Will a devaluation of domestic currency improve the balance of payments if the Marshall-Lerner condition holds?

The answer is not necessarily.

The Marshall-Lerner condition states that for a devaluation of domestic currency to improve the balance of payments, the sum of the price elasticities of demand for exports and imports must be greater than one.

A fall in the exchange rate will increase the price of imports in domestic currency which will lead to a decrease in the quantity demanded. If the demand for imports is price elastic, which means that the increase in the price will lead to a larger proportionate decrease in the quantity demanded, import expenditure will fall which will improve the balance of trade. If the demand for imports is price inelastic, which means that the increase in the price will lead to a smaller proportionate decrease in the quantity demanded, import expenditure will rise. However, this may not worsen the balance of trade as export revenue will also rise. A fall in the exchange rate will decrease the price of exports in foreign currency which will lead to an increase in the quantity demanded. As the price of exports in domestic currency will not be affected by a fall in the exchange rate, an increase in the quantity demanded will lead to an increase in export revenue. Therefore, if the sum of the price elasticities of demand for exports and imports is greater than one, which means that the Marshall-Lerner condition holds, the increase in export revenue will be greater than the increase in import expenditure which will improve the balance of trade resulting in an improvement in the current account and hence the balance of payments, assuming export revenue is equal to import expenditure initially. However, if the sum of the price elasticities of demand for exports and imports is less than one, which means that the Marshall-Lerner condition does not hold, the increase in import expenditure will be greater than the increase in export revenue which will worsen the balance of trade resulting in a deterioration in the current account and hence the balance of payments, assuming export revenue is equal to import expenditure initially.

Proof

Let
PX be the price of exports in foreign currency,
PM be the price of imports in domestic currency,
PXDC be the price of exports in domestic currency,
β”‚PEDMβ”‚ be the price elasticity of demand for imports,
β”‚PEDXβ”‚ be the price elasticity of demand for exports,
BOT be the balance of trade and
E be the exchange rate.

Assume that
β”‚PEDMβ”‚ = 0.6,
β”‚PEDXβ”‚ = 0.7,
BOT = PXDCQX – PMQM = 0 (i.e. PXDCQX = PMQM) and
E↓ = 10%.

Since β”‚PEDX + PEDMβ”‚ = 1.3, the Marshall-Lerner condition holds.

E↓(10%) β†’ PM­↑(10%) β†’ QM↓(6%) β†’ PMQM­↑(4%)(approximately)

E↓(10%) β†’ PX↓(10%) β†’ QX­↑(7%) β†’ PXDCQX­↑(7%)(approximately)
(Note: A fall in E will not affect PXDC.)

BOT­↑ = PXDCQX­↑ – PMQM­↑ = 7% – 4% = 3%

A devaluation of domestic currency will improve the BOT when the Marshall-Lerner condition holds.

The above example is based on the assumption that PXDCQX = PMQM initially. However, the result may not hold if PXDCQX < PMQM (i.e. BOT < 0) initially. In this case, a 7% increase in PXDCQX may be less than a 4% increase in PMQM. If this happens, the BOT will worsen, even though the Marshall-Lerner condition holds.

Assume that PXDCQX = 100, PMQM = 200, PXDCQX↑ = 7% and PMQM↑ = 4% .

Before the increase, BOT = PXDCQX – PMQM = 100 – 200 = –100.

After the increase, BOT = PXDCQX – PMQM = 107 – 208 = –101.

A devaluation of domestic currency will worsen the BOT even when the Marshall-Lerner condition holds.

The implication of this analysis is that when one discusses the limitation of exchange rate policy for correcting a BOP deficit, they should not say that exchange rate policy will be effective for correcting a BOP deficit if the Marshall-Lerner condition holds. Rather, the correct way of saying it is that exchange rate policy will not be effective for correcting a BOP deficit if the Marshall-Lerner condition does not hold.

In case you have not been convinced by the above explanation, you can try to derive the Marshall-Lerner condition using differential calculus and you will find that the assumption of a balanced trade is required.

A more elaborate explanation will be provided in economics tuition at Economics Cafe.

 

economics tuition, back to homepage

Economics Tuition Singapore @ Economics Cafe
Principal Economics Tutor: Mr. Edmund Quek