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Comparative advantage
Why a country better at everything still needs the others — proved in figures.
opportunity cost = what is sacrificed ÷ what is obtainedProblem / motivation
Imagine two countries. The first produces everything better than the second: more wheat, more wine, with the same resources. Has it the slightest interest in trading with so mediocre a partner?
The answer — yes, and both gain — is the most counter-intuitive result in economics, formulated by David Ricardo in 1817. It offends common sense, because common sense compares LEVELS: “I produce 1,200 tonnes, you produce 200, you have nothing to bring me”. But the right question is not “who produces most?” but “what must each of them GIVE UP in order to produce?”. Those two questions have different answers, and that is the whole subject.
This course will not settle for asserting it. It will set out a table of figures, compute who should produce what, deduce the price at which trade becomes possible — and compare, for each of the two countries, what it consumes BEFORE and AFTER. You will see both gains in figures, and you will also see under what condition they disappear.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Here are our two countries, with all their resources for a year. France can produce 1,200 tonnes of wheat, OR 300 hectolitres of wine. Portugal: 200 tonnes of wheat, OR 200 hectolitres of wine. The “OR” is essential: these are two extremes, and the country picks a point between them. Look at the levels first: 1,200 against 200 for wheat, 300 against 200 for wine — **France is better at BOTH**. This is exactly the case announced by the title, the one where common sense says “Portugal has nothing to offer”. France is said to have the ABSOLUTE advantage in both goods. But absolute advantage answers “who produces most?”, and that is not the question that decides trade.
The right question is: what has to be GIVEN UP to produce one more unit? In France, devoting resources to 1 hectolitre of wine means giving up wheat: since 300 hl take the same effort as 1,200 t, one hectolitre costs 1,200/300 = 4 tonnes of wheat. In Portugal, 200 hl take as much as 200 t, so a hectolitre costs only 1 tonne. There is OPPORTUNITY COST: what is sacrificed divided by what is obtained. Now turn the computation round: in France a tonne of wheat costs 300/1,200 = 0.25 hectolitre; in Portugal, 1 hectolitre. And observe: 4 × 0.25 = 1, and 1 × 1 = 1. **The two opportunity costs of one country are always inverses of each other.** Now let's compare the two countries, and follow the flip. Portugal sacrifices less than France for a hectolitre of wine (1 against 4). But within EACH country, the cost of wheat is the inverse of the cost of wine: so the Portuguese cost of wheat is 1/1 = 1, and the French one 1/4 = 0.25. In taking the inverse, the order has flipped — whoever was ahead on wine falls behind on wheat. This is the theorem that answers the poll: **a country cannot have the lowest cost in both goods**, because the two ratios flip together. Comparative advantage is NECESSARILY shared. One instructive exception: if the two countries have exactly the same opportunity costs, neither gives up less than the other — there is then no comparative advantage, and trade can bring nothing. What creates the gain is the DIFFERENCE in sacrifices, never the difference in production levels.
Let's compare: for one hectolitre of wine, France sacrifices 4 tonnes of wheat, Portugal only 1. Portugal gives up less: it has the comparative advantage in WINE, and France in wheat (0.25 hl against 1 hl per tonne). So each specialises where it gives up least. That leaves the exchange price to be fixed, and it is not decreed either — it is DEDUCED. Portugal will only part with a hectolitre if it is given more than one tonne of wheat, otherwise it would do better to produce that wheat itself. France will only buy a hectolitre if it pays less than 4 tonnes, for the same reason. The price must therefore fall **between 1 and 4 tonnes per hectolitre**: that is the range, and it is not an assumption, it is the consequence of each side's refusal. Outside it, one of the two prefers self-sufficiency and no trade takes place. This international price has a name worth knowing: the TERMS OF TRADE — the ratio at which goods actually exchange between the two countries, and therefore what decides how the gain is split.
There remains the beginner's question, and it is the right one: why does France, better at everything, need this mediocre partner? Because producing its own wine COSTS it wheat — 4 tonnes per hectolitre, a price it pays by giving up what it does best. By buying that same hectolitre from Portugal for 2 tonnes, it gets it at half price. Portugal does not bring it productivity, which is low; it brings it wine that is cheaper IN WHEAT than its own. There is the whole mystery: what is exchanged is not performance, it is sacrifices. Click each term:
Solving / calculation
Let's work through the complete proof, figure by figure. The numbers are a toy example — chosen to come out neatly and to be computed in your head — but the reasoning is exactly that of Ricardo's model.
- The capacities, and the observation that makes the paradox
France: 1,200 t OR 300 hl · Portugal: 200 t OR 200 hlFrance is better at BOTH - The opportunity costs of wine
France: 1,200/300 · Portugal: 200/2004 t against 1 t per hectolitre - The opportunity costs of wheat (the inverses)
France: 300/1,200 · Portugal: 200/2000.25 hl against 1 hl per tonne - Who specialises in what (whoever gives up least)
wine: 1 < 4 → Portugal · wheat: 0.25 < 1 → Franceone good each - The price range for a hectolitre, deduced from the refusals
more than 1 t (else Portugal refuses), less than 4 t (else France refuses)between 1 and 4 t — let's take 2 t - Before: each produces for itself (one chosen split, among others)
France 3/4 of its resources to wheat (900 t) and 1/4 to wine (75 hl) · Portugal half and half (100 t + 100 hl)world: 1,000 t and 175 hl - After: each makes only its own good
France 1,200 t of wheat · Portugal 200 hl of wineworld: 1,200 t and 200 hl - The exchange, at a price of 2 t per hectolitre
France parts with 200 t and receives 100 hlFrance 1,000 t + 100 hl · Portugal 200 t + 100 hl - ⭐ The gain, country by country
France: 900 → 1,000 t and 75 → 100 hl · Portugal: 100 → 200 t, wine unchangedBOTH consume more
The proof is complete: France consumes 100 tonnes and 25 hectolitres more than in self-sufficiency, Portugal 100 tonnes more without a drop less wine. Nobody worked harder — only the DIVISION of tasks changed. Three cautions, though. (1) The price mattered: at 2 tonnes per hectolitre both gain, but at 0.5 Portugal would refuse, and at 5 France would produce its own wine. The gain exists, its SHARING is negotiated, and the position within the range is a balance of power. (2) Here, the world produces more of both goods — but that follows from the starting split chosen. Redo the computation with a France at half and half: it would produce 600 t and 150 hl, so the world would start from 250 hl of wine… only to produce 200 after specialisation. World wine would FALL. The solid proof is the one about consumption after trade, never a simple “more is produced”. (3) The gain is the COUNTRIES' one; inside them, the French winegrower whose estate closes does not see it go by (interpretation, point 2).
OC = what is sacrificed / what is obtained; trade is possible if the price is inside the rangeSet the two countries' capacities and the exchange price. The simulator deduces everything else: the opportunity costs, who should specialise in what, the acceptable price range — and whether the price you chose really lets both gain. Try pushing it outside the range: you will see who refuses.
Economic interpretation
Three readings so as not to over-interpret: what the model really predicts, who gains inside the country, and what makes a comparative advantage move.
Ricardo predicts COMPLETE specialisation — each country abandoning one good entirely — and trade between very different countries. Reality is far from that. Most trade between developed countries is INTRA-INDUSTRY: France sells cars to Germany, which sells cars back, and the two countries are very much alike. That kind of trade is explained by the variety consumers want and by economies of scale, not by opportunity costs (the work of Paul Krugman, Nobel prize 2008). The Ricardian model remains the right tool for understanding WHY trade can benefit both sides; it is not a description of contemporary trade.
The proof is about the consumption of a COUNTRY, treated as a single person. Inside it, specialisation closes some workshops and opens others: in our example, French winegrowers must become cereal farmers. On paper that is instantaneous and costless — that is the full employment assumption. In practice, reconversion takes years, does not concern the same people or the same regions, and an overall gain can perfectly well coexist with lasting local losses. That is why a national gain never excuses failing to look at who pays for the adjustment, nor failing to organise compensation.
Nothing in the model says where opportunity costs come from: they are given. Yet they depend on skills, on equipment, on research — all things that are shaped. South Korea, specialised in textiles in the 1960s, dominates semiconductors today: its comparative advantage was built, not inherited. France, for its part, draws its exports from aerospace while its agri-food balance falls to its lowest level since at least 2000 — two specialisations on the move (course “The trade balance”). Finally, these costs in kind become prices in euros through wages and the exchange rate: a country with low productivity stays competitive if its wages or its currency are weaker (course “What is an exchange rate?”).
Limits / critiques
Exercises
A country can produce 800 t of wheat OR 200 hl of wine. What is the opportunity cost of one hectolitre of wine (in tonnes of wheat)?
Alpha can produce 600 t of wheat OR 300 hl of wine; Beta, 100 t OR 200 hl. Which should specialise in wine?
Same situation (costs of 2 t and 0.5 t per hectolitre). A price of 0.4 tonne per hectolitre is proposed. What happens?
True or false: two countries with identical opportunity costs still have an interest in specialising and trading.
In the same country (800 t OR 200 hl), what is the opportunity cost of one tonne of wheat (in hectolitres of wine)?
The opportunity costs of one hectolitre of wine are 2 t of wheat in one country and 0.5 t in the other. What is the maximum price, in tonnes of wheat, at which a hectolitre can be exchanged?
Back to the course: France specialises (1,200 t of wheat) and parts with 200 t in exchange for 100 hl of wine. How many tonnes of wheat does it then consume (in t)?
True or false: since trade makes both countries gain, every inhabitant of each country gains too.