by Steven M. Suranovic

# Definitions: Absolute and Comparative Advantage

To define absolute advantage it is useful to define labor productivity first. To define comparative advantage it is useful to first define opportunity cost. Each of these are defined formally below using the notation of the Ricardian model. The concepts are presented in the following order.

Labor Productivity
Opportunity Costs

Labor productivity is defined as the quantity of output that can be produced with a unit of labor. Since aLC represents hours of labor needed to produce one pound of cheese, its reciprocal, , represents the labor productivity of cheese production in the US. Similarly represents the labor productivity of wine production in the US.

A country has an absolute advantage in the production of a good relative to another country if it can produce the good at lower cost or with higher productivity. Absolute advantage compares industry productivities across countries. In this model we would say the U.S. has an absolute advantage in cheese production relative to France if

or if

The first expression means that the US uses fewer labor resources (hours of work) to produce a pound of cheese than does France. In other words the resource cost of production is lower in the US. The second expression means that labor productivity in cheese in the US is greater than in France. Thus the US generates more pounds of cheese per hour of work.

Obviously if then France has the absolute advantage in cheese. Also if then the US has the absolute advantage in wine production relative to France.

Opportunity cost is defined generally as the value of the next best opportunity. In the context of national production, the nation has opportunities to produce wine and cheese. If the nation wishes to produce more cheese, then because labor resources are scarce and fully employed, it is necessary to move labor out of wine production in order to increase cheese production. The loss in wine production necessary to produce more cheese represents the opportunity cost to the economy. The slope of the PPF, , corresponds to the opportunity cost of production in the economy.

To see this more clearly consider points A and B on the adjoining PPF diagram. Let the horizontal distance between A and B be one pound of cheese. Label the vertical distance X. The distance X then represents the quantity of wine that must be given up to produce one additional pound of cheese when moving from point A to B. In other words X is the opportunity cost of producing cheese.

Note also that the slope of the line between A and B is given by the formula . Thus the slope of the line between A and B is the opportunity cost which from above is given as . We can more clearly see why the slope of the PPF represents the opportunity cost by noting the units of this expression.

Thus, the slope of the PPF expresses the number of gallons of wine that must be given up (hence the minus sign) to produce another pound of cheese. Hence it is the opportunity cost of cheese production (in terms of wine). The reciprocal of the slope in turn represents the opportunity cost of wine production (in terms of cheese).

Since in the Ricardian model the PPF is linear, the opportunity cost is the same at all possible production points along the PPF. For this reason the Ricardian model is sometimes referred to as a constant (opportunity) cost model.

A country has a comparative advantage in the production of a good if it can produce that good at a lower opportunity cost relative to another country. Thus the US has a comparative advantage in cheese production relative to France if:

This means that the US must give up less wine to produce another pound of cheese than France must give up to produce another pound. It also means that the slope of the US PPF is flatter than the slope of France's PPF.

Starting with the inequality above, cross multiplication implies the following,

This means that France can produce wine at a lower opportunity cost than the US. In other words France has a comparative advantage in wine production. This also means that if the US has a comparative advantage in one of the two goods, France must have the comparative advantage in the other good. It is not possible for one country to have the comparative advantage in both of the goods produced.

Suppose one country has an absolute advantage in the production of both goods. Even in this case each country will have a comparative advantage in the production of one of the goods. For example, suppose aLC = 10, aLW = 2, aLC* = 20, aLW* = 5. In this case aLC (10) < aLC* (20) and aLW (2) < aLW* (5) so the US has the absolute advantage in the production of both wine and cheese. However, it is also true that so that France has the comparative advantage in cheese production relative to the US.

Another way to describe comparative advantage is to look at the relative productivity advantages of a country. In the US the labor productivity in cheese is 1/10 while in France it is 1/20. This means that the US productivity advantage in cheese is (1/10)/(1/20) = 2/1. This means the US is twice as productive as France in cheese production. In wine production the US advantage is (1/2)/(1/5) = (2.5)/1. This means the US is two and one-half times as productive as France in wine production.

The comparative advantage good in the US then is that good in which the US enjoys the greatest productivity advantage, wine. France's comparative advantage good however, is that good in which it has the least productivity disadvantage in production, namely cheese.

The only case in which neither country has a comparative advantage is when the opportunity costs are equal in both countries. In other words, when

then neither country has a comparative advantage. It would seem however, that this is an unlikely occurrence.

International Trade Theory and Policy - Chapter 40-4: Last Updated on 7/18/06