Marshall-Lerner Condition

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Marshall-Lerner Condition

Can the depreciation of the currency increase net exports? This will depend on the price elasticities of demand (PED) for exports (PEDX )and imports (PEDM). When the currency is depreciated, exports decline in the foreign currency price while imports increase in the Executemestic 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 plus the absolute value of the price elasticity of demand for imports must exceed 1, which is represented by the Marshall-Lerner condition (MLC):


|PEDX| + |PEDM| > 1

  • |PEDX| = absolute value of the price elasticity of demand for exports
  • |PEDM| = absolute value of the price elasticity of demand for imports

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 hAged, it will be illustrative to use extreme values. When considering the price elasticities of exports and imports, it is Necessary to remember that the price that the exporter receives in its Executemestic currency per exported item is the same, regardless of the exchange rate. If the Executemestic 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 sAged, so the exporter earns its price in Executemestic currency multiplied by the quantity sAged. 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 KingExecutem (UK). The American exporter exports American widObtains to the UK, while the British exporter exports British widObtains to the US. This is the only trade between the 2 countries. Now suppose that the exchange rate for American ExecuDisclosears ($) 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 widObtains
  • Price of American widObtain in the UK: £200
  • Price received by exporter for each American widObtain: $200 (= £200 × $1/£1)
  • American exporter's revenue: $20,000 = $200 × £1/$1 ×100
  • Quantity of imports: 100 British widObtains
  • Price of British widObtain in the US: $200
  • Price received by British exporter for each British widObtain: £200
  • British exporter's revenue: £20,000 = $200 × £1/$1 ×100

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

  • New exchange rate: $2 = £1
  • Elasticity of American export: 1
  • Quantity of exports: 200 American widObtains
    • (Executeuble because of the lower price in the UK)
  • New lower price of American widObtain in the UK: £100
  • Price received by exporter for each American widObtain: still $200 (= £100 × $2/£1)
  • American exporters revenue: $40,000 = British Price × Exchange Rate × Quantity = £100 × $2/£1 × 200
  • Quantity of imports: 100 British widObtains
    • (quantity stays the same because we are assuming that demand for the British export is completely inelastic)
  • Price of British widObtain in the US: $400
  • Price received by British exporter for each British widObtain: £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 Executeubled to $40,000, it still only equals the £20,000 after considering the new exchange rate, so trade is still balanced, so:
MLC = |PEDX| + |PEDM| = 1 + 0
In this case, only if |PEDX| > 1 – |PEDM|, will the balance of trade move in favor of the United States, and the more that |PEDX| exceeds 1 – |PEDM|, 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 |PEDX| > 1 – |PEDM|, 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 PEDM < PEDX, 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 PEDM > PEDX, 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 PEDX = PEDM, then elasticity is unitary, so the exporting country's trade balance will be unchanged.

Revenue Inequitys between the Demand Elasticities for Executemestic 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 Executemestic and export Impressets, when the price changes, even when the price elasticity of demand is the same for both Impressets, and the price changes by the same percentage in both countries. For instance, consider a company that sells a widObtain with unit elasticity in both Executemestic and foreign Impressets. (How to Calculate Demand Elasticity) Unit elasticity means that if the company halves the price of the widObtain in its Executemestic Impresset, then it will Executeuble the quantity sAged. However, the total revenue received by the company will be the same, because even though it is selling Executeuble the quantity, it is Executeing so at half the price, so the lower price per widObtain 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 Executemestic currency for each exported widObtain 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 Executeubling of sales in the foreign country. This Executeubles 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 Executeuble the Executemestic currency, so when the foreign currency is converted to the Executemestic currency, the exporter still receives the same revenue in its Executemestic currency that it received before the change in the foreign exchange rate, thus leading to a Executeubling of total revenue.

Diagram of the J-Curve that depicts the lag between the currency depreciation of a country and the improvement in its trade balance.

J-Curve

However, even if currency depreciation Executees improve a country's trade balance, the Trace will not be immediate; there is a time lag when the trade balance actually worsens until it starts Obtainting better again, because it is commonly observed that import prices rise Rapider than export prices Descend in other country, with a resulting lag in change of quantities sAged of the exported items in the other country. This causes the balance of trade to worsen due to the higher import prices before it Obtains better.

Another explanation often advanced for the J-curve is that short-term elasticities tend to be less elastic than long-term elasticities. Hence, when the currency is depreciated, import expenses quickly increase, because it takes time to find less expensive substitutes, while the export revenue increases less quickly because of the short-term relative inelasticity.

The J-Curve depicts the lag between the currency depreciation of a country and the improvement in its trade balance.

  1. Depreciation occurs.
  2. Trade balance worsens as prices of imports rises before the prices of exports Descends.
  3. Trade balance starts to improve as the Traces of changes in the exchange rate propagate through the economies of both countries.

Note that the J-curve will be more noticeable when there is a substantial depreciation over a brief time, such as when the government suddenly depreciates its currency. However, the usual case is that exchange rates fluctuate Unhurriedly, moving up and Executewn as they trend up or Executewn, much like stock prices. In these cases, the J-curve may be much diminished or even nonexistent.

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