International Trade: formula sheet

Key formulas

Opportunity cost of good X (in units of Y)

Opportunity cost of X = units of Y given up ÷ units of X gained

With labor-hours per unit: OC of X = (hours per unit of X) ÷ (hours per unit of Y). With output per worker: OC of X = (output of Y) ÷ (output of X).

Comparative advantage rule

Country has comparative advantage in X if OC of X (home) < OC of X (partner)

Opportunity costs of the two goods are reciprocal. If a country has the lower OC in one good, the other country has it in the other, unless the OCs are equal.

Absolute advantage rule

Absolute advantage in X if fewer inputs per unit of X, or more output per unit of input

Compares productivity only. It does not decide the pattern of trade.

Terms of trade range

OC of X (low-cost country) < trade price of X in Y < OC of X (high-cost country)

Both countries gain only if the terms of trade lie strictly between the two opportunity costs.

Heckscher-Ohlin pattern

Export the good intensive in the abundant factor; import the good intensive in the scarce factor

Differences in factor endowments drive trade. Ricardian drivers are technology differences.

Terms of trade

Terms of trade = Index of export prices ÷ Index of import prices

A rise means each unit of exports buys more imports. A rise is generally favorable.

Ricardian rule

Export the good with the lower opportunity cost (comparative advantage)

Based on relative labor productivity, not absolute productivity.

Heckscher-Ohlin rule

Export goods that use the abundant factor intensively; import goods that use the scarce factor intensively

Assumes identical technology and two mobile factors, capital and labor.

Specific-factors rule

Short run: owners of the specific factor in the export sector gain; in the import-competing sector lose; mobile labor is ambiguous

Capital is fixed to its industry in the short run.

Trade measure

Trade openness = (Exports + Imports) ÷ GDP

A common indicator of how large trade is relative to the economy.

Domestic price after tariff

P(tariff) = P(world) + tariff

For a small country that takes the world price as given. A per-unit tariff is added directly.

Tariff revenue

Revenue = tariff × imports after the tariff

Use imports with the tariff in place, not free-trade imports. Imports = domestic quantity demanded − domestic quantity supplied at the new price.

Deadweight loss of a tariff

DWL = ½ × (price rise) × (increase in Qs) + ½ × (price rise) × (decrease in Qd)

Two triangles. Each has base equal to the quantity change on its side and height equal to the domestic price rise. For a non-prohibitive tariff of a small country, the price rise equals the tariff. If the tariff is prohibitive, the price rise is only up to the no-trade price. Linear curves only.

Change in national welfare, small country tariff

Δ welfare = Δ consumer surplus + Δ producer surplus + tariff revenue = −DWL

For a small country that cannot move the world price. A large importing country can gain through a terms-of-trade effect, which can offset the DWL.

Quota rent

Quota rent = (domestic price − world price) × quota quantity

Goes to licence holders, to the government if licences are auctioned, or to foreign exporters under a VER.

Export subsidy welfare effect

Δ welfare = Δ CS + Δ PS − subsidy cost

Consumers lose, producers gain, taxpayers pay. Net national welfare falls for a small country.

Free trade area

Free trade among members; each member sets its own external tariffs

Lowest level of integration. No common external tariff.

Customs union

FTA + common external tariff

The common external tariff is what separates it from an FTA.

Common market

Customs union + free movement of labor and capital

Factor mobility is the added feature.

Economic union

Common market + common economic institutions and policy coordination

Policies are harmonized, but a single currency is not required.

Monetary union

Economic union + single currency and single monetary authority

Highest level of integration.

Trade creation vs diversion

Creation: high-cost domestic supplier → lower-cost member supplier (gain). Diversion: low-cost non-member supplier → higher-cost member supplier (loss)

The net welfare effect depends on which is larger.

Balance of payments identity

Current account + Capital account + Financial account = 0

Holds in theory; in practice a statistical discrepancy remains. The capital account is usually small, so the current account is roughly the mirror image of the financial account.

Current account components

CA = Net trade in goods and services + Net primary income + Net secondary income

Net exports are the largest part for most countries.

Savings-investment identity

CA = S − I, where S = Sp + Sg

Sp is private saving and Sg is government saving (T − G). A CA deficit means I > S.

Expenditure form of the identity

CA = S − I = (Sp − I) + (T − G)

X − M equals CA only when net income and transfers are zero. Use this form to see how a fiscal deficit or an investment boom affects the current account.

Income and expenditure approach

GDP = C + I + G + (X − M)

Subtract C and G from GDP, and adjust for net income and transfers, to get national saving; then S − I = CA.

Quick revision

• Comparative advantage means the lower opportunity cost, not the lower absolute cost.
• Both countries can gain from trade even if one is more efficient at everything.
• Opportunity cost of good X is the amount of good Y given up to make one more X.
• Ricardian model: differences in technology drive trade.
• Heckscher-Ohlin model: countries export goods that use their abundant factor intensively.
• A tariff raises the domestic price, helps producers, hurts consumers and raises government revenue.
• A quota restricts quantity; the quota rent goes to licence holders (importers or foreign exporters) unless the government auctions the licences, in which case the government captures it.
• An export subsidy helps exporters and is paid for by taxpayers, and it can distort world prices.
• Trade restrictions usually cause deadweight loss for the importing country.
• Trading bloc ladder: free trade area, customs union, common market, economic union, monetary union.
• A customs union adds a common external tariff to a free trade area.
• Balance of payments: the current account balance is offset by the sum of the capital and financial accounts (plus any statistical discrepancy), so the overall balance of payments is zero.

Common mistakes

• Treating absolute advantage as the basis for trade Fix: Always convert to opportunity cost. Trade is based on comparative advantage, and a country with an absolute advantage in both goods still gains by trading.
• Dividing the wrong way when computing opportunity cost Fix: Ask what is given up. With output per worker, OC of X = output of Y ÷ output of X. With hours per unit, OC of X = hours for X ÷ hours for Y.
• Saying HO explains trade by differences in technology. Fix: Ricardian means technology differs. HO means technology is the same and endowments differ.
• Using absolute productivity to decide who exports what. Fix: Compare opportunity costs. The country exports the good where its opportunity cost is lower, even if it is less productive in both goods.
• Using free-trade imports to compute tariff revenue. Fix: Recalculate imports at the new higher price. Revenue = tariff × imports after the tariff.
• Counting tariff revenue as part of deadweight loss. Fix: Revenue is a transfer to the government. Only the two triangles are deadweight loss.
• Treating all protectionist arguments as economically valid. Fix: Remember that economists see most as weak. Infant industry and national security have some logic, but cost and permanence are concerns.
• Confusing dumping with ordinary low prices from a more efficient foreign firm. Fix: Dumping means selling below cost or below the home-market price, often to gain market power. Low prices from true efficiency are legitimate comparative advantage.
• Saying an FTA has a common external tariff. Fix: Link the common external tariff only to the customs union and above. In an FTA each member keeps its own tariffs on outsiders.
• Treating a common market as only free trade in goods. Fix: A common market adds free movement of labor and capital. Goods trade is already covered by the customs union.

Exam tips

• Questions give a productivity table and ask who has comparative advantage. Compute opportunity cost for one good only, then reason by reciprocity for the other.
• Watch the wording. 'Absolute advantage' is a direct productivity comparison, and an option may be correct on that basis but wrong on comparative advantage.
• For Ricardian versus Heckscher-Ohlin, look for the keyword: technology or labor productivity means Ricardian; capital, labor or land abundance means Heckscher-Ohlin.
• If the terms of trade are listed as options, eliminate any that sit outside the two opportunity costs. That usually leaves one choice.
• With three options and no penalty, never leave a blank. Eliminate the option that claims one country has comparative advantage in both goods.
• Questions often ask you to name the model from a short description. Learn the one clue for each.
• Winner and loser questions are common. Ask who owns the abundant or export-sector factor.
• Remember the time frame: HO is long run with mobile factors, specific factors is short run.