# Marshall-Lerner condition

The Marshall-Lerner condition is an important condition that determines whether or not a exchange rate depreciation will cause the balance of trade to improve or to deteriorate. The condition was proposed by Alfred Marshall and Abba Lerner. The Marshall-Lerner condition states that

the sum of the long-term export demand elasticity and the import demand elasticity should be larger than one for the balance of trade to improve.

On this page, we discuss the Marshall-Lerner condition in detail. The Marshall-Lerner condition is an important consideration that has a strong impact on the net effect of a currency depreciation on exports and imports.

## Marshall-Lerner condition definition

To explain the concept, consider a country whose currency depreciates. Initially, the balance of trade will deteriorate. This is because the demand for imports is inelastic, meaning that the countriesâ€™ citizens and companies do not import less at first. In the long-run, though, people and companies will switch to other products that are cheaper than the ones they imported in the past. Similarly, exports also tend to be inelastic, with foreigners only gradually switching to the products that became cheaper due to the devaluation. This slow change in the demand is the quantity effect.

At the same time, there is also a negative cost effect. That is, the relative cost of the imports went up.

Thus, whether the net effect on the balance of trade will be positive or negative, depends on the net result of the quantity (we import less) and the cost effect (imports are more expensive).

## Marshall-Lerner condition formula

Formally, the Marshall-lerner condition states that for a currency devaluation to improve the balance of trade, the sum of the price elasticities of imports and demands must be greater than one. In particular, the absolute value has to be greater than one.

The classic Marshall-Lerner condition states that:

Another formulation is the generalised Marshall-Lerner condition

were Wx is het proportion of trade that is exported, Wm is the proportion of total trade that is imported, is the price elasticity of demand for export, and is the price elasticity of the demand for imports. Note that the latter formula reduces to the former when Wx = Wm.

## Marshall-Lerner condition interpretation

The ML condition states that a currency depreciation will lead to a greater improvement in the balance of trade when either imports or export demand is elastic (>1). In particular, a depreciation will have a bigger impact if

• there are close substitutes for the goods,
• the goods are a large part of consumer spending,
• or the goods are luxury good.

## Summary

Unlike what most people think, the balance of trade does not necessarily improve after and exchange rate depreciation or devaluation. The Marshall-Lerner conditions show that a depreciation will only improve the balance of trade when the demand for the goods imported or exported are sensitive to price changes.