338elast.doc 10/8/99
The Marshall-Lerner Conditions
Let the trade balance of Argentina in Pesos be TB  V E  V M , where V E is the value of exports and V M is the
value of imports. Let us represent the amount of the devaluation by dr , the elasticity of supply of imports by e SM , the
elasticity of supply of exports by e SE , the elasticity of demand for imports by e DM and the elasticity of demand for
exports by e DE . Then the elasticity of the trade balance with respect to the exchange rate is
eTB 
dTB
dr
 V  e e  1    e DM e SM  1 
  E  SE DE
   

V
 M  e SE  e DE    e SM  e DM 
Vm
r
The Marshall-Lerner Conditions say that if this elasticity is positive, a falling value of the Peso will make the trade
 e e  1 
balance more positive. Now assume that V E  VM and divide the top and bottom of  SE DE
 by e SE and the
 e SE  e DE 


 




 e e  1 
e DE  1 
e DM
.

top and bottom of  DM SM
 by e SM  1 . The conditions become eTB  
e DE   e SM
e DM 
 e SM  e DM 


 1 e
 
SE   e SM  1 e SM  1 

Now let e SE and e SM go to infinity.
e DE
e DM
and
will go to zero and
e SM  1
e SE
e SM
will go to one so that
e SM  1
 e  1   e DM 
eTB   DE
   1  or eTB  e DM  e DE  1 . Thus to have eTB  0 , if elasticities of supply are assumed to be
1

 

very large, we need e DM  e DE  1 . We can call these the Abbreviated Marshall-Lerner Conditions.
Example: Let us assume that US (foreign) elasticity of demand for Argentine beer is e DE  2 and that the
Argentine elasticity of demand for US liquor is e DM  0.5. Elasticities of supply are assumed to be infinite. The US
currently sells 1000 jars of liquor to Argentina at P1 (one peso) per jar. The peso is at par with the dollar so the US
earns $1000 or P1000 on its sales. Argentina sells 1000 six-packs of beer to the US at P1, netting $1000 or P1000.
The peso is now devalued by dr  10 % . The new rate is P1=$0.90. Because the elasticity of demand for the
beer is e DE  2 the 10% fall in price causes a 20% rise in quantity demanded to 1200 six-packs. The 1200 six-packs
still sell at P1 so Argentina earns P1200 a gain of e DE  dr  210%  20% or P200.
$1.00
 P1.111 , an 11.11% increase. If we multiply this by
0.90 $ P
e DM  0.5 , we find that sales of liquor fall by 5.56% to about 944 jars worth about P1049. Thus Argentina is paying
out P49 more for its imports, roughly 5%. The total Peso inflow as a result of the devaluation is P200-P49=P151, about
15%. Rough calculations put the gain in export receipts at e DE  dr  210%  20% and the increase in import
payments at dr  e DM  dr  10%  0.510%  5% . The total gain is Pesos is thus e DE  dr  dr  e DM  dr
The price of liquor in Argentina is now
 210%  10%  0.510%  20%  10%  5%  15%. Notice that these elasticities add to more than one, so that the
abbreviated Marshall-Lerner conditions predict that a devaluation will improve the balance of trade.
Now, look at the case where e DM  e DE  13 . If there is a devaluation of 10%, there is a gain in export
receipts of e DE  dr  13 10%  3.333 % . But there will be a loss of import receipts equal to the effect of the price rise
on the existing quantity demanded less the value of the change in the quantity demanded. This is
dr  e DM  dr  10%  13 10%  6.667 %. the net loss, in this case where the elasticities add to less than one so that the
abbreviated Marshall-Lerner conditions predict a loss, will be 3.33%.