Why have many economics teachers misunderstood the Marshall-Lerner condition?

The reason is that they do not fully understand the difference between current prices and base-year prices in the balance of payments and aggregate demand.

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,
│PEDM│ be the price elasticity of demand for imports,
│PEDX│ be the price elasticity of demand for exports,
BOT be the balance of trade and
E be the exchange rate.

Assume that
│PEDM│ = 0.6,
BOT = X – M = PXDCQX– PMQM = 0 (i.e. PXDCQX = PMQM) and
E↓ = 10%.

E↓(10%) → PM­↑(10%) → QM↓(6%) → PMQM­↑(4%)(approximately)

Since PMQM increases by 4%, the BOT will improve only if PXDCQX increases by more than 4%.

E↓(10%) → PX↓ (10%) → QX­↑

Since a fall in E will not affect PXDC, PXDCQX will increase by more than 4% only if QX increases by more than 4%, which means that │PEDX│ > 0.4. Therefore, a devaluation of domestic currency will improve the BOT only if │PEDX + PEDM│ > 1 (i.e. the Marshall-Lerner condition holds), assuming export revenue is equal to import expenditure initially.

The question is whether the Marshall-Lerner condition is also a requirement for a devaluation of domestic currency to increase aggregate demand.

The Marshall-Lerner condition is not a requirement for a devaluation of domestic currency to increase aggregate demand.

Aggregate demand is the total demand for the goods and services produced in the economy over a period of time and is comprised of consumption expenditure, investment expenditure, government expenditure on goods and services and net exports. Unlike net exports in the balance of payments which are measured at current prices, net exports in aggregate demand are measured at base-year prices. In other words, although net exports in the balance of payments are measured in nominal terms, net exports in aggregate demand are measured in real terms.

Balance of Trade (BOT) = X – M = PXDCQX– PMQM

In the above equation, PXDC and PM are the current prices of exports and imports.

Aggregate Demand (AD) = C + I + G + (X – M) = C + I + G + (PXDCQX– PMQM)

In the above equation, PXDC and PM are the base-year prices of exports and imports.

Although a fall in the exchange rate will affect the current prices of exports and imports, it will not affect the base-year prices. Therefore, when the quantity demanded of exports increases and the quantity demanded of import decreases, net exports in real terms will rise which will lead to an increase in aggregate demand, regardless of the price elasticities of demand for exports and imports, assuming the income effect of a fall in the exchange rate on consumption expenditure on domestic goods and services does not outweigh the substitution effect. In other words, the Marshall-Lerner condition is not a requirement for a devaluation of domestic currency to increase aggregate demand. However, net exports in nominal terms will increase and hence the balance of payments will improve only if the sum of the price elasticities of demand for exports and imports is greater than one. In other words, the Marshall-Lerner condition is a requirement for a devaluation of domestic currency to improve the balance of payments. The above analysis is based on the assumption that the income effect of a fall in the exchange rate on consumption expenditure on domestic goods and services does not outweigh the substitution effect. This assumption is likely to hold as the substitution effect will reduce the income effect.

To understand it in a somewhat different way, we can rewrite the aggregate demand function.

Aggregate Demand (AD) = C + I + G + (X – M)

Aggregate Demand (AD) = Cd + I + G + X, where Cd refers to consumption expenditure on domestic goods and services, assuming only households import goods and services which is a standard assumption made in economic textbooks for simplicity.

A fall in the exchange rate will decrease the price of exports in foreign currency which will increase the quantity demanded. As the price of exports in domestic currency will not be affected, both in nominal terms and in real terms, this will lead to an increase in X in real terms. Other things being equal, aggregate demand will increase. A fall in the exchange rate will also increase the price of imports in domestic currency. This will induce households to switch from imports to domestic goods and services which will lead to an increase in Cd in real terms resulting in an increase in aggregate demand .

In addition to the substitution effect of a fall in the exchange rate on Cd, there is, however, the income effect. An increase in the price of imports in domestic currency due to a fall in the exchange rate will reduce real income. When this happens, households will decrease consumption, including those of domestic goods and services resulting in an decrease in Cd in real terms. Therefore, as least in theory, Cd in real terms may not increase. The question is whether any potential fall in Cd in real terms will be greater the increase in X in real terms. The answer is ‘possible’. However, in my view, it is unlikely to happen due to several reasons. The substitution effect of a fall in the exchange rate on Cd is likely to be greater than the income effect as the substitution effect will decrease the income effect. If the income effect of a fall in the exchange rate on Cd is greater than the substitution effect, the fall in Cd in real terms is unlikely to be large as the substitution effect will partially offset the income effect. In the event that the decrease in Cd in real terms is greater than the increase in X in real terms resulting in a decrease in aggregate demand , the result is due to the large Cd in real terms as a component of aggregate demand and the large income effect of a fall in the exchange rate on Cd, and this has nothing whatsoever to do with the Marshall-Lerner condition.

The following numerical example should convince anyone who thinks that the Marshall-Lerner condition is a requirement for a devaluation of domestic currency to increase aggregate demand that it is indeed NOT the case.

Assumption 1: The base-year price of domestic goods and services is $10 and inflation is 20% which means that the current price is $12.

Assumption 2: The base-year price of imports (M) in domestic currency is $10 and foreign inflation is 20% which means that the current price is $12.

Assumption 3: The exchange rate falls by 10%.

The above assumptions are made for illustrative purpose and the validity of the results does not depend on the assumptions.

AD($300010) = C($100010) + I($100000) + G($100000) + X($10×10000=$100000) – M($10×10000=$100000)

AD($300010) = Cd(1x$10=$10) + I($100000) + G($100000) + X ($10×10000=$100000)

BOT ($0) = Nominal X ($12×10000=$120000) – Nominal M ($12×10000=$120000)

Suppose PEDx = 0.5 and PEDM = 0.3 which means that the Marshall-Lerner condition does not hold.

Question 1: Will the BOT increase or decrease?

Answer: The BOT will decrease. As the Marshall-Lerner condition does not hold, a devaluation of domestic currency will decrease the BOT and therefore worsen the BOP. You can refer to the explanation that I put forward earlier.

Question 2: Will aggregate demand increase or decrease?

Answer: Aggregate demand will increase. If the substitution effect of a fall in the exchange rate on Cd is greater than the income effect, Cd will increase. In this case, as Cd and X will both increase, aggregate demand will increase. If the income effect of a fall in the exchange rate on Cd is greater than the substitution effect, Cd will decrease. In this case, the decrease in Cd will be less than the increase in X and therefore aggregate demand will increase, even though the Marshall-Lerner condition does not hold.

You can refer to the Marshall-Lerner condition in high-level economics textbooks and you will find that it is never linked to aggregate demand. More will be explained in economics tuition.
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