southbay's 2 fish, so Northport has the comparative advantage in lumber. Fish: Southbay gives up 0.5 lumber per ton versus Northport's 0.67 lumber, so Southbay has the comparative advantage in fish.
Absolute advantage. Northport produces more of both goods per worker (12 > 6 fish; 8 > 3 lumber). Absolute advantage compares productivity levels; comparative advantage compares opportunity costs, which are ratios. Southbay is worse at everything in absolute terms, but it is least worse at fish, so its workers should produce fish. The mill owners are confusing the two concepts: being less productive everywhere is fully compatible with gaining from trade.
2. Show that at a negotiated price of 1 ton of fish for 0.6 tons of lumber, full specialization plus trade leaves both economies better off than their current bundles, and state the range of prices both would accept.
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Terms-of-trade band. Mutually beneficial trade requires a lumber price between the two opportunity costs: more than 1.5 fish but less than 2 fish per ton of lumber, equivalently between 0.5 and 0.67 tons of lumber per ton of fish. A price of 0.6 lumber per fish lies inside the band.
Specialize. Northport puts all 200 workers in lumber: 1,600 tons. Southbay puts all 200 in fish: 1,200 tons.
Trade. Northport wants to keep consuming 1,200 tons of fish; at 0.6 lumber per fish it pays 720 tons of lumber for them, leaving 1,600 − 720 = 880 tons of lumber. Its old bundle was 1,200 fish and 800 lumber, so it gains 80 tons of lumber with fish unchanged.
Southbay keeps 600 tons of fish (its old consumption) and sells the other 600 for 360 tons of lumber. Its old bundle was 600 fish and 300 lumber, so it gains 60 tons of lumber.
Both are strictly better off. If the price were pushed to 2 fish per ton of lumber, Southbay would capture the entire gain and Northport would be indifferent; at 1.5 fish, the reverse. The negotiated price therefore determines only how the gains are split, not whether they exist.
3. Suppose Southbay installs new milling equipment that raises lumber productivity to 6 tons per worker while fish productivity stays at 6 tons. Recompute the opportunity costs and determine how comparative advantage and the acceptable price range change.
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New Southbay opportunity costs. With 6 fish or 6 lumber per worker, 1 ton of lumber costs 6/6 = 1 ton of fish, and 1 ton of fish costs 1 ton of lumber. Northport is unchanged (1 lumber = 1.5 fish; 1 fish = 0.67 lumber).
The pattern reverses. Lumber now costs Southbay 1 fish versus Northport's 1.5, so Southbay gains the comparative advantage in lumber. Fish costs Southbay 1 lumber versus Northport's 0.67, so Northport gains the comparative advantage in fish. Northport still has the absolute advantage in both, which again shows why absolute productivity does not determine the trade pattern.
New price range. Mutually beneficial lumber prices now lie between 1 and 1.5 fish per ton, narrower than the earlier 1.5-to-2 band and shifted downward. Southbay's productivity gain works like an improvement in its terms of trade: it can demand more fish per ton of lumber, and Northport's share of the gains shrinks. Northport's real income still rises in absolute terms because it keeps buying lumber more cheaply than it could make it, but its advantage from trade is smaller. Both countries are richer overall because of Southbay's new equipment, but the division of the surplus has moved against Northport.