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Unit Code: 30074
Marshall-Lerner Conditions
International Ecnomics - The Marshall Lerner Conditions
When deriving the DD curve we assumed that a rise in the real exchange rate, E.P* / P , causes a rise in the
domestic country’s net exports or current account of the balance of payments. This need not always be true.
A set of conditions under which it is true are known as the Marshall-Lerner conditions.
1.
Notation/Definitions
To understand them, first define the domestic country’s current account of the balance of payments,
measured in terms of domestic output units, as
CA  EX - IM
So, if the domestic economy produces only cars and the foreign country only food, CA is the domestic
country’s current account measured as a number of cars.
And let
q= E.P* / P = the real exchange rate, the number of cars equal to one unit of wheat;
EX * = domestic imports measured in terms of foreign rather than domestic output, i.e. the number of units
of wheat the domestic economy imports
It follows that
IM  qEX * - i.e. converts imports in wheat units to imports in car units.
EX  EX (q) - Exports assumed to be primarily a function of the real exchange rate
EX *  EX * (q) - Domestic imports (measured in wheat) primarily a function of the real exchange rate;
So the current account can be written:
CA  EX(q) - q.EX * (q)
When q, (the number of cars equal to one unit of wheat), rises – i.e. the real value of the domestic currency
depreciates – three things happen:



The volume of cars the country can export will rise since they have become cheaper
The volume of wheat the domestic country wishes to buy will fall since wheat has become more
expensive. These two effects will tend to “improve” the current account if q rises
Each unit of wheat will cost more in terms of cars. This will tend to worsen the current account of the
balance of payments of the domestic economy
So there are two forces tending to ensure that a rise in q improves the current account and one force tending
to worsen it. One specific set of conditions that guarantees that the current account is improved is that the
sum of the price elasticities of demand for exports and imports is greater than 1.
Intuitively, if the volumes of wheat and cars demanded are highly responsive to a change in q then the first
two effects will be large.
2.
Proof
If a rise in q is to improve the current account of the balance of payments then
CA/q  0
This will be true if:
Mlcond.doc
Unit Code: 30074
Marshall-Lerner Conditions
EX/ q - q.EX */q - EX *  0
And this will be true if:
[ q / EX ][ EX / q  qEX * / q  EX * ]  0 since q / EX must be positive.
If we assume that, prior to the change in q, EX  qEX * was roughly zero then q / EX  1 / EX * and we can
write,
EX q
EX * q
.

 1.
q EX
q EX *
So the condition for the current account of the balance of payments to improve in response to a rise in q
can be written:
[ q / EX ][ EX / q  qEX * / q  EX * ] 
EX q
EX * q
.

1 0
q EX
q EX *
EX * q
is the
q EX *
domestic country’s price elasticity of demand for imports1. And since 1 / q is the price of foreign goods in
terms of domestic goods, the price elasticity of the rest of the world’s demand for the domestic economy’s
goods is by definition,
Since q is the price of foreign goods in terms of domestic goods it follows that -

EX 1 / q
EX
q 1 / q
EX
1 / q EX q
.

.

(q 2 )

.
(1 / q) EX
q (1 / q) EX
q
EX
q EX
So the condition for a rise in q improving the current account can be stated as:
EX q
EX * q
.

 1 or,
q EX
q EX *
the sum of the price elasticities of demand for exports and imports must be greater than 1.
This is the Marshall Lerner Condition.
It’s conventional to express own-price elasticities as non-negative numbers even though as price rises
demand falls. This is the reason for the negative sign in the expression for elasticity above.
1
Mlcond.doc