The Case for Free Trade - Comparative Advantage

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The Case for Free Trade - Comparative Advantage

In the numerical example in the last Learn-It, it was fairly obvious what the two countries should do. One was better at making wine, the other was better at making beer, so they each specialised, overall production rose and they were both better off after trading.

What should happen, though, if one of the two countries is best at making both the goods in question?

Assume that two countries, Germany and France, with similar amounts of resources (which is more or less true in the real world) both produce only two goods, wine and cheese (not so true in the real world!). The table below gives the production possibilities for a given year assuming that they each split their resources evenly between the production of wine and cheese.

  Wine Cheese
  (Millions of bottles) (Millions of kilos)
Germany 150 100
France 200 200
Total 350 300

In this example, where we assume that both countries produce only wine and cheese, France has an absolute advantage in the production of both wine and cheese. It is better at making both goods. Here are the relevant PPFs.

PPFs

As you can see, France's PPF is further to the right than Germany's. They are better at making both goods, so why bother trade with Germany?

This is where the theory of comparative advantage comes in. This theory states that in the situation above, both countries can still benefit from specialisation and trade. Germany must specialise in the good at which it is 'least bad' at making, and France should specialise in the product at which it is best (or 'most good') at making. We find out who should specialise in what by finding, for each country, the opportunity cost of making each good in terms of the other good. This is where the PPFs come in handy. It is easier to see what the opportunity costs are using a diagram.

France

Let's look at France first. France is initially at point A on its PPF, producing 200 million bottles of wine (from now on, W) and 200 million kilograms of cheese (from now on, C). If France was to make one more kilogram of cheese, you can see from the diagram that a bottle of wine would have to be sacrificed. So the opportunity cost of making 1C is 1W. If France were to make one more bottle of wine, it would have to sacrifice a kilogram of cheese. The opportunity cost of making 1W is 1C. The gradient of the PPF (which is -1) determines the size of the opportunity cost.

The calculation is a little more complicated for Germany, currently at point B on its PPF. To make one more kilogram of cheese you can see from the steeper slope of the PPF that Germany will have to give up more than one bottle of wine. To be exact, the opportunity cost of 1C is 1½W. Again the gradient of the PPF (which is -1½) holds the key. To make one more bottle of wine, you can see that Germany will be giving up less than one kilogram of cheese. To be exact, the opportunity cost of 1W is 2C/3.

The table above has been reproduced below, but the opportunity costs of making an extra unit of each product has been added in the relevant boxes.

  Wine Cheese
  (Millions of bottles) (Millions of kilos)
Germany 150 100
(1W costs C) (1C costs 1W)
France 200 200
(1W costs C) (1C costs 1W)
Total 350 300

Now that we have the opportunity costs of production, we can see which country is relatively better at making each good. In other words, we can see which country has a comparative advantage in producing which good. Let's look at wine first. France can make 1W at a cost of 1C, but Germany can make wine relatively more cheaply. It can make 1W for only 2C/3. Germany has a comparative advantage in the production of wine. With cheese, France can make 1C at a cost of 1W, but it is more costly in Germany, where 1C costs 1½W. France has a comparative advantage in the production of cheese.

Germany

So, Germany will specialise in wine and France will specialise in cheese. This gives the following table:

  Wine Cheese
  (millions of bottles) (millions of kilos)
Germany 300 0
France 0 400
Total 300 400

Notice that, although overall production has risen (700 units is bigger than 650 units), the extra 100 million kilograms of cheese have been produced with a loss of 50 million bottles of wine. This may seem like a bad deal if you particularly like wine! It is for this reason that the two countries in this situation are unlikely to specialise 100% in the product for which they have a comparative advantage. The table below gives a more sensible degree of specialisation which results in higher overall production of both goods.

  Wine Cheese
  (millions of bottles) (millions of kilos)
Germany 300 0
France 70 330
Total 370 330

Both wine and cheese lovers should be happy now! The two countries together now produce 20 million more bottles of wine and 30 million more kilograms of cheese. So now its time to trade. What will the terms of trade be?

If France was still a closed economy, it could produce an extra kilogram of cheese at the cost of exactly one bottle of wine. Hence, France will not want to trade a kilogram of cheese for anything less than one bottle of wine. The domestic trade off is one kilogram of cheese for one bottle of wine, so France would hope to do better than that.

Similarly, if Germany was still a closed economy, it could produce an extra bottle of wine at the cost of only two-thirds of a kilogram of cheese. Germany would hope to get at least two-thirds of a kilogram of cheese for each bottle of wine that it trades with France. 1W for 2C/3 is the same as 1C for 1½W.

So the 'price' will be somewhere between 1C for 1W and 1C for 1½W. France would rather the price was as close as possible to 1C for 1½W and Germany will hope that the price is as close as possible to 1C for 1W.

Let's say that the two countries agree on a price of 1C for 1¼W, and decide to trade 112 million kilograms of cheese for 140 million bottles of wine.

The final, post-trade, table will look like this:

  Wine Cheese
  (millions of bottles) (millions of kilos)
Germany 160 112
France 210 218
Total 370 330

Both countries now have more cheese and wine than they had before they specialised and traded. Germany has 10 million more bottles of wine and 12 million more kilograms of cheese. France has 10 million more bottles of wine and 18 million more kilograms of cheese. In a sense, their PPFs have moved out as a result of specialisation and trade.

As with the absolute advantage example, it should be noted that we have assumed that there are no transport costs for the delivery of the exports of each product. Also, we have assumed that there are no negative externalities in the production process, or from the consumption of wine and cheese (which is definitely not the case in the real world!).

If the numerical example above doesn't make much sense, think of the concept of comparative advantage in terms of a lawyer and his secretary.

Assume that a lawyer can charge his services out at 100 pounds an hour (it is probably more nowadays!). Also assume that he/she happens to be a very quick typist, and can type 80 words a minute. His secretary is fairly good, typing 60 words a minute. The secretary is paid 12 pounds an hour.

The lawyer has an absolute advantage in being a lawyer and being a secretary! But he is much better at being a lawyer and only a little bit better at typing. He has a comparative advantage in the law and the secretary has a comparative advantage at typing.

If the lawyer decides to type a letter, or a report, because he is a bit quicker than the secretary, he would lose out overall. Let's say that it takes him 15 minutes to type a report. The secretary types 25% slower, so it would take him/her 20 minutes. It costs the lawyer four pounds to hire the secretary for 20 minutes, but if he types the report, he has wasted 15 minutes for which he could have earned 25 pounds being a lawyer!

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