Orchard Acreage, Pest Damage, and the Gains from Trade
Maple Hollow Orchard has 40 acres and can plant apples or pears. Each acre yields either 12 tons of apples or 8 tons of pears, and yields are constant regardless of how the acreage is split. The orchard currently plants 25 acres in apples and 15 in pears. A neighboring fruit cooperative offers a standing trade: 120 tons of apples for 90 tons of pears. The orchard's own storage can handle any mix, but the owner wants to know whether the trade beats producing pears directly. Then a pest arrives that cuts pear yields to 6 tons per acre while leaving apple yields unchanged; the cooperative's offer stays the same. The orchard must decide how to allocate its 40 acres and whether to accept the trade before the next planting season. The owner is also worried that specializing too much will leave the orchard dependent on one crop and one trading partner.
1. Before the pest, what is the orchard's opportunity cost of one ton of pears in tons of apples? Does the cooperative's offer improve the orchard's options? Show the comparison.
Read the worked answer
The opportunity cost of a ton of pears is the apples given up per ton of pears. One acre produces 12 tons of apples or 8 tons of pears, so 1 ton of pears costs 12/8 = 1.5 tons of apples. The cooperative asks for 120 tons of apples for 90 tons of pears, or 120/90 = 1.33 tons of apples per ton of pears. Since 1.33 < 1.5, the orchard gives up fewer apples per pear by trading than by shifting its own acreage. For example, starting at 25 acres apples and 15 acres pears, output is 300 apples and 120 pears. Move 10 acres from pears to apples: 420 apples and 40 pears. Trade 120 apples for 90 pears: 300 apples and 130 pears. The orchard keeps the same apples and gains 10 pears, so the offer improves its options before the pest.
2. After the pest cuts pear yield to 6 tons per acre, recompute the opportunity cost of pears. How does the pest change the production possibilities frontier, and does the case for accepting the trade strengthen or weaken?
Read the worked answer
After the pest, one acre yields 12 tons of apples or 6 tons of pears, so the opportunity cost of a ton of pears is 12/6 = 2 tons of apples. The trade price remains 1.33 apples per pear, so trading now saves 2 - 1.33 = 0.67 apples per pear, versus about 0.17 before. The production possibilities frontier rotates inward along the pear axis: maximum pears fall from 40 x 8 = 320 to 40 x 6 = 240, while maximum apples stay 480. The slope of the frontier becomes steeper, reflecting the higher opportunity cost of pears. The case for accepting the trade strengthens, because the orchard's comparative advantage in apples is now larger. The pest reduces the orchard's own pear output, not the cooperative's offer, so the gains from specializing in apples and trading for pears are greater.
3. The owner says, 'We can grow pears more efficiently than the cooperative, so trading would be a mistake.' Evaluate this reasoning using comparative advantage.
Read the worked answer
The owner is confusing absolute and comparative advantage. 'We grow pears more efficiently' is a statement about absolute advantage: fewer resources per ton. But trade is driven by opportunity cost. The orchard's opportunity cost of pears is 1.5 apples before the pest and 2 after; the cooperative's offer implies a price of 1.33 apples per pear, so the cooperative can supply pears at a lower opportunity cost in apples. That gives the cooperative a comparative advantage in pears and the orchard a comparative advantage in apples. Even if the orchard is better at both crops in absolute terms, it should specialize where its opportunity cost is lowest, which is apples, and trade. The pest makes this even clearer. The dependency concern is a risk-management issue, not an argument against the gains from trade; the orchard could keep some diversification while still trading at the margin.