Lecture 2: The Ricardian model in class (Denmark and Greece)

The second lecture works through the Ricardian model with one concrete example: Denmark and Greece, agricultural goods and manufactured goods. The book chapter on the Ricardian model (Ch. 2) explains the general idea; this chapter follows the numbers from the lecture step by step, because the multiple choice exam asks exactly this kind of reasoning: which country has which advantage, what happens to prices and real wages, and how far relative wages can move.

The assumptions

• Two countries, Denmark (D) and Greece (G), and two goods, agricultural goods (A) and manufactured goods (M).
• Labour is the only factor of production, and within a country all workers are identical, so they all earn the same wage.
• Labour productivity differs between countries, for example because of different technology.
• Productivity is constant: producing more does not make a worker more or less productive. Production is Q = a × L, so doubling labour doubles output (constant returns to scale). The average product of labour Q/L and the marginal product ΔQ/ΔL are both equal to a.
• Perfect competition, so the price of each good equals its marginal cost and its average cost.

With wage W and productivity a, the cost of one unit is the wage divided by productivity: AC = TC/Q = WL/Q = W/(Q/L) = W/a. Equivalently, AC is the wage times the labour requirement. Under perfect competition this is also the price.

The example: who is better at what?

Denmark needs fewer hours for both goods, so Denmark has an absolute advantage in both. That does not decide the pattern of trade. What matters is where each country is relatively best:

• In A, Greece has 1/2 of Danish productivity (2 hours against 1).
• In M, Greece has only 1/4 of Danish productivity (4 hours against 1).

Greece is less behind in A, so Greece has a comparative advantage in A. Denmark is four times as productive in M but "only" twice as productive in A, so Denmark has its comparative advantage in M. Every country has a comparative advantage in something, even a country that is worse at everything.

Opportunity cost gives the same answer. In Greece one unit of A costs 2 hours, which could have made 2/4 = 0.5 unit of M. In Denmark one unit of A costs 1 hour, which could have made 1 unit of M. Greece gives up less M for each unit of A, so A is relatively cheap to make in Greece.

Relative prices in autarky

With price equal to average cost:

The wage drops out: a relative price only depends on the labour requirements. In Greece A costs half as much labour as M, so A costs half as much as M. In Denmark both cost the same. Note the rule: in autarky, a good is relatively cheaper in the country with the comparative advantage in that good. A is relatively cheap in Greece; M is relatively cheap in Denmark.

Real wages in autarky

A real wage tells how much of a good one hour of work buys. In Greece:

• in terms of A: W^G/P^A,G = W^G/(2W^G) = 0.5 unit of A per hour;
• in terms of M: W^G/P^M,G = W^G/(4W^G) = 0.25 unit of M per hour.

In Denmark the real wage is 1 in terms of both goods. Without trade, the real wage simply equals labour productivity: what a worker produces in an hour is what he can buy with an hour's wage. Real wages are higher in the more productive country.

Consumption in autarky

Suppose each country has one worker who supplies one unit of labour. The lecture assumes the Greek worker spends half her time (income) on each good: 0.25 unit of A and 0.125 unit of M. The Danish worker spends 80% on M and 20% on A: 0.8 unit of M and 0.2 unit of A. In autarky the production point and the consumption point are the same point (point a on the production possibility frontier), because a country can only consume what it makes.

The production possibility frontier (PPF) shows all combinations of A and M a country can make with its labour. Greece with one unit of labour: at most 0.5 A or 0.25 M, on a straight line between those points. Denmark: at most 1 A or 1 M. The slope of the PPF is the autarky relative price.

Free trade

With free trade (no tariffs or other barriers) one common relative price P^A/P^M holds in both countries. It must lie between the two autarky prices: 0.5 < P^A/P^M < 1. (It could equal one of the bounds if one country is very large, but the lecture ignores that case.) For the example the lecture takes P^A/P^M = 0.8.

Each country now specializes fully in its comparative advantage good: Greece makes only A (0.5 unit), Denmark makes only M (1 unit).

Are there gains from trade?

Trade must be balanced: the value of exports equals the value of imports, P^A × X^A = P^M × IM^M, so

Suppose the Greek worker keeps her autarky consumption of A (0.25) and exports the other 0.25. She can import 0.8 × 0.25 = 0.20 unit of M. (The slide prints this as "=20"; the correct number is 0.20.) That is more M than the 0.125 she had in autarky, with the same amount of A.

Denmark imports those 0.25 units of A, more than the 0.2 the Danish worker consumed in autarky. Denmark makes 1 unit of M and exports 0.20, so it still consumes 0.80 unit of M, as before. Both countries consume at least as much of everything, and more of something: the world produces more of both goods because each country does what it is relatively good at.

The gains can also be spread over both goods. If the Greek worker consumes 0.28 A and exports 0.22, she imports 0.8 × 0.22 = 0.176 M. She then has more of both goods than in autarky (0.28 > 0.25 and 0.176 > 0.125). The Danish worker consumes 0.5 − 0.28 = 0.22 A and 1 − 0.176 = 0.824 M: also more of both than in autarky (0.2 A and 0.8 M). Higher consumption of both goods means higher real incomes: that is what gains from trade means.

Real wages show the same thing. Under free trade the Greek wage still buys 0.5 unit of A per hour (Greece still produces A at cost 2W^G). In terms of M it now buys 0.5 × 0.8 = 0.4 unit, instead of 0.25 in autarky. Trade raises the real wage in terms of the imported good, even though the trading partner is more productive in everything.

Relative wages: how high and how low can the Greek wage be?

For Greece to survive in free trade it must be able to produce at least one good more cheaply than Denmark. For A that requires

The Greek wage can be at most 50% of the Danish wage, because Greek workers have 50% of Danish productivity in A. If the Greek wage were lower than a quarter of the Danish wage, Greece would even make M more cheaply (4W^G < W^D), and Denmark could produce nothing competitively. So

The bounds are the productivity ratios in the two goods. Example: with W^G = 0.4 and W^D = 1, AC^A,G = 0.8 < AC^A,D = 1 and AC^M,G = 1.6 > AC^M,D = 1, so Greece makes A and Denmark makes M. Where exactly the relative wage ends up within the range depends on relative demand: if world demand for A rises, demand for Greek labour rises and W^G/W^D moves towards 1/2.

Changes in foreign productivity

Can a trading partner's productivity growth hurt you? Start in free trade and let Denmark become more productive in A: it now needs only 0.666 unit of labour per unit of A. Greece keeps its comparative advantage in A (it now has 0.666/2 = 33% of Danish productivity in A against 25% in M), so it still specializes in A. But the range of the relative wage shrinks:

Greek wages can now be at most 33% of Danish wages. Take W^D = 1, a Greek wage of 0.4 before and 0.3 after the change. Prices equal average costs, Greece makes A and Denmark makes M:

The real wage in terms of A does not change (Greece still makes A itself), but in terms of M it falls from 0.4 to 0.3. So productivity growth abroad in the good in which you have your comparative advantage can lower your overall real wage: the foreign country becomes a stronger competitor in your export sector, which pushes down your relative wage and therefore what your wage buys of imports.

The lecture ends with a question: would the same happen if Denmark became more productive in M? No. M is Greece's import good; if Denmark makes M with less labour, M becomes cheaper, and the Greek real wage in terms of M rises. Productivity growth abroad in your import sector helps you, in your export sector it can hurt you.

Reservations about the Ricardian model

• It ignores other factors of production (capital, land), so it says nothing about who wins and who loses within a country. Everyone gains, because there is only one kind of worker. The specific factors model (Ch. 3) fills that gap.
• It is a long-run model. It ignores the transition period, which can last long, in which workers from the comparative-disadvantage sector may be unemployed.
• It predicts complete specialization: a country either imports or exports a good. In reality countries both export and import the same products (France exports and imports cars), which the model cannot explain. Imperfect competition (Ch. 9) explains this intra-industry trade.