Modeling Capital-Induced Labor Migration for Indonesian Regional Convergence
DOI:
https://doi.org/10.30871/jaic.v10i3.12713Keywords:
Capital-Induced Labor Migration, Capital diffusion, Mathematical Modeling, Non-linear ODE System, Spatial inequalityAbstract
Regional inequality in Indonesia presents a persistent structural challenge characterized by capital concentration and labor agglomeration in core regions. Conventional models often fail to capture the endogenous feedback between capital accumulation, dynamic labor migration, and regional ecological limits. To address this theoretical gap, we formulate a four-dimensional non-linear ordinary differential equation (ODE) system integrating the Solow neoclassical growth framework, logistic population dynamics bounded by regional carrying capacities (κ), and Capital-Induced Labor Migration (CILM). The model is empirically calibrated using Statistics Indonesia macroeconomic data (2020-2024), classifying regions into Core and Periphery based on a strict 2.63% Gross Regional Domestic Product (GRDP) equal-distribution threshold. Analytical validity is rigorously established through mathematical proofs of Positive Invariance and Ultimate Boundedness. Numerical simulations using the Runge-Kutta 4th Order method reveal a critical phenomenon termed "deceptive convergence" a scenario where the spatial inequality ratio artificially compresses not due to genuine economic expansion in the periphery, but solely because the core region reaches its absolute ecological saturation. Furthermore, high labor mobility sensitivity is proven to act as a divergence multiplier, triggering massive labor drains from peripheral regions. Ultimately, a synthesized policy mix simulation demonstrates that aggressive physical capital diffusion combined with strict human capital retention policies is mathematically proven as the most effective strategy to transform the agglomeration curse into equitable structural convergence.
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