Why the Marshall-Lerner Condition Holds

Idea

The Marshall-Lerner condition is the elasticity test behind any claim that a currency depreciation improves the balance of trade. It holds because a depreciation has a definite effect on export revenue but an elasticity-dependent effect on import expenditure, so whether the trade balance improves turns on how responsive demand is.

Mechanism

A depreciation lowers the price of exports in foreign currency and raises the price of imports in domestic currency.

• Exports. The price of exports in domestic currency is unchanged by the depreciation, while the lower foreign-currency price raises the quantity demanded. Export revenue ($X$) therefore rises — a definite increase, whatever the export elasticity.

• Imports. The higher domestic-currency price reduces the quantity of imports demanded. Whether import expenditure ($M$) rises or falls depends on elasticity: if import demand is price-elastic, quantity falls more than proportionately and expenditure falls; if price-inelastic, quantity falls less than proportionately and expenditure rises.

The balance of trade improves if the rise in export revenue outweighs any rise in import expenditure. Summing the two responsiveness conditions gives the formal threshold $PED_X + PED_M > 1$: above it, the favourable export and import effects together dominate and the trade balance improves; at or below it, they do not.

Considerations

• Short run versus long run — the J-curve. Immediately after a depreciation, demand is slow to adjust (buyers are locked into contracts and habits), so elasticities are low and the condition may fail — the trade balance can worsen before it improves as quantities respond over time, tracing a J-shaped path. (The J-curve itself is not separately examined here, but it is the standard caveat to the condition.)

• Scope. At this level the condition is to be known and applied, not derived; the algebraic proof is not required.