MATHEMATICAL MODELING OF ECONOMIC GROWTH IN UZBEKISTAN: A CALIBRATED AUGMENTED SOLOW MODEL WITH PHYSICAL AND HUMAN CAPITAL

Abstract

This paper develops and numerically solves a dynamic mathematical model of economic growth for Uzbekistan based on the augmented Solow framework with physical and human capital. The model is formulated as a system of two nonlinear differential equations for capital per effective worker, with a Cobb–Douglas production function. Parameters are calibrated to the structural characteristics of the Uzbek economy: a high investment rate, a young and growing population, and an expanding education sector. The steady state is derived analytically, the speed of convergence is obtained by linearization, and transitional dynamics are simulated with a fine-step explicit Euler scheme over a 30-year horizon. Four policy scenarios are compared. The results show that the convergence rate is about 3.6% per year, implying a half-life of roughly 19 years. Raising the investment rate from 35% to 40% of GDP increases steady-state output per effective worker by 12.4%, while raising human capital investment from 6% to 8% of GDP increases it by 19.7%. A combined policy yields a 34.5% gain. The findings suggest that, at Uzbekistan’s current investment intensity, further returns from physical capital accumulation are smaller than those from human capital, and that education and skills policy should be treated as a core element of the national growth strategy.