Tutorial on Comparative Advantage

By Dan Jacoby

If it weren't for small miracles the world would be a very boring place indeed and economics would be considerably more "dismal" than it is. Fortunately, however, the miracle of comparative advantage is one of the most incredible ideas ever summoned forth. The essence of this principle is that individuals, organizations, or political entities can produce wealth simply by producing and trading what they do best. What is so heretical about this idea?

Trade makes it possible to do that which an individual may find impossible by him or herself. Not only that, but everyone, according to this concept has something to trade (can economics really be the foundation for statements in support of diversity?). No matter how bad I am at singing, carpentry, or statistics I am less bad at some of these activities. According to the theory of comparative advantage, even if you sing, hammer, or compute better than me, we'll both be better off by trading the things we do comparatively well. What more felicitous statement can there be than the idea that no one is a complete loser. Yet, that statement is, and deserves to be, argued. And indeed, after we "prove" our point, we will examine the situation more closely.

To prove a point we must agree on the nature of the proof. So consider the following proposition. Suppose a person can produce a few things--lets call them their production possibility set. Suppose further that a person's time is limited so that producing one of these things means producing less of another. We can imagine that there is a maximum amount of each good a person can produce, but that producing that maximum means producing nothing else. Rather than specialize completely in the production of one good, a person with no trading partners will typically trade off some of the production of one good in order to have a variety of goods. Conceptually, there is a "possibility frontier" which expresses all the possible combinations of goods that person may produce if they don't waste any resources. To produce less is inefficient, to produce more is impossible. The nature of our proof that trade can make all parties better off is that both parties can consume a combination of goods that was impossible without trade. If we can agree that this establishes our proof, we will turn the rest of the argument into math on the presumption that it is harder to argue with math than with words.

To make the math relatively easy we will simplify the problem in three ways--though we could make the same proof using linear algebra. The simplifications are these. First, we will imagine a world in which there are only two goods. Lets call them food and clothing. Second, let's imagine a world in which each of can alter the amount of food or clothing we make at a constant rate. Suppose, that is, that the maximum food I can produce is 100 units, then let's say that for every 5 units of food I produce, I could instead produce one unit of clothing. It should be clear then that if instead of producing 100 units of food, I could produce 20 units of clothing or some other combination at the same rate of transformation. Let's think about this rate of transformation as the cost of production. In other words, to produce one unit of clothing I have to give up--or it costs me--5 units of food. We will return to this problem in a moment, but, for now, let's make the last simplification in our proof. That simplification is that that there are only two traders, each capable of producing the same two goods, although at different costs.

If this is so, consider the following set of tables.

We know that it costs Clarissa five units of food to produce one unit of clothing. Consequently we can also calculate how much clothing Clarissa would have if she produced only 50 units of food.

Since one unit of clothing costs five units of food and we have given up 50 units of food, she will have 10 units of clothing. Using everyday language we can restate this as follows:

Clarissa has a total cost of 50 units of food. If the cost of each unit of clothing is 5 units of food, then

Total Cost/Unit Cost =Number of units gained

Or 50 F/5F = 10 C

This is exactly the kind of calculation you make going to the supermarket. That is if green beans cost $2 per pound and the total costs is $40, then you can buy 20 pounds.

In the table below, we'll elaborate the production possibility frontier for Clarissa. You'll want to confirm that you know how each number appeared where it did, and also that you can fill in the missing space.

Clarissa's PPF

When it comes to Brentano, we have an additional question. What is the cost of a unit of food for him? Here the calculation will be exactly the same…the only difference is what is unknown.

So starting with:

Total cost/Cost per unit = Number of Units

We can rearrange

Total Cost/Number of Units = Cost per Unit

Being specific. We see that if Brentano produces only Food, he produces 200 units. Thus to produce only clothing he reduces food by 200. That means that the total cost of 50 units of clothing is 200 units of food.

So:

TC/# units = Cost per unit

200F/50C = 4F

Or, in other words, producing 1 unit of clothing costs 4 units of food.

Now it is possible to determine who has a comparative advantage in producing cloth by comparing the relative costs in terms of food forgone.

*Clarissa's cost of producing clothing is 5 units of food.

*Brentano's cost of producing clothing is 4 units of food.

Given this, Brentano is the low cost clothing producer and it will pay for him to sell clothing for food, while Clarissa trades food for clothing. All that is necessary is to find a price that makes trade worthwhile. Think of it this way, Clarissa is buying clothing and thus wants a price that that is lower than her own cost of production (5F). Brentano is selling clothing and therefore wants a price that is more than the cost he faces to make it on his own (4F). Consequently, any price between these two will make each better off than producing food or clothing on there own. To see this, we can examine the production possibilities for both of these two individuals and augment to these their trade possibilities.

But if we assume trade occurred at a price of 4.25 units of food for each unit of clothing, then the following post trade possibility curve occurs

Comparison between the two sets of production possibility frontiers indicates that each party can achieve bundles of goods that exceed those available to them when they did not trade. It is worth noting that Clarissa's Consumption Possibility Table depicts the changes that occur as she first specializes by producing only food (in the top cell of her table Clarissa produces only food), and then allocates increasing amounts of her food production to buying clothing. Likewise, Brentano specializes by producing only clothing (at the bottom cell of the table he produces all clothing and trades no food) and then allocates differing quantities of clothing to buy food. By comparing Clarissa's production with her consumption possibility sets, we see that at every level of food consumption she can have the same or more clothing than she would by producing herself. To compare Brentano's pre and post trade position we see that at every level of clothing production he can consume the same or more food than he would if he produced only on his own.

The main points to be noted in this example of comparative advantage are these:

1. trade makes it possible to achieve that which was impossible to achieve by oneself
2. to achieve the benefits of trade requires some degree of specialization for the market
3. as long as there are differences in production costs between one entity or person and another, each party has a comparative advantage and can benefit from trade
4. mutual benefit depends upon setting a trade price between the costs of the two producers
5. mutual benefit does not assume equal benefit (i.e., we could have set the price at 4.5 units of food per unit of clothing but that would have conveyed the wrong message). Supply and demand, not any abstract notion of equality, determine the actual price. In this example more of the gains from trade go the clothing buyer since the price is 3/4 of unit below his cost of production and only 1/4 of unit above the clothing seller. No matter how unequal, both have more to consume after the trade.
6. The maximum gain from trade in this problem consists of 1 unit of food for each unit of clothing (i.e. the difference between the two individual's costs--5 and 4 units of food per unit of clothing). If costs of trading, like taxes or transportation were equaled one unit of food per unit of clothing traded, there would be no gain from trade.

Appendix 1:

Graphing the problem

Appendix 2:

Getting confused. Units of analysis.