The J-Curve and Marshall–Lerner Condition: Why Trade Can Worsen First

Let E mean units of home currency H needed to buy one unit of foreign currency F.

If E rises from 100 H/F to 110 H/F, the home currency has depreciated: it takes more H to buy the same F.

With the reverse quote, F per H, the number falls instead.

State the quote direction before saying a currency “rose” or “fell.”

Here the trade balance is the value of exports minus the value of imports, measured in H over a stated period.

In a simple goods example, B_H = export receipts in H − import payments in H.

A published balance may cover goods alone or goods and services, so check its definition.

The trade balance is not the full current account, which also includes primary income and transfers. {source:imfWeo2007ExchangeRatesExternalAdjustment}

A home-currency balance is a nominal value measure.

It combines prices and quantities after amounts are converted into H.

A balance measured in another currency, an export-minus-import volume index, and a real effective exchange-rate index answer different questions.

Terms of trade and the trade balance explains why relative prices and recorded trade values can move differently.

The J-curve is a name for one possible time path after a depreciation.

If the home-currency trade balance first falls, then later rises, the plotted path can resemble the letter J.

The initial downturn can happen while contract prices and order quantities are slow to change; a later improvement is possible if relative prices lead buyers to import less and foreign customers to buy more exports.

The shape is not a law, a forecast, or a policy prescription.

A depreciation can have a different short-run path, no visible J, or no eventual improvement.

The exchange rate may move alongside demand, supply, commodity prices, financing conditions, or other shocks that affect trade.

An observed sequence alone does not show that depreciation caused it. {source:imfWp16107ExternalAdjustmentOilExporters}

The Marshall–Lerner condition asks a different question: in a simplified model, are the import and export quantity responses to relative prices strong enough to offset the price effect on the home-currency trade balance?

It is an elasticity condition, not the name of the time path.

A country could meet a long-run elasticity condition and still see the balance worsen first if quantities respond with a lag.

An exchange rate can change the home-currency price of a foreign-currency invoice as soon as it is converted.

But goods already ordered, shipped, or covered by contracts may not be repriced or replaced right away.

Import volumes can therefore remain near their earlier level even as the amount paid in H changes.

Export volume also takes time to respond.

Buyers abroad may need to find a supplier, renegotiate a contract, or adjust production plans.

Exporters may face capacity limits or rely on imported materials whose home-currency costs have risen.

A more competitive export price does not instantly create more supply.

Behar and Fouejieu’s IMF working paper describes price effects as immediate and potential quantity effects as typically delayed. {source:imfWp16107ExternalAdjustmentOilExporters}

A Federal Reserve study finds that trade-flow responsiveness and exchange-rate pass-through differ between the United States and Japan. {source:fedIfdp456ExchangeRatesPricesExternalAdjustmentUsJapan}

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The following numbers are invented to make the accounting visible.

They are not observed data or a forecast.

Assume the home currency is H, the foreign currency is F, and E is H per F.

Also assume the balance starts at zero, export prices are sticky in H, imports are invoiced in F with full conversion into H, and quantities do not change immediately.

At the starting quote of 100 H/F, suppose 100 export units sell for H10 each.

Export receipts are H1,000.

Suppose 100 import units cost F0.10 each; at E = 100 H/F, each costs H10, so the import bill is also H1,000.

The home-currency balance is H0.

Now E rises by 10%, to 110 H/F.

In the first period, keep the assumed quantities unchanged.

Export receipts stay at 100 × H10 = H1,000.

The foreign-currency import invoice remains F0.10 per unit, but conversion raises its home-currency price to H11.

The import bill becomes 100 × H11 = H1,100, so the balance falls to −H100.

For a later, separately assumed adjustment, let exports rise to 120 units and imports fall to 90, holding those home-currency unit prices at H10 and H11.

Export receipts are H1,200 and the import bill is H990, so the balance is now +H210.

The path H0 → −H100 → +H210 illustrates a possible J-curve.

Its result depends on the stated pricing and volume assumptions; it is not a typical or guaranteed response.

The earlier J-curve example assumed that converting a foreign-currency import invoice fully changed its price in H.

Now suppose, purely for illustration, that only 40% of the exchange-rate change reaches the import unit price in the first period.

The quote rises from 100 H/F to 110 H/F, a 10% increase, but assume the H10 import price reflects only 40% of that change.

Under this simplified linear calculation, the import price becomes H10 × (1 + 0.40 × 0.10) = H10.40.

If the assumed quantity stays at 100 units, the import bill is H1,040 against export receipts of H1,000, so the balance is −H40.

That initial decline is smaller than the −H100 in the full-conversion example above.

The 40% rate is invented for arithmetic and is not an observed estimate.

Here, pass-through means the exchange-rate change reaching the border import price; it does not mean importer costs have passed through to retail prices or consumer inflation.

Different pass-through changes the relative prices buyers face, so the elasticity sum from a full-pass-through model cannot stand alone as a test of the trade-balance response. {source:imfWeo2007ExchangeRatesExternalAdjustment}

In the traditional simplified case, the trade balance starts at zero, exchange-rate changes pass fully through to import prices at home and abroad, and elasticities are measured against relative prices.

Under those assumptions, a depreciation improves the nominal home-currency trade balance if the absolute price elasticity of export demand plus the absolute price elasticity of import demand exceeds one: |ε_X| + |ε_M| > 1.

Here, the elasticities measure how strongly export and import volumes respond to relative prices.

With incomplete pass-through, the simple sum-above-one threshold is not sufficient: the relevant condition also depends on how exchange-rate changes affect import and export prices and the terms of trade. {source:imfWeo2007ExchangeRatesExternalAdjustment}

That threshold is not a universal rule for every exchange-rate move.

If trade starts in deficit or surplus, export and import values are not equal, so their starting weights matter; the simple sum-above-one test no longer applies by itself.

And even when the long-run condition holds, it does not specify how many months or quarters quantity adjustment will take.

Behar and Fouejieu’s working paper emphasizes the competing price and volume effects and notes that empirical J-curve findings differ across the studies it reviews. {source:imfWp16107ExternalAdjustmentOilExporters}

A price elasticity describes how much quantity demanded responds, in percentage terms, when the price buyers face changes by 1%.

When a price increase reduces quantity demanded, that elasticity is negative, which is why the traditional formula adds absolute values.

An elasticity with an absolute value of 0.7 means that a 10% price decline corresponds to roughly 7% more quantity near the starting point.

That is a local approximation; it does not say a large price change produces exactly the same proportional volume response.

For an invented illustration, suppose the export-demand elasticity has an absolute value of 0.7 and the import-demand elasticity is 0.6.

Their sum is 1.3, but these example values are not observations and do not predict an improvement for any country.

The sum-above-one result applies only alongside the traditional assumptions, including an initially balanced trade position and full pass-through to relevant import prices at home and abroad.

Elasticities can differ by product coverage and time horizon.

Buyers may have few alternatives while contracts are fixed, then respond more after they can switch suppliers or change sourcing.

A measured unit-value change can also reflect a shift in the products traded, not just a price change for the same product.

Check the sample, period, and price definition before treating an estimated elasticity as a stable country characteristic. {source:imfWeo2007ExchangeRatesExternalAdjustment}

For a simple goods account, export value is the home-currency unit price multiplied by export quantity; import value is calculated the same way.

A change in the trade balance therefore combines changes in export and import prices with changes in traded quantities.

Suppose, in an invented example, an import unit price rises from H100 to H104 while quantity falls from 100 units to 98.

The new bill is H104 × 98 = H10,192, which is 1.92% above the previous H10,000.

This arithmetic shows how a higher unit price and lower quantity can partly offset; it does not estimate an actual demand response.

After an exchange-rate move, an import bill may rise less if quantity falls, or the increase may arrive later if the border price adjusts after a delay.

For exports, distinguish the price seen by foreign buyers, the receipt converted into H, and the number of units sold.

The H value of export receipts can change with conversion even if the foreign-currency selling price does not, so revenue alone does not reveal how foreign demand responded.

This multiplication is an accounting decomposition, not a way to identify causes.

Compare matched price and volume measures with the same currency, product coverage, and period before attributing a balance change to either component. {source:imfWeo2007ExchangeRatesExternalAdjustment}

Pass-through and invoice currency matter. If exporters keep a foreign-currency price unchanged, home-currency import prices may rise with E.

If prices are sticky in the buyer’s currency, or a supplier absorbs part of the change in its margin, the local price response can be smaller or delayed.

An unchanged exporter-currency price is producer-currency pricing; a price held fixed in the buyer’s currency is buyer-currency (local-currency) pricing.

“The currency depreciated 10%” therefore does not mean every import and export price changes by exactly 10%. {source:imfWeo2007ExchangeRatesExternalAdjustment} {source:fedIfdp456ExchangeRatesPricesExternalAdjustmentUsJapan}

Household income and production costs also matter.

A depreciation can reduce households’ real purchasing power as imports become more expensive. {source:imfWp16107ExternalAdjustmentOilExporters}

Exporters that use imported fuel, machinery, or components may face higher costs, which can limit their ability to expand output. {source:imfWp16107ExternalAdjustmentOilExporters}

Weak export-supply response can prevent the volume effect assumed in a textbook sketch. {source:imfWp16107ExternalAdjustmentOilExporters}

Fiscal policy is a separate channel: government spending can also affect imports and external balances, especially in oil-exporting economies.

Behar and Fouejieu analyze this fiscal channel separately from the exchange-rate response. {source:imfWp16107ExternalAdjustmentOilExporters}

The initial position and product mix matter. A country that imports essential inputs or has few domestic substitutes may reduce import quantities only slightly.

An exporter with unused capacity may expand sales more easily than one near capacity.

Commodity pricing, long contracts, and the split between goods and services can all change the measured balance.

There is no single elasticity number that settles every case.

The real effective exchange rate is a trade-weighted measure adjusted for relative prices, not a bilateral nominal quote.

Use it for the question it answers, and keep it separate from the home-currency trade balance.

The current account and trade balance explains the wider external-account boundary.

NEER and REER explains the effective-rate indexes. {source:fedIfdp456ExchangeRatesPricesExternalAdjustmentUsJapan}

First line up the date of the exchange-rate move with the periods covered by the price and trade-volume statistics.

A border import-price index moving before import or export volumes can fit a possible adjustment path, but it does not prove that path caused the change.

Monthly exchange rates compared with quarterly trade data can make contract dates, shipping times, or survey windows look like an economic lag.

Check the frequency, reference period, seasonal adjustment, and product coverage, and compare like with like.

Trade values alone cannot separate price effects from volume effects.

Where available, review home-currency import and export unit prices, volume indexes, invoice currency, coverage, and later revisions together.

Unit values may change because the mix of goods changed, so they are not always clean prices for an unchanged product.

A nominal balance and a volume index can move in different directions without contradiction if their definitions or observation dates differ. {source:imfWp16107ExternalAdjustmentOilExporters} {source:fedIfdp456ExchangeRatesPricesExternalAdjustmentUsJapan}

Even after checking the time order, causality needs separate evidence.

Domestic and foreign demand, commodity costs, financing conditions, or other shocks can change alongside the exchange rate.

A J-shaped chart describes an observed sequence; without a counterfactual comparison, it does not identify the exchange-rate effect.

First, identify the exchange-rate quote and direction: does a higher number mean H has weakened or strengthened?

Then identify the balance’s currency, coverage, and period.

A statement about the local-currency value of goods trade is not automatically a statement about export and import volumes or the full current account.

Next, check prices and quantities separately.

Look for the currency used on invoices, the extent of exchange-rate pass-through, the timing of contracts, import and export volumes, and any imported inputs.

Finally, distinguish a possible short-run J-curve from the assumptions behind the Marshall–Lerner condition.

Report the observed data and sample period; do not turn either concept into a forecast of what a future depreciation will do.