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Gains From Trade: An Example

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09/01/2010

Can two people still gain from trade even if one person is a lot better at something than the other person? Consider two people: there’s Stan, who is really, really good at sweeping driveways and mowing lawns. There’s also Bob, an immigrant from the future who doesn’t have driveways or lawns in his time and is worse than Stan at both. In the course of a weekend, Stan can sweep a hundred driveways or mow fifty lawns. Bob, on the other hand, can sweep only one driveway or mow only two lawns.

For every driveway Stan sweeps, he gives up the opportunity to mow half a lawn. For every lawn he mows, he gives up the opportunity to sweep two driveways. For every driveway Bob sweeps, he gives up the opportunity to mow two lawns. For every lawn Bob mows, he gives up the opportunity to sweep half a driveway. Stan has an absolute advantage in both because he could sweep more driveways or mow more lawns than Bob could. However, Bob has a comparative advantage in lawn-mowing because for every lawn he mows he only gives up the opportunity to sweep half a driveway whereas Stan gives up the opportunity to sweep two driveways if he decides to mow a lawn. Stan has a comparative advantage in sweeping driveways: for every driveway he sweeps, he only gives up the opportunity to mow half a lawn whereas Bob gives up the opportunity to mow two lawns for every driveway he sweeps.

Suppose they both devote half their weekend to each activity. Thus, Stan sweeps fifty driveways and mows 25 lawns, while Bob sweeps half a driveway and mows one lawn.

Bob, while wiping the sweat from his brow after mowing one lawn and sweeping half a driveway one weekend, remembers something from his econ class about something called “comparative advantage.” He knows that Stan can get lawns mowed in one of two ways. Either Stan can mow the lawn himself (at the cost of two driveway sweepings), or he can trade and get someone else to do it. If Stan can get someone else to mow lawns at a price of fewer than two driveway sweepings, he will be made better off. He also knows that if Stan can trade his driveway-sweeping skills for more than half a lawn-mowing, he will be made better off.

Similarly, Bob knows that he can get driveways swept in one of two ways. Either Bob can do it himself, forgoing the opportunity to mow two lawns in the process, or he can trade his lawn-mowing services to someone who can sweep driveways. If he can get a driveway swept in exchange for fewer than two lawn mowings, he will be made better off. He also knows that if he can trade his lawn-mowing skills for more than half a driveway sweeping, he will be made better off.

Bob approaches Stan one weekend and offers a trade. Bob suggests that he completely specialize in lawn mowing while Stan specializes more in driveway sweeping, sweeping 51 driveways and mowing 24.5 lawns. He then proposes that Stan trade him a full driveway sweeping for 0.75 lawn mowings. As a result of the trade, Stan ends up with 50 driveways swept and 25.25 lawns mowed, and Bob has one driveway swept and 1.25 lawns mowed.

They are both strictly better off. Bob has an additional half-driveway sweeping, and they each have an additional quarter lawn-mowing. Even though Stan is much better than Bob at both tasks, they are both made better off through specialization and trade.

Here’s a clip from the South Park episode that inspired this example. The clip is safe for work and classroom use. The entire episode most definitely is not.

Mike Hammock commented on an early version of this example.

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