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Comparative Advantage

The reasons why free trade is desirable can be developed by extending the discussion of the Crusoe economy that is commonly used to illustrate production-possibilities frontiers. Suppose that Robinson Crusoe, living on an almost deserted desert isle, can either catch four fish a day or find eight coconuts. One day, he discovers that Friday also lives on the island. If Friday can either catch six fish a day or find seven coconuts, can Crusoe and Friday profit by specialization and trade? The answer is clearly "yes." Crusoe is the better coconut gatherer, and Friday the better fisherman.

However, suppose that Friday can either catch ten fish or find ten coconuts. Friday is now better than Crusoe in both activities. Can there be mutual benefit from trade in this case? Or should Friday do all the work and Crusoe none? Or should Friday refuse to trade since he is better in both? It was a major achievement of David Ricardo early in the 19th century to show that in this second Crusoe-Friday story both parties could benefit from trade. His results contributed to the long reign of relatively free trade in 19th century England, and thus to the prosperity that England enjoyed in this period.

To see that mutually beneficial trade is possible even though Friday is better in all activities, one must look to opportunity costs. Individually, both Friday and Crusoe trade with nature in the production process. Crusoe can get another fish only by giving up time in which he could find two coconuts, and in getting another coconut he sacrifices one-half of a fish. Thus, a fish costs Crusoe two coconuts and a coconut costs one-half of a fish. Friday can get another fish by giving up the time during which he can find another coconut, or one-tenth of the day. During this time, he could find one coconut. For Friday, trading with nature means that one fish costs one coconut and vice versa. Looking at these opportunity costs tells us that Crusoe finds coconuts cheaper and Friday finds fish cheaper. The table below summarizes these results.

Opportunity Cost of Fish and Coconuts

For Friday:

1 Fish Costs 1 Coconut

1 Coconut Costs 1 Fish

For Crusoe

1 Fish Costs 2 Coconuts

1 Coconut Costs 1/2 Fish

We still have not discovered whether Friday and Crusoe could do better trading with each other rather than with nature. A way to answer this question is to try a few prices. Suppose that one fish was worth one-half a coconut, or one coconut was worth two fish. With this trading ratio both would find fish cheap and coconuts expensive. Therefore, both would want to sell coconuts and buy fish. Hence, at this price no trading would take place.

Suppose that the trading ratio were one fish for 1.8 coconuts (and thus one coconut cost 5/9 fish). With this ratio, Crusoe would find fish cheap--rather than spend two coconuts to catch one, he could spend 1.8 coconuts and buy one. Hence, Crusoe would be willing to sell coconuts. Friday would find coconuts cheap--rather than give up one fish by gathering his own coconuts, he could sell 5/9th of a fish and get one. Hence, Friday would be willing to sell fish. Trade will take place because both individuals find that it improves their well-being.

In the above example, trade occurs because of comparative advantage. Friday is better in everything than Crusoe, but he is "more better" in catching fish and "less better" in finding coconuts. Crusoe is worse than Friday in everything, but he is "less worse" in finding coconuts. Although they both benefit from trade, Friday will maintain a higher standard of living.

The example of Crusoe and Friday also illustrates that exchange is not a zero-sum game, but a positive-sum game. In a zero-sum game, whatever anyone wins comes at someone else's expense. In poker, for example, if one person wins $100, some other person(s) must have lost $100. If the amount of winnings is added up and the amount of losings is subtracted away, the result will be zero. The term "zero-sum game" reflects this total. In contrast, both parties in a voluntary exchange can benefit. Because total winnings exceed any losses, the name "positive-sum" game is appropriate. A negative-sum game, in which winnings will be less than losses, is also possible. War is one example and a bad marriage is another.

A possible reason that few people prior to Adam Smith seem to have recognized this mutually beneficial aspect of exchange may be that in his day much exchange involved bargaining.1 In bargaining, the seller tries to get as high a price as he can and the buyer as low a price as possible. If the seller can get $2.50 for a product rather than $2.00, he benefits from the higher price at the expense of the buyer. People do discuss who got the "better of the bargain." This feature of exchange, which is of vital importance to those involved in a market, can obscure the fact that no exchange will take place unless both parties believe that they benefit from it. Bargaining determines how big the producer's surplus will be relative to the size of the consumer's surplus, but unless both buyer and seller each have some surplus, no trade will take place.

Crusoe and Friday could be replaced by two nations. The principle of comparative advantage continues to hold, and it implies that the world as a whole will not be operating on its production-possibilities curve--that it will be production inefficient--if each nation is self-sufficient.

This inefficiency can be illustrated by putting the numbers of the second Crusoe-Friday into production-possibilities tables. Suppose that in self sufficiency Crusoe chooses three fish and two coconuts, and Friday chooses five fish and five coconuts. The total island production is then eight fish and seven coconuts. But with total specialization, with Crusoe producing only coconuts and Friday producing only fish, island production would be ten fish and eight coconuts, which means that under self-sufficiency island resources were used inefficiently. Or, suppose that originally Crusoe was self-sufficient at one fish and six coconuts, and Friday was self-sufficient at five fish and five coconuts. Island production is six fish and eleven coconuts. In this case, only partial specialization might be desirable. If Friday produces three coconuts and Crusoe produces eight, island production could be eleven coconuts and seven fish, which is a gain of one fish compared to production with no specialization.2

Production Possibilities
Crusoe
Friday
fish
coconuts
fish
coconuts
4
0
10
0
3
2
9
1
2
4
7
3
1
6
5
5
0
8
0
10

We finish with a discussion of barriers to trade.


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1However, two thousand years before Smith, Plato wrote: " So if one man gives another what he has to give in exchange for what he can get, it is because each finds that to do so is for his own advantage." (Francis MacDonald Cornfield, [trans.], The Republic of Plato. London: Oxford University Press, 1941, p. 56.)

2 Another conclusion that can be drawn from this example is that by specializing in production and then exchanging, both Friday and Crusoe can push their consumption-possibilities frontiers beyond their individual production-possibilities frontiers. This conclusion was the point of Adam Smith's famous story of the pin factory.


Copyright Robert Schenk