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We are now going to look at a numerical example that shows why it makes sense for two countries to trade when each has an absolute advantage in one of the two goods being traded.

The method used below is one based on the final output of the goods in question assuming each country has the same resources and that they are distributed evenly to the production of each good. Some textbooks prefer to illustrate the same concept by comparing the relative costs in terms of resources required to make one unit of the good in question. The first method has been chosen mainly because a diagram can be used to illustrate what is going on (in terms of a production possibility frontier, or PPF) as well as some numerical analysis.

#### The 'pre-specialisation' situation

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, beer and wine (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 beer and wine.

Wine Beer
(Millions of bottles) (Millions of bottles)
Germany 150 300
France 200 200
Total 350 500

This information can be illustrated on two PPFs, one for each country

As the resources have been split equally between the productions of the two goods, we see that each country is producing at the mid-point on their respective PPFs (points A and B). Germany, for example, could produce 600 million bottles of beer if it concentrated all of its resources on the production of beer.

You can probably see that we have to make a number of assumptions for this model to be valid. First, each country is on rather than within its PPF. We assume, therefore, that each country is using all of their resources and in the most efficient way.

Secondly, the PPFs are straight lines. This means we are assuming that all resources used are equally good at making beer or wine (a bit dubious - most PPFs are convex to the origin). The straight line PPF also means that we are assuming that returns to scale are constant. If Germany does decide to concentrate on the production of beer, they do not experience economies of scale (they probably would in the real world).

Looking back at the table, we have a situation here where France has an absolute advantage in the production of wine and Germany has an absolute advantage in the production of beer. In this situation, it makes sense for each country to specialise and produce the good that they are best at making, and then trade. So, Germany concentrates on beer production and France concentrates on wine production.

#### The situation after specialisation

Wine Beer
(Millions of bottles) (Millions of bottles)
Germany 0 600
France 400 0
Total 400 600

France is now producing at point C on its PPF and Germany is producing at point D on its PPF. Notice that total production of both goods has now risen because each country is concentrating on the production of the good in which they have an absolute advantage. The question now is what will be the terms of trade?

If France was still a closed economy, it could produce an extra bottle of beer at the cost of exactly one bottle of wine. Hence, France will not want to trade a bottle of wine for anything less than one bottle of beer. The domestic trade off is one bottle of beer 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 beer at the cost of only half a bottle of wine. Germany would hope to get at least half a bottle of wine (from now on, W) for each bottle of beer (from now on, B) that it trades with France.

So the terms of trade (or the price) will be somewhere between 1B for W (or 2B for 1W) and 1B for 1W. France will hope the agreed price will be nearer to 2B for 1W and Germany will hope that the price is nearer 1B for 1W.

Let's say that they agree on 1½B for 1W, and decide to trade 255 million bottles of beer for 170 million bottles of wine.

#### The situation after specialisation and trading

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

Wine Beer
(Millions of bottles) (Millions of bottles)
Germany 170 345
France 230 255
Total 400 600

Both countries now have more beer and wine than they had before they specialised and traded. Germany has 20 million more bottles of wine and 45 million more bottles of beer. France has 30 million more bottles of wine and 55 million more bottles of beer. In a sense, their PPFs have moved out as a result of specialisation and trade.

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 these alcoholic products (which is definitely not the case in the real world!).