Ch. 2: The Ricardian Model: Comparative Advantage and the Gains from Trade

Lecture 2 (Feenstra and Taylor, Chapter 2) presents the oldest and simplest explanation of why countries trade: differences in technology, that is in labour productivity. The lecture covers four topics: (1) the concepts of absolute advantage and comparative advantage; (2) how international trade affects real wages and why it places limits on relative wages (domestic versus foreign); (3) how productivity changes abroad can help or harm domestic workers; and (4) the limitations of the model. The lecture uses two countries, Greece (G) and Denmark (D), and two goods, an agricultural good (A) and a manufacturing good (M).

Main assumptions of the Ricardian model

• Two countries (Denmark and Greece) and two goods (A and M).
• Labour is the only factor of production, and all workers within a country are identical.
• Labour productivity differs across countries, for example because of differences in technology.
• Labour productivity is constant as output changes: each extra unit of labour adds the same output. Marginal and average cost are therefore constant, and the production possibilities frontier (PPF) is a straight line.
• Perfect competition prevails, so prices equal marginal and average cost (no profits).
• Labour can move freely between sectors within a country, but not between countries. Workers in the same country earn the same wage.

Unit labour requirements, absolute and comparative advantage

The key data are the unit labour requirements: the number of units of labour needed to produce one unit of each good. In the lecture example:

Productivity is the inverse of the unit labour requirement (output per unit of labour, the marginal product of labour MPL). In Greece one worker produces 1/2 unit of A or 1/4 unit of M; in Denmark one worker produces 1 unit of A or 1 unit of M.

Comparative advantage, not absolute advantage, determines the pattern of trade. A country that is less productive in everything still has a good in which it is relatively least bad, and trade based on that good benefits both countries.

Opportunity cost gives the same answer. In Greece, producing one unit of A uses 2 units of labour that could have produced 2/4 = 0.5 units of M, so the opportunity cost of A is 0.5 M. In Denmark it is 1/1 = 1 M. Greece has the lower opportunity cost of A (CA in A); Denmark has the lower opportunity cost of M (1 A versus 2 A in Greece).

Relative prices in autarky

Under perfect competition the price of each good equals its average cost, which is the unit labour requirement times the wage W:

Under autarky the relative price of A is lower in Greece (0.5) than in Denmark (1). This is general: comparative advantage implies that under autarky the relative price of the good in which a country has CA is lower than in the other country. Good M is relatively cheap in Denmark.

Real wages in autarky

The real wage measures how many units of a good a worker can buy with the wage from one unit of labour. In autarky:

In autarky real wages equal labour productivity: a Greek worker who supplies one unit of labour produces half a unit of A and can buy exactly half a unit of A. Real wages are higher in the more productive country (Denmark).

A hypothetical consumption pattern in autarky

Suppose a Greek worker spends half her income on each good. With real wages of 0.5 A and 0.25 M, she buys 0.25 units of A and 0.125 units of M. A Danish worker who spends 80% on M and 20% on A buys 0.8 units of M and 0.2 units of A. Autarky consumption is therefore (0.25 A, 0.125 M) in Greece and (0.2 A, 0.8 M) in Denmark. In autarky production and consumption coincide at this point (point a in each country's diagram), because a country cannot consume more of a good than it produces without trade.

In a diagram with A on the horizontal and M on the vertical axis, the Greek PPF (one worker) runs from 0.25 M on the vertical axis to 0.5 A on the horizontal axis, with slope equal to minus the relative price of A (0.5). The Danish PPF runs from 1 M to 1 A (slope 1). Point a lies on each PPF.

Free trade and the world relative price

With free trade (no regulations or taxes) goods are traded at a single world relative price P A / P M. It must lie between the two autarky prices: 0.5 < (P A/P M) < 1. If the world price were below 0.5, both countries would want to produce only M; above 1, both would want to produce only A. The borderline cases (equal to 0.5 or 1, when a large country keeps its autarky price) cannot be excluded a priori but are ignored here. For illustration the lecture assumes a free-trade relative price of 0.8.

Each country now specialises completely in its CA good: Greece in A, Denmark in M. For Greece the price of A rises from 0.5 to 0.8 (in terms of M); for Denmark the price of M rises from 1 to 1/0.8 = 1.25 (in terms of A). Each country gets a better price for its export good than in autarky.

Are there gains from trade? Worked example

Assume one worker in each country who supplies one unit of labour. The Greek worker produces 0.5 units of A. She keeps her autarky consumption of 0.25 A and exports the remaining 0.25 A to obtain M.

Greece consumes as much A as before and more M (0.20 instead of 0.125). Denmark consumes as much M as before (0.8) and more A (0.25 instead of 0.2). Both countries gain. This is possible because world production of both goods rises when each country specialises according to CA: world output of A goes from 0.25 + 0.2 = 0.45 to 0.5, and of M from 0.125 + 0.8 = 0.925 to 1.

In the diagram the free-trade consumption point C lies outside each country's PPF, on a trade line through the production point Q with slope equal to the world relative price. This is only possible through trade.

Workers can also gain in both goods at once. For example, the Greek worker could consume 0.28 A and export 0.22 A, importing 0.8 × 0.22 = 0.176 M. Then the Danish worker consumes 0.5 minus 0.28 = 0.22 A and 1 minus 0.176 = 0.824 M. Compared with autarky, Greece has more A (0.28 > 0.25) and more M (0.176 > 0.125), and Denmark has more A (0.22 > 0.2) and more M (0.824 > 0.8). Higher consumption of both goods means gains from trade and higher real incomes in both countries.

In terms of real wages: under free trade a Greek worker still earns 0.5 A (she produces A), but her real wage in terms of M rises from 0.25 to 0.5 × 0.8 = 0.40 M. A Danish worker earns 1 M and now 1/0.8 = 1.25 A instead of 1 A. With free trade the real wage in terms of the imported good rises, while the real wage in terms of the exported good is unchanged.

Relative wages under free trade

How high can the Greek wage be relative to the Danish wage (W G / W D)? Greece must be able to produce at least one good more cheaply, otherwise no Greek producer survives under free trade. Greece produces A, so its cost of A must not exceed Denmark's:

Example: if W G = 0.4 and W D = 1, then AC A in Greece = 2 × 0.4 = 0.8 < AC A in Denmark = 1, and AC M in Greece = 4 × 0.4 = 1.6 > AC M in Denmark = 1. So Greece produces A and Denmark produces M, as expected.

Where exactly the relative wage lies within the range depends on the relative demand for the two goods. An exogenous increase in the relative demand for A raises the demand for Greek labour and hence W G/W D (towards 0.5).

The same logic explains why low-wage countries are not automatically a threat. Wages reflect productivity: a country with very low productivity, such as Haiti in the textbook question, has very low wages but is not competitive across the board; a country such as China, whose productivity in manufacturing is relatively high compared with its wages, can undercut producers in industrial countries in those goods.

Changes in foreign productivity

In autarky real wages equal productivity, and with free trade the real wage in terms of the imported good rises, even when the trading partner is more productive in both goods. What happens if, starting from free trade, Denmark becomes even more productive?

Suppose Denmark's productivity in A rises so that it needs only 0.666 (two thirds) units of labour per unit of A. Greece keeps its CA in A: it now has 0.666/2 = 33% of Denmark's productivity in A and still 25% in M. The range for the relative wage becomes 1/4 ≤ W G/W D ≤ 1/3: Greek wages can now be at most 33% of Danish wages.

Relative wages matter to people (the lecture refers to a Harvard survey showing that people care about their position relative to others), but what happens to real wages? Assume W G/W D = 0.4 before and 0.3 after the productivity rise, with W D = 1, so W G = 0.4 and then 0.3. Under free trade with full specialisation, the price of A equals Greece's AC and the price of M equals Denmark's AC (1 × W D = 1).

The real wage in terms of A is unchanged (it equals Greek productivity in A), but the real wage in terms of the imported good M falls from 0.4 to 0.3. So a rise in the partner's productivity in the good in which Greece has CA can lower the overall real wage in Greece: the foreign country becomes a stronger competitor in Greece's export good, which lowers Greece's relative wage and its terms of trade.

Could the same result obtain if Denmark became more productive in M, the good Greece imports? No, in general Greece would then gain: the price of its import good M (equal to Denmark's cost a LM × W D) falls, so the Greek real wage in terms of M rises, while the real wage in terms of A stays at 0.5. Productivity growth abroad in the goods a country imports tends to benefit it; productivity growth abroad in the goods it exports can harm it.

The textbook formulation (Feenstra and Taylor, Chapter 2)

The textbook expresses the same ideas with marginal products of labour (MPL). With wage W and price P, competitive firms hire labour until P × MPL = W. If both goods are produced in autarky, the wage is the same in both industries, so P W × MPL W = P C × MPL C, which gives the no-trade relative price:

The textbook also stresses that the PPF of a Ricardian country is a straight line whose slope equals the relative price, that with trade each country specialises completely unless the world price equals its autarky price, and that each country's consumption with trade lies on a higher indifference curve than in autarky.

Worked exercises (FT Chapter 2 problems)

Problems 2 to 5 (cars and TVs). At Home each worker produces 3 cars or 2 TVs and there are 4 workers. In Foreign each worker produces 2 cars or 3 TVs, also with 4 workers.

Check: Home's 9 cars need 3 workers, leaving 1 worker for 2 TVs, so (9, 2) lies on the PPF; similarly for Foreign. With a world price P C/P TV = 1, which lies between 2/3 and 3/2, Home specialises in cars (12) and Foreign in TVs (12). If Home keeps 9 cars and exports 3 cars, it can import 3 TVs (price 1), consuming 9 cars and 3 TVs, more than the 2 TVs of autarky. Foreign then consumes 3 cars and 9 TVs instead of 2 cars and 9 TVs. Home's exports (3 cars) equal Foreign's imports, and both gain because both reach a higher indifference curve.

Problem 6 (bicycles and snowboards). Per hour, Home makes 4 bicycles or 6 snowboards, Foreign 2 bicycles or 8 snowboards. Home has the absolute advantage in bicycles (4 > 2), Foreign in snowboards (8 > 6). The opportunity cost of a bicycle is 6/4 = 1.5 snowboards at Home and 8/2 = 4 snowboards in Foreign. Home has the CA in bicycles and exports them; Foreign has the CA in snowboards and exports them.

Problem 7 (wages and prices). Home: wage 12 in both sectors, MPL TV = 2, P C = 4. Foreign: wage 6, MPL C = 1, P TV = 3. Using P = W/MPL:

With a world price P TV/P C = 1, Home exports cars (TVs are relatively expensive to make at Home) and Foreign exports TVs. In the trade equilibrium Home specialises in cars and its real wage is MPL C = 3 cars, which buys 3 TVs at the world price; before trade it was 3 cars or 2 TVs, so the real wage in terms of TVs rises. Foreign specialises in TVs: its real wage is 2 TVs or 2 cars, compared with 2 TVs or 1 car before trade, so it gains in terms of cars. Home workers earn more than Foreign workers (3 units versus 2) because they are more productive in the good they produce.

Other textbook questions: if the number of Home workers doubles, the PPF shifts out proportionally but its slope and thus the no-trade relative price are unchanged. Technological progress in wheat makes the PPF steeper on the wheat axis (more wheat possible) and lowers the no-trade relative price of wheat; progress in cloth lowers the relative price of cloth. A rise in the world relative price of a country's export good raises its utility; for the other country, which imports that good, a rise lowers utility until the price reaches its own autarky level, at which point it gains nothing from trade.

Reservations regarding the Ricardian model

• It ignores other factors of production such as capital and land, so it is silent on distributional issues: in the model all workers gain from trade. The specific factors model addresses this.
• It is a long-run model and pays no attention to the (possibly long-lasting) transition, during which workers previously employed in the comparative-disadvantage sector may be unemployed.
• It does not describe actual trade patterns well, since it predicts that a country either exports or imports a good; it cannot explain why, for example, France both exports and imports cars (intra-industry trade). It also predicts complete specialisation, which is rarely observed.