Importance of international trade: formula sheet

Key formulas

Opportunity cost of good X

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

The country with the lower opportunity cost of a good should specialise in it.

Terms of trade range

Own opportunity cost of X < price of X in units of Y < partner's opportunity cost of X

Both countries gain only if the trade price lies strictly between their opportunity costs.

Average cost under scale economies

Average cost = total cost ÷ output

Economies of scale mean average cost falls as output rises over the relevant range.

Gain from trade

Gain = consumption after trade − consumption without trade

Measured for the same country and in the same units.

Opportunity cost of good X (in terms of Y)

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

With a production table, divide the output of Y by the output of X when all resources go to one good. Assumes a constant trade-off, as in the simple Ricardian model.

Opportunity cost from labour hours

Opportunity cost of X = hours per unit of X ÷ hours per unit of Y

Use when the data are hours (or other inputs) needed per unit. The lower the ratio, the stronger the comparative advantage.

Absolute advantage test

Absolute advantage in X if hours per unit of X are lower, or output of X per hour is higher

Compares raw productivity only. It does not decide who should specialise.

Comparative advantage test

Comparative advantage in X if opportunity cost of X is lower

Compare opportunity costs, not outputs.

Mutually beneficial trade range

Lower opportunity cost of X < trade price of X < higher opportunity cost of X

Price is measured in units of Y per unit of X. Inside this range both countries gain.

Net barter terms of trade

ToT index = (Export price index ÷ Import price index) × 100

Both indices must share the same base year. Above 100 is an improvement, below 100 a deterioration.

Balance of trade

Balance of trade = Value of exports − Value of imports

Use goods only unless the question says goods and services. Positive is surplus, negative is deficit.

Change in terms of trade

New ToT = Old ToT × (1 + export price change) ÷ (1 + import price change)

Use decimals for the changes, for example 10% = 0.10.

Current account

Current account = Trade in goods + Trade in services + Primary income + Secondary income

Each item is net: receipts minus payments.

Balance of payments identity

Current account + Capital account + Financial account + Net errors and omissions = 0

This follows the usual sign convention where a financial account inflow of funds is shown as net borrowing. Check the sign convention the question uses.

Domestic price under a tariff

P_tariff = P_world + t (specific tariff); P_tariff = P_world × (1 + t%) (ad valorem)

Applies to a small country that cannot change the world price.

Imports

Imports = Qd − Qs at the given price

Compare imports at the world price and at the tariff-inclusive price.

Tariff revenue

Revenue = t × (Qd − Qs) at the tariff price

Use imports after the tariff, not before.

Deadweight loss from a tariff

DWL = ½ × t × (Qs_tariff − Qs_world) + ½ × t × (Qd_world − Qd_tariff)

Two triangles. This works when supply and demand are straight lines.

Net welfare effect of a tariff (small country)

Net change = −(consumer surplus loss) + producer surplus gain + tariff revenue = −DWL

Domestic welfare falls in this case.

Quota rent

Quota rent = (P_domestic − P_world) × quota quantity

Equals the tariff revenue rectangle if the quota matches the post-tariff import level. It goes to licence holders unless the government auctions licences.

Exchange rate (direct quote)

Home currency price of 1 unit of foreign currency = ₹ per $

State which currency is the base. ₹84/$ means $1 costs ₹84.

Converting prices

Foreign price = Home price ÷ Exchange rate (₹ per foreign unit)

Use this to find what an export costs a foreign buyer.

Percentage change in currency

% change = (New rate − Old rate) ÷ Old rate × 100

With a ₹ per $ quote, a positive change means the rupee has depreciated.

Marshall-Lerner condition

Sum of price elasticities of demand for exports and imports > 1

Roughly, a depreciation improves the trade balance only if this holds, starting from balanced trade.

Trade effect of depreciation

Depreciation → exports cheaper abroad, imports dearer at home

Appreciation has the opposite effect.

Quick revision

• Trade lets countries specialise, enjoy larger markets, wider choice and often lower prices.
• Absolute advantage means producing a good with fewer resources than another country.
• Comparative advantage means producing a good at a lower opportunity cost than another country.
• Trade can be beneficial even if one country has an absolute advantage in every good.
• Opportunity cost of good X in terms of Y is the amount of Y given up to make one more unit of X.
• Terms of trade compare the price of exports with the price of imports; a rise means each export buys more imports.
• A trade balance is exports minus imports of goods (and sometimes services, depending on definition); state which you use.
• Tariffs are taxes on imports; quotas limit the quantity of imports; subsidies support domestic producers.
• Protection helps some domestic producers but usually raises prices for consumers and can invite retaliation.
• Arguments for protection include infant industries and national security; always weigh them against the costs.
• A weaker currency makes exports cheaper abroad and imports dearer at home, other things equal.
• Trading blocs reduce barriers between members, which can create trade among them but may divert trade from outsiders.

Common mistakes

• Listing gains with no explanation. Fix: Write cause, effect and result for each gain in one or two sentences.
• Using absolute output instead of opportunity cost to choose specialisation. Fix: Compare units of the other good given up. Specialise where that is lower.
• Treating absolute advantage as the basis for specialisation. Fix: Specialise by comparative advantage. A country best at both goods still gains by trading.
• Dividing in the wrong direction when finding opportunity cost. Fix: Opportunity cost of X = Y given up ÷ X gained. Check units: it should read 'units of Y per unit of X'.
• Inverting the ratio, using import prices over export prices. Fix: Remember: exports on top. Higher export prices relative to import prices means an improvement.
• Saying that improved terms of trade always improve the trade balance. Fix: State that the effect depends on how quantities respond. Higher export prices may reduce export volumes.
• Saying a tariff and a quota always have identical effects. Fix: State that they match on price and quantity only if set equivalently. The difference is who gets the rectangle, and effects differ when demand or supply shifts or the market is not competitive.
• Calculating tariff revenue on pre-tariff imports. Fix: Revenue = t × imports after the tariff, which is Qd − Qs at the tariff-inclusive price.
• Saying a weaker currency always improves the trade balance. Fix: Mention elasticities and the Marshall-Lerner condition. Add that imports cost more and the effect can take time (J-curve).
• Mixing up appreciation and depreciation when the quote is ₹ per $. Fix: With ₹ per $, a higher number means each dollar costs more rupees, so the rupee has fallen. Check by asking what one unit of the home currency buys.

Exam tips

• In 'explain' questions, write each gain as a short chain of reasoning, not a single word.
• For numerical questions, always compute opportunity cost and show it, even if the MCQ seems to need only the answer.
• Check that any trade price lies strictly between the two opportunity costs.
• In 'discuss' questions, add at least one cost or limit to earn the evaluation marks.
• Use the exact terms: specialisation, economies of scale, opportunity cost, larger market.
• Always write the opportunity cost calculation with units, such as 'cloth per wheat'. Examiners award marks for method.
• Distinguish clearly between absolute and comparative advantage in your answer. Many questions test only this difference.
• In MCQs, look for options that confuse the two. A country with the higher output need not have the lower opportunity cost.