Comparative advantage

Definition FACT

One workshop makes every item faster than its neighbor. Intuition suggests that it has nothing to gain from the other and should make everything itself. Yet in the costless-trade model described below, different opportunity costs create the possibility of a surplus through reallocation and exchange.

A party has an absolute advantage in producing a good when it produces more of it with the same resources. It has a comparative advantage in that good when its opportunity cost—what it must give up to produce one additional unit—is lower than that of the other party.

In the simple model studied here—two parties, two goods, constant unit labor requirements, and costless exchange—comparative advantage indicates the direction of a reallocation that may increase total output. For the volume constructed below, a price strictly between the two opportunity costs allows each party to retain its initial number of tables and obtain more chairs. If each strictly prefers more chairs when its number of tables does not decrease, this bundle constitutes an individual gain. Absolute advantage measures unit productivity; it is neither necessary nor sufficient to determine the direction of specialization in this model.

A constructed numerical model ANALOGY

Two workshops produce tables and chairs. Workshop A has 100 hours per period, and workshop B has 120 hours. The unit production times are as follows.

Workshop A is faster at producing both goods: it has the absolute advantage in both. Intuition stops there. Opportunity cost tells a different story.

For A, making one table takes 2 hours, the time needed to make 2 chairs: one table costs it 2 chairs. For B, one table takes 12 hours, the time needed to make 4 chairs: one table costs it 4 chairs.

A gives up less for a table (2 < 4): its comparative advantage lies in tables. B gives up less for a chair (0,25 < 0,5): its comparative advantage lies in chairs—even though it takes three times as long as A to make one.

The additional output, before any exchange ANALOGY

Suppose first that each workshop operates in isolation. A devotes its time to 20 tables and 60 chairs ($20 \times 2 + 60 \times 1 = 100$20×2+60×1=100 hours). B produces 5 tables and 20 chairs ($5 \times 12 + 20 \times 3 = 120$5×12+20×3=120 hours). Together: 25 tables and 80 chairs.

Now reallocate work according to comparative advantage, without adding a single hour. B stops making tables and switches entirely to chairs: 40 chairs ($40 \times 3 = 120$40×3=120 hours). A takes over the 5 tables B no longer makes, bringing its output to 25 tables, which takes $25 \times 2 = 50$25×2=50 hours; the remaining 50 hours yield 50 chairs ($25 \times 2 + 50 \times 1 = 100$25×2+50×1=100 hours).

The same number of tables and ten more chairs, with exactly the same resources. The additional output is no sleight of hand: the 5 tables that B used to make cost it 20 chairs, whereas they cost A only 10 chairs. Moving their production from B to A releases exactly the difference—10 chairs, the additional output observed.

This reallocation is not intended to describe an equilibrium: it is chosen so that the total number of tables remains unchanged, making the additional output visible in a single dimension. Notice that it fully specializes B but leaves A producing both goods: complete specialization by both parties is not necessary for additional output to appear.

This point deserves emphasis: the additional output appears before any exchange, solely through the reallocation of tasks. At this stage B holds 40 chairs and no tables, a bundle it could have produced on its own but had not chosen. This reallocation is not yet sufficient to establish an individual gain for either party; exchange is precisely what distributes the surplus.

Sharing the gain and the terms of trade ANALOGY

B wants tables; their price, expressed in chairs, remains to be set.

This price, called the terms of trade in this bilateral two-good model, is not determined by the principle. For the positive volume selected here, in the absence of exchange costs and under the assumption that each party strictly prefers more chairs when the number of tables is unchanged, both gain strictly if the price of one table lies strictly between their two opportunity costs, that is, between 2 and 4 chairs.

The reason is symmetrical. A will not give up a table for fewer than 2 chairs, because it could simply forgo one table and make 2 chairs itself. B will not give more than 4 chairs for a table, because at that price it could do just as well by making the table itself.

Choose 3 chairs per table, and suppose B buys 5 tables for 15 chairs.

Each recovers exactly the number of tables it had in isolation, plus five additional chairs. The 10-chair surplus has been divided into two equal shares—a consequence of the chosen price, not of the principle.

Nor is the volume of 5 tables any more determined than the price: it is chosen here because it restores each party's initial number of tables, making the gain visible in a single dimension. With the price fixed at 3 and as long as B accepts a higher volume, A can produce and then transfer one additional table: it sacrifices 2 chairs in production and receives 3, for a net gain of one chair. The traded volume and the reallocation then increase together.

For the selected volume of five tables, the price determines how the ten additional chairs are divided. At 2 chairs per table, if A agreed to transfer 5 tables for 10 chairs, it would end up with 20 tables and 60 chairs, its isolated position: the entire gain would go to B. At 4 chairs per table, if B agreed to give 20 chairs for 5 tables, it would return to 5 tables and 20 chairs: the entire gain would go to A. Between these two bounds, both parties gain strictly under the stated preference; at the bounds, one party is indifferent and may refuse the exchange. The model establishes the existence of a potential surplus and bounds the prices that can divide it; it guarantees neither that an exchange will occur nor where the price will settle. In a competitive market with specified supply and demand, their interaction may determine the price; in a bilateral exchange, a bargaining mechanism must be specified.

The implication of reciprocal opportunity costs in the two-party–two-good case FACT

In the case of two parties and two goods, it is impossible for one party to have the comparative advantage in both, except when opportunity costs are equal—in which case no reallocation based on those costs alone creates a surplus.

The proof takes one line. A given party's two opportunity costs are reciprocals of one another: if one table costs $a$a chairs, one chair costs $1/a$1/a table. Let $a$a be A's cost of one table and $b$b B's, both strictly positive because the production times are positive. Suppose $a < b$a<b: A has the comparative advantage in tables; and because $a$a and $b$b are strictly positive, $a < b$a<b implies $1/a > 1/b$1/a>1/b, so B gives up less for one chair—the comparative advantage in chairs therefore necessarily belongs to B. The case $b < a$b<a is symmetrical, and the case $a = b$a=b is the equality case, in which neither party has a comparative advantage in either good. In our example, $a = 2$a=2, $b = 4$b=4, and $1/a = 0{,}5 > 1/b = 0{,}25$1/a=0,5>1/b=0,25.

If their relative productivities differ, even the party that is less productive in both goods therefore has a comparative advantage in one of them. What underpins the potential surplus is not the absolute productivity gap, but the comparison of productivity ratios, which here produces the same ranking as the comparison of opportunity costs. If those costs were identical, no reallocation based on them would add anything—even if one party were ten times faster than the other at producing both goods.

What this model assumes FACT

• A single, homogeneous scarce resource, transferable at a fixed rate. The entire argument rests on a single factor—hours—which is moved from one good to the other without loss. Constant unit labor requirements make the production frontier linear here and give each good an opportunity cost independent of the quantity produced. The number of factors alone is not sufficient to determine the shape of that frontier.
• Constant opportunity costs. The example assumes that a table always costs A 2 chairs. With a differentiable frontier and increasing costs, a price-taking producer that maximizes the value of its output equates, in an interior solution where it produces both goods, marginal opportunity cost with the relative price. A corner solution, in which it produces only one good, remains possible. The precise result then depends on technology, prices, and demand.
• Two parties, two goods, and divisible quantities. The proof based on the reciprocal relationship between $a$a and $1/a$1/a applies exactly within this framework. Models with multiple goods or multiple parties require a ranking and additional assumptions; this article does not automatically extend the conclusion to them.
• Resources mobile within each party, not between them. The argument reallocates A's hours between tables and chairs. It never transfers them from A to B. If resources moved freely between the parties, the question would no longer be the same.
• Full employment of resources in both situations. The comparison is between two allocations that use all available hours. The measured gain comes from a better allocation, not from putting idle resources to work.
• A preference strictly increasing in chairs over the bundles compared. In the constructed division, each workshop retains its initial number of tables and receives more chairs; the strict gain assumes that it prefers this bundle. Without demand for tables, B has no reason to exchange, and without a preference for more chairs, the additional chairs do not necessarily constitute a gain.
• An aggregate gain for each party whose internal distribution is not guaranteed. The principle compares workshop A with itself, not its members with one another. Specialization changes who does what: those whose activity disappears are not automatically compensated by the aggregate gain. The model includes no mechanism for internal compensation.
• Exchange costs assumed to be zero in the calculation. Transport and contracting consume resources in reality. Nonzero costs narrow the interval of mutually beneficial prices and may eliminate it: when the gap between the two opportunity costs is small, the gain does not cover the transfer.
• Given technology and endowments. The unit times in the table are assumed to be fixed. This static example takes technology and endowments as given; it does not explain their endogenous evolution.

Summary

In the two-good, constant-cost model, shifting production toward the party with the lower opportunity cost creates a potential surplus; under the explicitly stated preference strictly increasing in chairs, a strictly positive volume exchanged at a price strictly between the two costs can benefit both parties.

Main references FACT

• David Ricardo — On the Principles of Political Economy and Taxation, chapter on foreign trade
• OpenStax — Absolute and Comparative Advantage
• OpenStax — Absolute Advantage in All Goods
• World Trade Organization — Comparative Advantage
• John Stuart Mill — Of the Laws of Interchange between Nations
• International Monetary Fund — International Trade: Commerce among Nations, “Why trade reform is difficult” section
• Alan Deardorff — The Ricardian Model