Marshall-Lerner Condition

Can the depreciation of the currency increase net exports? This will depend on the price elasticities of demand (PED) for exports (PED_X )and imports (PED_M). When the currency is depreciated, exports decline in the foreign currency price while imports increase in the domestic currency price. For net exports to increase, and for the trade balance of the exporting country to improve, the absolute value of the price elasticity of demand for exports + the absolute value of the price elasticity of demand for imports must exceed 1, which is represented by the Marshall-Lerner condition (MLC):

Because the quantities demanded declines with increases in prices, price elasticity is negative, so absolute values are used.

Whether a lower foreign exchange rate will improve the trade balance of an exporting country can be more simply considered by noting that the total revenue of exports must increase more than any increase in total expenses paid for imports:

(Export Revenue − Import Expenses) before Depreciation > (Export Revenue − Import Expenses) after Depreciation

To see why MLC must hold, it will be illustrative to use extreme values. When considering the price elasticities of exports and imports, it is important to remember that the price that the exporter receives in its domestic currency per exported item is the same, regardless of the exchange rate. If the domestic currency is depreciated with respect to the foreign currency, then the foreign customer pays a lower price in terms of its own currency. This increases the quantity of exports sold, so the exporter earns its price in domestic currency multiplied by the quantity sold. But, an increase in export revenue must exceed any increase in import expense, for the balance of trade to move in favor of the exporting country. This will be easier to understand with an illustration.

Consider 2 exporters, one in the United States (US) and one in the United Kingdom (UK). The American exporter exports American widgets to the UK, while the British exporter exports British widgets to the US. This is the only trade between the 2 countries. Now suppose that the exchange rate for American dollars ($) and British sterling pounds (£) is initially 1 to 1, or $1 = £1. Let assume the following initial facts:

• Initial exchange rate: $1 = £1
• Quantity of American exports: 100 American widgets
• Price of American widget in the UK: £200
• Price received by exporter for each American widget: $200 (= £200 × $1/£1)
• American exporter's revenue: $20,000 = $200 × £1/$1 ×100
• Quantity of imports: 100 British widgets
• Price of British widget in the US: $200
• Price received by British exporter for each British widget: £200
• British exporter's revenue: £20,000 = $200 × £1/$1 ×100

Assume now that the US dollar is depreciated by 50%, so that $2 = £1, but the elasticity of the American export is 1, meaning that the quantity sold in Britain is doubled with a halving of price, and that British imports are perfectly inelastic, meaning that the quality does not change with a doubling of price in the US, so elasticity = 0:

• New exchange rate: $2 = £1
• Elasticity of American export: 1
• Quantity of exports: 200 American widgets
• (double because of the lower price in the UK)
• New lower price of American widget in the UK: £100
• Price received by exporter for each American widget: still $200 (= £100 × $2/£1)
• American exporters revenue: $40,000 = British Price × Exchange Rate × Quantity = £100 × $2/£1 × 200
• Quantity of imports: 100 British widgets
• (quantity stays the same because we are assuming that demand for the British export is completely inelastic)
• Price of British widget in the US: $400
• Price received by British exporter for each British widget: £200
• British exporter's revenue: £20,000 = $400 × £1/$2 ×100
• Balance of trade: $40,000 × £1/$2 = £20,000

Note that, even though the revenue of the American exporter has doubled to $40,000, it still only equals the £20,000 after considering the new exchange rate, so trade is still balanced, so:
MLC = |PED_X| + |PED_M| = 1 + 0
In this case, only if |PED_X| > 1 − |PED_M|, will the balance of trade move in favor of the United States, and the more that |PED_X| exceeds 1 − |PED_M|, more positive that the balance of trade will move in favor of the exporter. If it is less than 1, then the balance of trade will move in favor of the other country, which in this case is the UK.

If |PED_X| > 1 − |PED_M|, then a lower foreign exchange rate will cause the quantity of exported items to increase more than enough to offset any increase in import expense, thus improving the trade balance for the exporting country. But since PED_M < PED_X, the amount paid for imports will either not increase as much as the increase in revenue from exports or import expenses might even decline. However, if PED_M > PED_X, then a decrease in the foreign exchange rate for the exporting country will cause total revenue from exports to be less than the change in expenses paid for imports, thus increasing the trade deficit for the exporting country. On the other hand, if PED_X = PED_M, then elasticity is unitary, so the exporting country's trade balance will be unchanged.

Revenue Differences between the Demand Elasticities for Domestic and Exported Products

As illustrated in the above example, the key to understanding the MLC is to realize that revenue changes differently for a product between domestic and export markets, when the price changes, even when the price elasticity of demand is the same for both markets, and the price changes by the same percentage in both countries. For instance, consider a company that sells a widget with unit elasticity in both domestic and foreign markets. (How to Calculate Demand Elasticity) Unit elasticity means that if the company halves the price of the widget in its domestic market, then it will double the quantity sold. However, the total revenue received by the company will be the same, because even though it is selling double the quantity, it is doing so at half the price, so the lower price per widget offsets the increase in quantity, resulting in no change in revenue.

But for an exported product, the revenue calculation for the exporter is different. If the price of the product is half because of a change in the exchange rate, then the product is half the price in the foreign currency, but the exporter still receives the same price in domestic currency for each exported widget as before the change in foreign exchange rates. So, if the exported product has unit elasticity in the foreign country, then the 50% reduction in price will lead to a doubling of sales in the foreign country. This doubles the revenue received by the exporter because even though it receives half of the foreign currency that it received before the exchange rate change, the foreign currency is now worth double the domestic currency, so when the foreign currency is converted to the domestic currency, the exporter still receives the same revenue in its domestic currency that it received before the change in the foreign exchange rate, thus leading to a doubling of total revenue.