Model Derivation

In this study, the typical gravity model for aggregate goods is re-specified into a
commodity-specific model to analyze trade flows in textiles. We follow the approach used by
Koo and Karemera (1991), where they derive a single commodity gravity model for wheat trade.
The approach derives its foundation from Linneman (1966) and Bergstrand (1985, 1989), where
the gravity model is specified as a reduced form equation from partial equilibrium demand and
supply systems. The import demand equation for a specific commodity can be derived by
maximizing the constant elasticity of substitution (CES) utility function (Uij) subject to income
constraints in the importing country as follows:

^N

Uj = (∑ X ) ^j                                       (1)

i=1

where

Xij    = the quantity of a commodity imported from country i to country j (and N is the

number of exporting countries).

It is assumed that a commodity can be differentiated by country of origin such that in the
exponent, θj = (σj - 1)/ σj, where σj, is the CES among imports. Consumption expenditures are
limited by the income constraints (Yj) of importing country j as:

N_                   _

Y_j=∑ PijX_ij; Where Pij =P_ijT_ijC_ij/E_ij           (2)

i=1

where

Pij    =     the unit price of country i’s commodity sold in country j’s market;

Tij     =       1 + tij where tij is import tariff rates on j’s imports;

Cij    =      the transport cost of shipping i’s commodity to country j; and

Eij     =      the spot exchange rate of country j’s currency in terms of i’s currency.

By using the Lagrangian function to maximize utility (equation 1) subject to income constraint
(equation 2), the procedure generates the import demand equation as:

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