Deriving the Marshall Lerner Condition - Supplementary Notes Owen revised 1 PDF

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TB = Trade Balance (domestic currency terms) e = exchange rate  domestic currency/ foreign currency P = Price of exports (Price in domestic currency) P*= Price of imports (Price in foreign currency) X = Quantity of exports I = Quantity of imports Y = Output of domestic economy Y* = Output of foreign economy

Correspond to the domestic and foreign absorption effects in the equation. The associated interpretation is that as the domestic and foreign countries grow they absorb more products from each other.

A general equation determining the functioning of a representative home country’s trade balance can be represented as follows:

N.B. The following derivation does not consider the endogeneity of the absorption effects to changes in the value of the exchange rate, via the GNP identity relation, where domestic and foreign GNP are given, respectively, by the formulas Y = C + I + G + TB and Y* = C* + I* + G* - TB. A more complete analysis and 1

derivation, which includes such absorption effects, is left as an exercise. Note, nonetheless, that such absorption effects add two additional negative terms in the overall derivation, which is then known as the Harberger Condition. The Harberger Condition entails more restrictive conditions for ensuring that an exchange rate devaluation/depreciation will result in a favorable effect on a given country’s trade balance.

First, take the derivative of the TB w.r.t. e :

Set

and divide by

Rearranging,

and multiply by 1, specifically where

, for the first term in this equation

2

Rearranging again,

After defining

, as the foreign demand elasticity for the home

country’s export, and

, as the home import demand elasticity, and

, it follows that:

Devaluations (depreciations) of domestic currency improve the trade balance, TB, if:

Hence, an associated necessary and sufficient condition is that:

If there is balanced trade then, and the foregoing expression, which determines whether the trade balance will improve, can be expressed in a simpler form, which is:

However, if

, which is the case when there is an initial trade balance deficit,

then, , there must be a larger corresponding value of currency devaluation/depreciation to improve the trade balance. 3

for a...