How to Apply the Marshall-Lerner Condition
Add the absolute price elasticities of export demand and import demand: if the sum is greater than 1, a currency depreciation improves the trade balance.
The Marshall-Lerner Condition formula
Calculator
Enter both demand elasticities and the size of a depreciation to test the condition and size the trade balance change.
How strongly foreign buyers respond to cheaper exports, entered as a positive number.
How strongly domestic buyers respond to costlier imports, entered as a positive number.
Percent fall in the value of the domestic currency.
The condition is derived from balanced trade, so both sides start at this value.
The two responses add to 1.4, which clears 1, so quantities move enough for a cheaper currency to help the balance.
- Marshall-Lerner verdict
- Condition met
- Change in export value
- 8%
- Change in import value
- 4%
- Trade balance after the depreciation
- $20B
Above 1 the depreciation improves the trade balance, below 1 it makes the balance worse, and at exactly 1 the balance does not move.
Export prices abroad fall by the depreciation, so export value rises 8%.
Import prices rise the full 10% while volume falls 6%, leaving import spending 4% higher.
Exports of $540B against imports of $520B leave a balance of $20B, measured from a starting point of balanced trade.
How to calculate Marshall-Lerner Condition, step by step
- 1Take both elasticities as positive numbers. Price elasticity of demand is negative by definition, so strip the signs before adding. Adding the raw negative values would make the test against 1 meaningless.
- 2Add them and compare with 1. If the sum of the two absolute elasticities is greater than 1, quantities respond enough for a cheaper currency to improve the trade balance.
- 3Trace the export side. A depreciation cuts the foreign-currency price of exports, so export volume and export value both rise by the export elasticity times the size of the depreciation.
- 4Trace the import side. Imports cost more in domestic currency, so their price rises by the full depreciation while volume falls by the import elasticity times it. The value change is what is left over, (1 − |εm|) times the depreciation.
- 5Size the change in the balance. Starting from balanced trade, the balance improves by the trade value times the depreciation times the amount by which the elasticity sum clears 1.
- 6Allow time for the response. Elasticities are small in the first months and larger after a year, which is why a balance often worsens before it improves, tracing the J-curve.
Worked example: Marshall-Lerner Condition
A currency depreciates 10%. Export demand has an elasticity of 0.8 and import demand 0.6, so the sum is 0.8 + 0.6 = 1.4, above 1, and the condition is met. With exports and imports both starting at $500 billion, export value rises by 0.8 × 10 = 8% to $540 billion. Import prices rise the full 10% while import volume falls 0.6 × 10 = 6%, so import value rises by (1 − 0.6) × 10 = 4% to $520 billion. The trade balance moves from zero to 540 − 520 = +$20 billion, which matches 500 × 0.10 × (1.4 − 1) = $20 billion.
Marshall-Lerner Condition questions
Why do you use absolute values of the elasticities?
Price elasticity of demand is negative, so adding the raw figures would give a number below zero and the comparison with 1 would never work. The condition asks how large the two quantity responses are, which is what the absolute values measure.
What is the J-curve?
Just after a depreciation, contracts and buying habits hold quantities almost fixed, so the elasticity sum sits below 1 and the trade balance worsens. Over the following months buyers switch suppliers, the elasticities rise past the threshold, and the balance improves, tracing a J shape.
Does the condition assume trade starts balanced?
The simple form does. It is derived from a starting point where exports equal imports. If the country already runs a deficit, the export response works from a smaller base, so the elasticities have to be larger than the plain test suggests.
Why can a weaker currency fail to fix a trade deficit?
Because value equals price times quantity. If buyers barely change quantities, the higher price of imports outweighs the extra export volume and spending on imports rises, so the balance gets worse rather than better.
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