SCALAR PARAMETERS BEHAVIOR DYNAMICS OF ECONOMIC GROWTH MODEL

Анотація

The modern economic system is influenced by factors like technological innovation, globalization,
and demographic shifts. Dynamic models are essential for analyzing economic growth, but
understanding their internal mechanisms is crucial to avoid errors that could compromise results on
new data. Adapting these models to address challenges like financial crises, climate change, and
technological transformation is increasingly important. This study examines the dynamics of economic
growth models, focusing on investments, human capital, and innovation, to identify key patterns
over time and their alignment with significant events.
As a model, we will use the endogenous model of economic growth with foreign trade and
investment and its modification with the division of the economy into sectors in the context of their
interaction, which is described in detail in [1-3].
In the model, the main factors of production are private capital Kpr, public capital Kgov,
human capital (knowledge) H, labor L and the variable factor R. Variable factor R in a single-sector
production model is responsible for the land factor N. A modified Cobb-Douglas function of the
form:
Yp=AKprKgovH N L 1-α-β-γ-φ,
where α – is the coefficient of elasticity of private capital, β – public capital elasticity coefficient, γ
– human capital elasticity coefficient, φ – elasticity of the variable factor, in this case, land [2,3].
In the multisectoral model, the factor R depends on the sector. For the primary sector
Yagr land is a factor, similar to the single-sector model. For the secondary sector Yind factor is the
output of the primary sector Yagr. For the tertiary sector Yserv factor is the output of the secondary
sector Yind.
For a multi-sector model, the production function takes the form:
Yp=A1Kagrα1Kgovβ1Hagrγ1 N φ1Lagr 1-α1-β1-γ1-φ1 +A2Kindα2Kgovβ2Hindγ2 Yagr
φ2Lind 1-α2-β2-γ2-φ2 +A3Kservα3Kgovβ3Hservγ3 Yind φ3Lserv 1-α3-β3-γ3-φ3 ,

wherein Yp=Yagr+Yind+Yserv, similarly Kpr=Kagr+Kind+Kserv and H=Hagr+Hind+Hserv,
L =Lagr+Lind+Lserv.
The innovation sector generates new knowledge by the production function:
ΔH=BKrdLrd 1-υ ,
where Krd – capital raised in the innovation sector, Lrd – labor involved in the innovation sector, –
capital elasticity in the innovation sector. Total capital in the economy Kfull can be found by the
formula: Kfull=Krd+Kpr+Kgov, similar to labor: Lfull=Lrd+L .
Capital has been divided into private and public, and investment is made through aggregate
savings, so capital dynamics can be expressed through three indicators: private sector capital intensity,
public sector capital intensity, and aggregate savings per unit of labor [2,3].
The capital stock of the private sector grows through investment (domestic and foreign) and
decreases through depreciation of fixed capital. In equation form, this can be written as:
kpr•=iin+if-dpr+nkprwhere kpr=KprL – capital intensity of the private sector, dpr – depreciation ratio of private capital,
n – average growth rate of the employed labor force, iin=IinL – domestic investment per unit of
labor, if=IfL – foreign investment per unit of labor.
The growth of public capital comes from taxes paid to the state budget, and the decrease,
similar to the private sector, comes from capital disposals (depreciation). The equation for the capital
intensity of the public sector is as follows:
kgov•=g-dgov+nkgov+tx,