Terms of trade and offer curves

The terms of trade are the prices at which a country’s exports exchange for its imports (Hyderabad 2014; JNU 2010). The usual measure is the commodity or net barter terms of trade: the price index of exports divided by the price index of imports (Hyderabad 2013, 2016, 2018). When it rises, the terms of trade have improved: each unit of exports buys more imports.

With two countries, one’s exports are the other’s imports, so the partner’s terms of trade are the inverse of the home country’s. UGC NET 2023 pairs that true statement with a false one that defines the terms of trade with the cost of exports instead of their price.

UGC NET 2024 matched these names. The income terms of trade can improve while the net barter terms worsen, if export volumes grow fast enough: Lesson 7 uses this.

Ricardo explained the supply side: costs set the band. J. S. Mill added the demand side in his Principles of Political Economy (1848), from an essay of 1844. Each country’s demand for the other’s good is a demand to be paid for with its own exports. Mill called this reciprocal demand. The terms of trade settle where the value of each country’s exports equals the value of its imports, so that what England wants to sell for wine matches what Portugal wants to buy with wine.

A reciprocal demand schedule lists the quantities of exports a country will offer for various quantities of imports at different terms of trade (Hyderabad 2013). It has a clear consequence: the country whose demand for the other’s good is stronger gets the worse terms, because it has to bid more to get what it wants. A small country trading with a large one often gets terms near the large country’s autarky price and so takes most of the gains: the importance of being unimportant.

Alfred Marshall drew Mill’s idea as a curve in 1879, and F. Y. Edgeworth developed it. A country’s offer curve shows how much of its export good it is willing to give for each amount of its import good, at every possible terms of trade (CUET 2025). It is built from the country’s production frontier and its tastes. Three things to know about its shape:

• It starts at the origin along the country’s autarky price: at that price it doesn’t want to trade.
• It lies on the side of that ray where the terms of trade are better than autarky.
• It bends toward the axis of the country’s import good. Each extra unit of imports is worth less, and each extra unit of exports costs more, so the country demands better and better terms to trade more.

Put two offer curves together. Where they cross, what one country offers is exactly what the other wants. The ray from the origin through that point is the equilibrium terms of trade (JNU 2020; Hyderabad 2020).

Elasticity. The offer curve also gives the elasticity of the country’s demand for imports. Draw the tangent at a point; let it meet the export axis at T, and drop a vertical from the point to C. Then the elasticity is OC/OT. Tick the box in the lab and compare it with the number calculated directly. Where the curve is vertical, T and C coincide and the elasticity is 1; where it bends back, demand is inelastic.

A tariff makes a country less willing to trade at every world price, so its offer curve rotates toward the axis of its import good (UGC NET 2023). Lesson 5 returns to tariffs.

Ricardo’s argument used labour values, which fail once there is more than one factor. Gottfried Haberler’s answer, in 1930, was to measure cost by the other good given up: the opportunity cost theory. Its tool is the production possibility curve (CUET 2022), and its slope is the opportunity cost. Nothing in Lesson 2 changes, but the theory no longer needs the labour theory of value. UGC NET 2024 sorted the contributors this way: Ricardo the supply side, Marshall and Edgeworth the demand side, Haberler opportunity cost.

Haberler also allowed the opportunity cost to rise as a country makes more of a good. Resources aren’t all equally good at everything: factors aren’t homogeneous, and goods don’t use them in the same fixed proportions. To make more wheat a country must use land and labour less and less suited to wheat (Hyderabad 2019). The frontier then bows outward: it is concave to the origin.

JNU asked the specialisation row twice (2018 and 2021). And because demand now helps set autarky prices, two countries with identical concave frontiers can still trade if their tastes differ: each exports the good it likes less (JNU 2020).

Add tastes, drawn as community indifference curves, to a concave frontier. In autarky the country produces and consumes where an indifference curve just touches the frontier, and the slope there is the autarky price. Open trade at a different world price, and two things happen:

• Production moves along the frontier until its slope equals the world price, toward the good the country has a comparative advantage in. This is the gain from specialisation.
• Consumption moves along the world price line to a higher indifference curve. This is the gain from exchange, and it exists even if production can’t change at all.

The right triangle between the production and consumption points, with the price line as its hypotenuse, is the trade triangle. Its sides are exports and imports, and since both are valued at the same prices, the value of exports equals the value of imports (Hyderabad 2019).

With a convex production set and convex preferences, some trade is always better than no trade for a country of any size (JNU 2015). The gains from trade are the net benefit to the agents involved, so they can be measured as consumer plus producer surplus (UGC NET 2024): not a gross benefit, and not one surplus minus the other.