Economy Essay No. 9: The Marshall-Lerner Theorem

Introduction:

In class, Chris briefly mentioned the Marshall-Lerner theorem, which got me both curious and interested! I browsed the web and tried to get a good understanding of this theorem. Here are my results: an essay on the Marshall-Lerner theorem. Enjoy guys and girls! By the way, don’t worry, if I am right, this is only on the A2 syllabus and not on the AS!

First of all, here is some terminology that we might already have been talking about in class. You really need to understand the meaning of the following words in order to understand the rest of this essay:

1. Current account balance – equals the balance of trade (total exports of goods and services minus the total imports of goods and services) plus the net unilateral transfers from abroad (which basically means the gifts and transfers from individuals or transfers from governments from abroad) plus the net factor income from abroad (which basically means the net flow of property income and the net flow of compensation of employees). If you want to learn more about Current Account Balance, there is a poster in the hallway that will give you some information.

2. Depreciation – means the reduction in value of assets. This can happen because of usage, passing of time, outdating of technology and many other things. Sometimes depreciation is also used as a synonym for devaluation of a currency.

The basics of the Marshall-Lerner theorem:

The Marshall-Lerner Theorem exists of a condition. This condition states that, if we want the devaluation of a currency (simplified: the exchange rate goes down) to have a positive impact on the current account balance (which means either a increase in the current account surplus or an decrease in the current account deficit), the sum of price elasticity of exports and imports must be bigger than 1. Thus if the sum (of the absolute values) of price elasticity of exports and imports is bigger than 1, the devaluation of currency has a positive impact in current account balance. If that sum is less than 1, the impact is not positive. So briefly said, the best explanation of the theorem is:

The Marshall-Lerner condition states that: “Following a fall in the value of a country’s currency or depreciation there will be an improvement in the economy’s current account position if the sum of elasticities of exports and imports is greater than one.”

So, a necessity for this condition is the following:

|PED exports| + |PED imports| > 1

You will get a better understanding of the Marshall-Lerner condition by the following. If you want to show the result of the Marshall-Lerner condition in an image, you use the J-curve. A J-curve is a graph that shows a successful improvement in the current account balance as a result of devaluation of the currency or depreciation. It looks like this:

This image shows a clear improvement in the current account balance after the depreciation (depreciation in this case as am example, could just have been devaluation of currency). This means that the sum of the price elasticity of exports and imports was bigger than 1. You can also see that the improvement does not take place immediately. It takes some time. I will try to illustrate the Marshall-Lerner theorem by the following example:

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Country X is facing a devaluation of its currency.

The PED Exports of country X = +3

|PED Exports| = 3

The PED Imports of country X = -1.8

|PED Imports| = 1.8

|PED Exports| + |PED Imports| = 3 + 1.8 = 4.8

4.8 > 1

Therefore the Marshall-Lerner theorem states that the current account balance of country X will improve as a result of the devaluation of its currency.

However, the J-curve shows us that this will not happen immediately, it will take some time for the improvement to take place.

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The Marshall-Lerner theorem is named after two famous economists Alfred Marshall and Abba Lerner.

On a side note:

In 1992 the British government made a huge mistake. On the 16th of september, they were forced to withdraw the pound (GBP) from the European Exchange Rate Mechanism, because the devaluation of the sterling had continued for too long: it fell below its agreed lower limit. This event is nowadays referred to as "black wednesday".

The way the Marshall-Lerner theorem works:

So now that you hopefully know what the basic meaning of the Marshall-Lerner theorem is and you know how the theorem works, we are going to find out why it works the way it does.

The devaluation of a currency means that the exchange rate goes down. This also means that the prices for exports go down and the prices for imports go up. Do you remember? (S.P.I.C.E.D. = Strong Pound Import Cheap Export Dear) As a result, the quantity demanded for exports will increase and the quantity demanded for imports will decrease.

This will cause an improvement in the current account balance if the exported goods are elastic. Being elastic, the demand for the goods will proportionately increase more than the price will decrease. This means that the current account balance will improve as it causes the total revenue of exports to increase. Also if the imported goods are elastic, the demand will decrease proportionately more than the price will increase. Therefore the total import expenditure will decrease.

The J-curve can be explained too. Goods seem to be inelastic in the short term, because it takes some time to change consuming patterns. This means the devaluation will worsen the current account balance at first, as seen in the J-curve: the graph lowers. In the long term, consuming patterns will adapt to the new prices and the trade balance will improve: the graph rises. This is how the J-curve will get its shape.

A numerical example of the Marshall-Lerner theorem:

At a given moment is the exchange rate between the sterling and the American dollar the following:

£1:$2

The total exports of England exist of just one good, namely 100,000 wooden tables a year, which are being sold to a company in the USA for £50 ($100) each. The total imports of England exist of just one good as well, namely 100,000 wooden chairs a year, which are being bought from a company in the USA for £30 ($60) each. We will ignore the net unilateral transfers from abroad and the net factor income from abroad, just to keep things simple. We can than conclude:

[BEFORE DEVALUATION]

Total exports: £5,000,000

Total imports: £3,000,000

England’s current account balance: a £2,000,000 surplus.

Given is the following:

PED wooden tables (exports) = -2

PED wooden chairs (imports) = -1.5

[DEVALUATION]

Later, the exchange rate for the sterling goes down. The exchange rate between the sterling and the American dollar is than:

£1:$1,80

Which is a decrease of 10% in the value of the sterling compared to the first exchange rate.

With the new exchange rate given, the prices for the wooden tables, which are England’s export, will decrease. Therefore the quantity demanded will increase as shown:

PED exports = -2 = (% ch. demand) / (% ch. price)

(% ch. price) = 50 * 1.8 = 90 = -10%

PED exports = -2 = (% ch. demand) / (-10%)

(% ch. demand) = -2 * -10% = +20%

New demand = 120,000

New price = £50 = $90

Total exports = 120,000 * £50 = £6,000,000

With the new exchange rate given, the prices of the wooden chairs, which are England’s import, will increase. Therefore the quantity demanded will decrease as shown:

PED imports = -1.5 = (% ch. demand) / (% ch. price)

(% ch. price) = 60 / 1,8 = 33.33 = +11.11 %

PED imports = -1.5 = (% ch. demand) / (+11.11%)

(% ch. demand) = -1.5 * +11.11% = -16.665%

New demand = 83,335

New price = $60 = £33.33

Total imports = 83,335 * £33.33 = £2,777,555.55

[AFTER DEVALUATION]

Total exports: £6,000,000

Total imports: £2,777,555.55

England’s current account balance: a £3,222,444.45 surplus.

As you can clearly see, as a result of the devaluation of the sterling, there was an improvement in the current account balance. This is being described by the Marshall-Lerner theorem.

Another numerical example of the Marshall-Lerner theorem:

Again, at a given moment is the exchange rate between the sterling and the American dollar the following:

£1:$2

The total exports of England still exists of just one good, namely 100,000 wooden tables a year, which are being sold to a company in the USA for £50 ($100) each. The total imports of England exists of just one good as well, namely 100,000 wooden chairs a year, which are being bought from a company in the USA for £30 ($60) each. We will ignore the net unilateral transfers from abroad and the net factor income from abroad, just to keep things simple. We can than conclude:

[BEFORE DEVALUATION]

Total exports: £5,000,000

Total imports: £3,000,000

England’s current account balance: a £2,000,000 surplus.

Given is the following:

PED wooden tables (exports) = -0.6

PED wooden chairs (imports) = -0.6

[DEVALUATION]

Later, the exchange rate for the sterling goes down. The exchange rate between the sterling and the American dollar is than:

£1:$1,80

Which is a decrease of 10% in the value of the sterling compared to the first exchange rate.

With the new exchange rate given, the prices for the wooden tables, which are England’s export, will decrease. Therefore the quantity demanded will increase as shown:

PED exports = -0.6 = (% ch. demand) / (% ch. price)

(% ch. price) = 50 * 1.8 = 90 = -10%

PED exports = -0.6 = (% ch. demand) / (-10%)

(% ch. demand) = -0.6 * -10% = +6%

New demand = 106,000

New price = £50 = $90

Total exports = 106,000 * £50 = £5,300,000

With the new exchange rate given, the prices of the wooden chairs, which are England’s import, will increase. Therefore the quantity demanded will decrease as shown:

PED imports = -0.6 = (% ch. demand) / (% ch. price)

(% ch. price) = 60 / 1,8 = 33.33 = +11.11 %

PED imports = -0.6 = (% ch. demand) / (+11.11%)

(% ch. demand) = -0.6 * +11.11% = -6.66%

New demand = 93,330

New price = $60 = £33.33

Total imports = 93,330 * £33.33 = £3,110,688.9

[AFTER DEVALUATION]

Total exports: £5,300,000

Total imports: £3,110,688.9

England’s current account balance: a £2,189,311.1 surplus.

As you can clearly see, as a result of the devaluation of the sterling, there was an improvement in the current account balance, even though both the imports and exports were inelastic! This is being described by the Marshall-Lerner theorem.

The Marshall-Lerner theorem in chart:

This link shows a chart that shows the result of the Marshall-Lerner condition. You can see that when the currency depreciates (exchange rate goes down), the current account balance improves, which is exactly what the Marshall-Lerner theorem states. The value of the currency (the USD in this case) is indicated with the blue graph while the value of the current account balance (as a percentage of the GDP) is indicated with the red graph. This chart is a good way to show the results of the Marshall-Lerner condition. I hope it helps you to understand the condition.

Important addition:

Please notice the following:

If the imports and exports are both inelastic, and if (AND ONLY IF) "|PED imports| + |PED exports| > 1", (for example: 0.6 + 0.6 > 1) the Marshall-Lerner theorem does certainly apply. Any devaluation of currency will have a positive impact on the current account balance. If the sum of the elasticities is not bigger than one, the Marshall-Lerner theorem does not apply.

A few things to mention:

I really hope I gave a good explanation of the Marshall-Lerner theorem and made you learn something! I am not sure though, as I never learned about it before! Please comment to tell me if I am correct or need to adjust some of the information given. Thanks for reading and remember, this is in the A2 syllabus.

References:

http://en.wikipedia.org/wiki/Current_account

http://www.oppapers.com/essays/Net-Factor-Income-Abroad/129921

http://business.baylor.edu/Tom_kelly/2307ch19.htm

http://en.wikipedia.org/wiki/Marshall-Lerner_Condition

http://www.bized.co.uk/virtual/dc/trade/theory/th12.htm

http://tutor2u.net/blog/index.php/ib-diploma/comments/marshall-lerner-and-the-j-curve/

http://www.economyprofessor.com/economictheories/marshall-lerner-principle.php

http://www.economicshelp.org/blog/trade/testing-marshall-lerner-condition/

http://tutor2u.net/economics/revision-notes/a2-macro-balance-of-payments-deficits_clip_image008.gif