The following hypothetical examples explain the reasoning behind the theory. In Example 2 all assumptions are italicized for easy reference, and some are explained at the end of the example.

Example 1

Two men live alone in an isolated island. To survive they must undertake a few basic economic activities like water carrying, fishing, cooking and shelter construction and maintenance. The first man is young, strong, and educated and is faster, better, more productive at everything. He has an absolute advantage in all activities. The second man is old, weak, and uneducated. He has an absolute disadvantage in all economic activities. In some activities the difference between the two is great; in others it is small.

Is it in the interest of either of them to work in isolation? No, specialization and exchange (trade) can benefit both of them.

How should they divide the work? According to comparative, not absolute advantage: the young man must spend more time on the tasks in which he is much better and the old man must concentrate on the tasks in which he is only a little worse. Such an arrangement will increase total production and/or reduce total labour. It will make both of them richer.

Example 2

Suppose for example we have two countries of equal size, Northland and Southland, that both produce and consume two goods, Food and Clothes. The productive capacities and efficiencies of the countries are such that if both countries devoted all their resources to Food production, output would be as follows:

Northland: 100 tonnes

Southland: 200 tonnes

If all the resources of the countries were allocated to the production of clothes, output would be:

Northland: 100 tonnes

Southland: 100 tonnes

Assuming each has constant opportunity costs of production between the two products and both economies have full employment at all times. All factors of production are mobile within the countries between clothing and food industries, but are immobile between the countries. The price mechanismperfect competition. must be working to provide

Southland has an absolute advantage over Northland in the production of Food. Both countries are equally efficient in the production of clothes. There seems to be no mutual benefit in trade between the economies. The opportunity costs shows otherwise. Northland's opportunity cost of producing one tonne of Food is one tonne of Clothes and vice versa. Southland's opportunity cost of one tonne of Food is 0.5 tonne of Clothes. The opportunity cost of one tonne of Clothes is 2 tonnes of Food. Southland has a comparative advantage in food production, because of its lower opportunity cost of production with respect to Northland. Northland has a comparative advantage over Southland in the production of clothes, the opportunity cost of which is lower in Southland with respect to Food than in Northland.

To show these different opportunity costs lead to mutual benefit if the countries specialize production and trade, consider the countries produce and consume only domestically. The volumes are:

Production and consumption before trade
	Food	Clothes
Northland	50	50
Southland	100	50
World total	150	100

This example includes no formulation of the preferences of consumers in the two economies which would allow the determination of the international exchange rate of Clothes and Food. Given the production capabilities of each country, in order for trade to be worthwhile Northland requires a price of at least one tonne of Food in exchange for one tonne of Clothes; and Southland requires at least one tonne of Clothes for two tonnes of Food. The exchange price will be somewhere between the two. The remainder of the example works with an international trading price of one tonne of Food for 2/3 tonne of Clothes.

If both specialize in the goods in which they have comparative advantage, their outputs will be:

Production after trade
	Food	Clothes
Northland	0	100
Southland	200	0
World total	200	100

World production of food increased. Clothing production remained the same. Using the exchange rate of one tonne of Food for 2/3 tonne of Clothes, Northland and Southland are able to trade to yield the following level of consumption:

Consumption after trade
	Food	Clothes
Northland	75	50
Southland	125	50
World total	200	100

Northland traded 50 tonnes of Clothing for 75 tonnes of Food. Both benefited, and now consume at points outside their production possibility frontiers.

Assumptions in Example 2

Two countries, two goods - the theory is no different for larger numbers of countries and goods, but the principles are clearer and the argument easier to follow in this simpler case.

Equal size economies - again, this is a simplification to produce a clearer example.

Full employment - if one or other of the economies has less than full employment of factors of production, then this excess capacity must usually be used up before the comparative advantage reasoning can be applied.

Constant opportunity costs - a more realistic treatment of opportunity costs the reasoning is broadly the same, but specialization of production can only be taken to the point at which the opportunity costs in the two countries become equal. This does not invalidate the principles of comparative advantage, but it does limit the magnitude of the benefit.

Perfect mobility of factors of production within countries - this is necessary to allow production to be switched without cost. In real economies this cost will be incurred: capital will be tied up in plant (sewing machines are not sowing machines) and labour will need to be retrained and relocated. This is why it is sometimes argued that 'nascent industries' should be protected from fully liberalised international trade during the period in which a high cost of entry into the market (capital equipment, training) is being paid for.

Immobility of factors of production between countries - why are there different rates of productivity? The modern version of comparative advantage (developed in the early twentieth century by the Swedish economists Eli Heckscher and Bertil Ohlin) attributes these differences to differences in nations' factor endowments. A nation will have comparative advantage in producing the good that uses intensively the factor it produces abundantly. For example: suppose the US has a relative abundance of capital and India has a relative abundance of labor. Suppose further that cars are capital intensive to produce, while cloth is labor intensive. Then the US will have a comparative advantage in making cars, and India will have a comparative advantage in making cloth. If there is international factor mobility this can change nations' relative factor abundance. The principle of comparative advantage still applies, but who has the advantage in what can change.

Perfect competition - this is a standard assumption that allows perfectly efficient allocation of productive resources in an idealized free market.

Attorney example

There is an illuminating example illustrated in the well known book Economics by Paul Samuelson. Imagine a city where the best lawyer happens also to be the best secretary, that is he would be the most productive lawyer and he would also be the best secretary in town. However it is quite clear that this lawyer would focus on the task of being an attorney by employing a secretary instead of doing all the paperwork by himself. This can easily be explained with the concept of comparative advantage: He is the best secretary AND the best lawyer, however by comparing what he can earn as a secretary with the income he could earn by running a law firm AND employing a secretary one can clearly see that the latter option is the better one.