# 2.5: Definitions- Absolute and Comparative Advantage

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Learning Objectives

1. Learn how to define labor productivity and opportunity cost within the context of the Ricardian model.
3. Learn to identify comparative advantage via two methods: (1) by comparing opportunity costs and (2) by comparing relative productivities.

To define absolute advantage, it is useful to define labor productivity first. To define comparative advantage, it is useful to first define opportunity cost. Next, each of these is defined formally using the notation of the Ricardian model.

## Labor Productivity

Labor productivity is defined as the quantity of output that can be produced with a unit of labor. Since $$a_{LC}$$ represents hours of labor needed to produce one pound of cheese, its reciprocal, $$\frac{1}{a_{LC}}$$, represents the labor productivity of cheese production in the United States. Similarly, $$\frac{1}{a_{LW}}$$ represents the labor productivity of wine production in the United States.

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 United States has an absolute advantage in cheese production relative to France if

$a_{LC} < a_{LC}^∗ \nonumber$

or if

$\frac{1}{a_{LC}} > \frac{1}{a_{LC}^*} \nonumber .$

The first expression means that the United States 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 United States. The second expression means that labor productivity in cheese in the United States is greater than in France. Thus the United States generates more pounds of cheese per hour of work.

Obviously, if $$a_{LC}^* < a_{LC}$$, then France has the absolute advantage in cheese. Also, if $$a_{LW} < a_{LW}^*$$, then the United States has the absolute advantage in wine production relative to France.

## Opportunity Cost

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, $$−( \frac{a_{LC}}{a_{LW}}$$), corresponds to the opportunity cost of production in the economy.

To see this more clearly, consider points $$A$$ and $$B$$ in Figure $$\PageIndex{1}$$. 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

$slope = \frac{rise}{run} = -\frac{X}{1} \nonumber .$

Thus the slope of the line between $$A$$ and $$B$$ is the opportunity cost, which from above is given by $$−( \frac{a_{LC}}{a_{LW}}$$). We can more clearly see why the slope of the PPF represents the opportunity cost by noting the units of this expression:

$−\frac{a_{LC}}{a_{LW}} \frac{[hrs/lb]}{[hrs/gal]} = [gal/lb] \nonumber .$

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, $$−( \frac{a_{LW}}{a_{LC}}$$), 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.

### Using Opportunity Costs

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 United States has a comparative advantage in cheese production relative to France if

$\frac{a_{LC}}{a_{LW}} < \frac{a_{LC}^*}{a_{LW}^*} \nonumber .$

This means that the United States 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 U.S. PPF is flatter than the slope of France’s PPF.

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

$\frac{a_{LC}}{a_{LW}} < \frac{a_{LC}^*}{a_{LW}^*} \Rightarrow \frac{a_{LW}^*}{a_{LC}^*} < \frac{a_{LW}}{a_{LC}} \nonumber .$

This means that France can produce wine at a lower opportunity cost than the United States. In other words, France has a comparative advantage in wine production. This also means that if the United States 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 $$a_{LC} = 10$$, $$a_{LW} = 2$$, $$a_{LC}^* = 20$$, and $$a_{LW}^* = 5$$. In this case, $$a_{LC} (10) < a_{LC}^* (20)$$ and $$a_{LW} (2) < a_{LW}^* (5)$$, so the United States has the absolute advantage in the production of both wine and cheese. However, it is also true that

$\frac{a_{LC}^*}{a_{LW}^*} \left( \frac{20}{5} \right) < \frac{a_{LC}}{a_{LW}} \left( \frac{10}{2} \right) \nonumber$

so that France has the comparative advantage in cheese production relative to the United States.

### Using Relative Productivities

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

The comparative advantage good in the United States, then, is that good in which the United States enjoys the greatest productivity advantage: wine.

Also consider France’s perspective. Since the United States is two times as productive as France in cheese production, then France must be $$1/2$$ times as productive as the United States in cheese. Similarly, France is $$2/5$$ times as productive in wine as the United States. Since $$1/2 > 2/5$$, France has a disadvantage in production of both goods. However, France’s disadvantage is smallest in cheese; therefore, France has a comparative advantage in 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

$\frac{a_{LC}}{a_{LW}} = \frac{a_{LC}^*}{a_{LW}^*} \nonumber ,$

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

KEY TAKAWAYS

• Labor productivity is defined as the quantity of output produced with one unit of labor; in the model, it is derived as the reciprocal of the unit labor requirement.
• Opportunity cost is defined as the quantity of a good that must be given up in order to produce one unit of another good; in the model, it is defined as the ratio of unit labor requirements between the first and the second good.
• The opportunity cost corresponds to the slope of the country’s production possibility frontier (PPF).
• An absolute advantage arises when a country has a good with a lower unit labor requirement and a higher labor productivity than another country.
• A comparative advantage arises when a country can produce a good at a lower opportunity cost than another country.
• A comparative advantage is also defined as the good in which a country’s relative productivity advantage (disadvantage) is greatest (smallest).
• It is not possible that a country does not have a comparative advantage in producing something unless the opportunity costs (relative productivities) are equal. In this case, neither country has a comparative advantage in anything.

Exercise $$\PageIndex{1}$$

1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
1. The labor productivity in cheese if four hours of labor are needed to produce one pound.
2. The labor productivity in wine if three kilograms of cheese can be produced in one hour and ten liters of wine can be produced in one hour.
3. The term used to describe the amount of labor needed to produce a ton of steel.
4. The term used to describe the quantity of steel that can be produced with an hour of labor.
5. The term used to describe the amount of peaches that must be given up to produce one more bushel of tomatoes.
6. The term used to describe the slope of the PPF when the quantity of tomatoes is plotted on the horizontal axis and the quantity of peaches is on the vertical axis.
2. Consider a Ricardian model with two countries, the United States and Ecuador, producing two goods, bananas and machines. Suppose the unit labor requirements are $$a_{LB}^{US} = 8$$, $$a_{LB}^E = 4$$, $$a_{LM}^{US} = 2$$, and $$a_{LM}^E = 4$$. Assume the United States has 3,200 workers and Ecuador has 400 workers.
1. Which country has the absolute advantage in bananas? Why?
2. Which country has the comparative advantage in bananas? Why?
3. How many bananas and machines would the United States produce if it applied half of its workforce to each good?
3. Consider a Ricardian model with two countries, England and Portugal, producing two goods, wine and corn. Suppose the unit labor requirements in wine production are $$a_{LW}^{Eng} = 1/3$$ hour per liter and $$a_{LW}^{Port} = 1/2$$ hour per liter, while the unit labor requirements in corn are $$a_{LC}^{Eng} = 1/4$$ hour per kilogram and $$a_{LC}^{Port} = 1/2$$ hour per kilogram.
1. What is labor productivity in the wine industry in England and in Portugal?
2. What is the opportunity cost of corn production in England and in Portugal?
3. Which country has the absolute advantage in wine? In corn?
4. Which country has the comparative advantage in wine? In corn?

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