Comparative advantage

Definition

The comparative advantage of an organization (individual, firm, or country) is in the activity that the organization can do with the maximum difference between the benefit and the opportunity cost. In other words, it is what the individual or country has the most advantage relative to other things the individual or country can do, and relative to things that others can do.

If organizations choose to work according to their comparative advantage, then social utility (and hence, social surplus) is maximized. In principle, comparative advantage can emerge both in a market economy (through the effect of gains from trade) and in a centrally planned economy, subject to a method for comparing the value or utility of different types of activities.

There are two related, but distinct, aspects of comparative advantage.

The law of comparative advantage itself, which offers a guide to what a particular organization should do or how certain activities should be allocated between organizations.
The systemic processes through which the law of comparative advantage gets implemented, i.e., the process by which each organization acquires the knowledge and incentives to perform the activities in which it has comparative advantage.

Example

A simple example involving two persons and two tasks

Suppose an economy has two individuals $A$ and $B$ and two activities $M$ and $N$ . Further, suppose that:

$A$ can generate $f(A,M)$ units of worth per hour doing $M$ and $f(A,N)$ units per hour doing $N$ .
$B$ can generate $f(B,M)$ units of worth per hour doing $M$ and $f(B,N)$ units per hour doing $N$ .

Suppose, further, that each person can choose to do exactly one of the two tasks, and they must do different tasks.

Since each can choose to do exactly one task, and they must do different tasks, there are two possible assignments:

$A$ does $M$ and $B$ does $N$ , yielding a total of $\!f(A,M)+f(B,N)$ .
$A$ does $N$ and $B$ does $M$ , yielding a total of $\!f(A,N)+f(B,M)$ .

If $\!f(A,M)+f(B,N)>f(B,M)+f(A,N)$ , then the first allocation is optimal. If $\!f(B,M)+f(A,N)>f(A,M)+f(B,N)$ , then the second allocation is optimal. This has three equivalent interpretations:

Condition for $A$ to do $M$ and $B$ to do $N$	Verbal formulation of interpretation
$\!f(A,M)+f(B,N)>f(B,M)+f(A,N)$	We are comparing the total output generated under the two possible configurations, and choosing the one that generates greater output.
$\!f(A,M)-f(A,N)>f(B,M)-f(B,N)$	Here, we are treating $N$ as the alternative activity and comparing (Between $A$ and $B$ , the gain in doing $M$ over and above the opportunity cost.
$\!f(A,M)-f(B,M)>f(A,N)-f(B,N)$	Here, we are comparing the competitive advantage of $A$ over $B$ in both $M$ and $N$ and allocating to $A$ the activity where the competitive advantage is greater.

Comparative advantage differs from two other possible allocation rules: each person does what that person is best at and each activity is done by the person who is best at that activity. The problem with the first allocation rule is that it may allocate both people to the same task, and the problem with the second allocation rule is that it may allocate both tasks to a single person. On the other hand, the law of comparative advantage always makes sense and maximizes total output.

Note, however, that if either of those rules does give a unique allocation, then that agrees with the allocation given by comparative advantage.

These two rules are contrasted with comparative advantage below:

Informal description of rule	Mathematical condition for $A$ to do $M$ , $B$ to do $N$	Corresponding description of comparative advantage rule	Key difference
Each person does what that person is best at	$\!f(A,M)-f(A,N)>0>f(B,M)-f(B,N)$	$\!f(A,M)-f(A,N)>f(B,M)-f(B,N)$	Comparative advantage is only a comparative rule and does not require anything about the signs of the expressions $f(A,M)-f(A,N)$ and $f(B,M)-f(B,N)$
Each activity is done by the person best at that activity	$\!f(A,M)-f(B,M)>0>f(A,N)-f(B,N)$	$\!f(A,M)-f(B,M)>f(A,N)-f(B,N)$	Comparative advantage is only a comparative rule and does not require anything about the signs of the expressions $f(A,M)-f(B,M)$ and $f(A,N)-f(B,N)$

Here are some examples to illustrate how different rules would give different predictions:

Mathematical condition	Numerical values that illustrate it	Comparative advantage says ...	Each individual doing what that individual is best at gives ...	Each activity done by the person best at it gives ...
$\!f(A,M)>f(B,M)$ , $\!f(B,N)>f(A,N)$ , $\!f(A,M)>f(A,N)$ , $\!f(B,N)>f(A,N)$	$\!f(A,M)=20,f(B,M)=15$ , $\!f(A,N)=16,f(B,N)=18$	$A$ does $M$ , $B$ does $N$	$A$ does $M$ , $B$ does $N$	$A$ does $M$ , $B$ does $N$
$\!f(A,M)>f(B,M)$ , $\!f(A,N)>f(B,N)$ , $\!f(A,M)>f(A,N)$ , $\!f(B,N)>f(B,M)$	$\!f(A,M)=20,f(B,M)=15$ , $\!f(A,N)=18,f(B,N)=16$	$A$ does $M$ , $B$ does $N$	$A$ does $M$ , $B$ does $N$	This rule does not work since it would allocate $A$ with both $M$ and $N$ .
$\!f(A,M)>f(B,M)$ , $\!f(B,N)>f(A,N)$ , $\!f(A,M)>f(A,N)$ , $\!f(B,M)>f(B,N)$	$\!f(A,M)=20,f(B,M)=18$ , $\!f(A,N)=15,f(B,N)=16$	$A$ does $M$ , $B$ does $N$	This rule does not work since both $A$ and $B$ would choose $M$	$A$ does $M$ , $B$ does $N$

A more sophisticated example involving marginal costs and marginal utilities

In the previous example, we assumed that each person could choose to do exactly one task, and the two persons had to choose different tasks. If this constraint were absent, each person would simply do what he or she were best at, and the comparative advantage phenomenon may not arise.

Although a rigid limit on the number of people who can do each task may not exist in real life, there are a number of realistic features that could give rise to the same observations. These include:

Increasing marginal cost of production (typically, in terms of some other factor of production) for each type of activity, that makes it worthwhile, after a certain point, to start doing another activity. For instance, there may be some land that is suitable for growing wheat and some land that is suitable for growing rice. Using land suitable for one crop to grow another is counterproductive. This leads to a tendency for some farmers to grow wheat and others to grow rice. Who chooses to grow which crop is then determined by comparative advantage. A similar case can be made when the capital stock for each type of productive activity is limited.
Decreasing marginal utility: A society may gain a lot of utility from a bit of this and a bit of that, but less utility if only one type of good is produced. This has to do with the fact that the marginal utility from having more of a good is decreasing: the more there is, the less additional quantity of the good yields worth.

Key features

Comparative advantage requires a multiplicity of both organizations and activities

The concept of comparative advantage makes sense when:

there is more than one organization, and
there is more than one type of activity for the organizations to choose from.

Thus, comparative advantage does not make sense in a world where there is only one organization, even if there is a multiplicity of task types to be performed. If there is only one organization, the organization chooses to do tasks based on the utility generated.

Similarly, comparative advantage does not make sense in a world where there is only one type of activity. In such a world, the organization that is best at the activity gets a priority in doing that activity, and if there is still more of the activity that needs to be done, then other organizations also engage in the activity.

Comparative advantage as a sign of mixed partial

Building on the observation that comparative advantage requires a multiplicity of both organizations and activities, we also note that the direction of comparative advantage depends, roughly, on the sign of a mixed partial derivative with respect to both organizations and activities. We consider comparative advantage and the other allocation rules:

Informal description of rule	What kind of partial derivative does it depend upon?
Each organization does what that organization is best at	The partial derivative with respect to variation in activities, holding the organization constant.
Each activity is done by the organization best at that activity	The partial derivative with respect to variation in organizations, holding the activity constant.
Comparative advantage	The mixed partial derivative (this is a second-order derivative) with respect to both organizations and activities.

Dependence of comparative advantage on relative value

Determining what allocation of activities to organizations is in keeping with the law of comparative advantage requires some way of measuring and comparing the value generated by different types of activities. In particular, a change in the exchange value between two types of activities can affect the direction of comparative advantage. We consider comparative advantage and the two alternative rules:

Informal description of rule	What kind of notion of value does this depend upon?
Each organization does what that organization is best at	It should be possible to compare (ordinally) the value of different types of activities that the organization can do. The best activity choice is invariant under order-preserving transformations of the mapping from activities to their value measurement for each fixed organization.
Each activity is done by the organization best at that activity	It should be possible to compare (ordinally) the value of the same activity done by different types of organizations. The best activity choice is invariant under order-preserving transformations of the mapping from organizations to the value measurement for each fixed activity.
Comparative advantage	This requires a quantitative (cardinal) measurement of the value across organizations and activities. A change in the cardinal measurements, even if it preserves the relative ordering of individual activities, can change the comparisons of the sums and differences, and hence affect the direction of comparative advantage.

Implementation of comparative advantage

Comparative advantage in a market economy

In a market economy, the relative value of activities is determined through their exchange value, i.e., how they trade relative to one another (which may be measured through money or through barter). Thus, trade and exchange two related purposes:

It determines the direction of comparative advantage, by determining the exchange value through the free buying and selling of goods and the price mechanism.
It helps implement the comparative advantage by creating incentives for each organization to stick to its comparative advantage.

Comparative advantage in a planned economy

In a planned economy:

To determine the direction of comparative advantage, a suitable exchange value needs to be determined. In the absence of a price mechanism and free buying and selling of goods, this exchange value must be based on explicit calculations and assumptions, such as a utilitarian calculus.
To implement the comparative advantage, explicit rewards, punishments, and incentives needs to be created to substitute for the natural incentives that would arise in a market economy.

Comparative advantage, division of labor, and specialization

The basic definition and formulation of comparative advantage does not depend on any assumption about greater gain in skills due to specialization. Comparative advantage suggests a division of labor even without the benefits of skill gains that may arise from specialization.

Comparative advantage and trade

Comparative advantage is closely linked to the concept of trade, because in a market economy, the main market mechanism that leads people to do tasks according to their comparative advantage is through trade. However, the principle of comparative advantage makes sense even without trade.

References

Online articles explaining comparative advantage

Article	Author	Location	Comment
Comparative Advantage: An Economics By Topic Detail	Lauren F. Landsburg	Library of Economics and Liberty	Excerpts from and links to historically important writings on the subject
A Brief History of the Concept of Comparative Advantage	Morgan Rose	Library of Economics and Liberty	Historical overview, and current context (as of 2001)
Comparative Advantage	Donald Boudreaux	Concise Encyclopedia of Economics, available online at the Library of Economics and Liberty	Explanation with mathematical example of comparative advantage plus trade
Treasure Island. The Power of Trade. Part I	Russell Roberts	Library of Economics and Liberty	A short story illustrating comparative advantage and trade.
Ricardo's Difficulty Idea	Paul Krugman	personal web space at MIT	Discussion of why comparative advantage is hard to grasp
The Theory of Comparative Advantage -- Overview	Steven Suranovic	internationalecon.com	An explanation of comparative advantage, its relation with and distinction from the concept of advantageous trade, and its interpretation.

Expository book references

The Undercover Economist by Tim Harford, 10-digit ISBN 0345494016, 13-digit ISBN 978-0345494016 (paperback)^{More info}, Page 206-211, Chapter 9 (Beer, Chips and Globalisation)
Book:CultureAndProsperity^{More info}, Page 84-86, 92, 125