Page 119 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.82, # 2, 2025, pp. 117-137

max = − [(1 + ) + ] (2)

whereby, denotes the total demand in the country for the -th group of goods and

services, and is the price per unit of products or services in that group. –

represents the quantity of imports for the i-th group, is the import price, and

is the tariff rate. denotes the quantity of domestic production sold in the local

market for the i-th group, and is its price.

Thus, for various groups of goods and services in the economy, we consider the
problem of maximizing the objective function (2) subject to constraint (1). This is a
conditional optimization problem that can be solved using the method of Lagrange
multipliers (Hosoe, N.; Gasawa, K.; Hashimoto, H. (2021)). Solving this problem
allows us to estimate the portion of total demand for each type of goods and services
that should be met by domestic production and the portion that should be fulfilled by
imported products. From the first-order condition of this optimization problem, the
ratio of imported to domestic products can be expressed as follows (Annabi, N.;
Cockburn, J.; Decaluwé, B. (2006)):

= ( ∙ ) (3)

Apparently, this ratio depends on the prices of imported and domestic products,
distribution parameters, and the elasticity coefficient. The higher the elasticity, the
more sensitive the import-to-domestic product ratio is to changes in the price ratio. In
other words, even a small change in the price of imported or domestic products can
lead to a substantial change in consumer demand. Conversely, when elasticity is low,
even large changes in the price ratio result in only minor adjustments to the import-
to-domestic product ratio.

Similarly, the producer can choose to sell products in the domestic market or export
them. In doing so, the producer maximizes the following objective function to sell

of the total production in the domestic market and to export the volume (Hosoe,

N.; Gasawa, K.; Hashimoto, H. (2021)):

max = − [(1 + ) + ] (4)

In the i-th sector, the allocation of total production between exports and the domestic
market is represented using a CES-type function known as the CET (Constant Elasticity
of Transformation) function (Annabi, N.; Cockburn, J.; Decaluwé, B. (2006)).

1

= ( + ) (5)

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