Solow model with logistically growing labour force and technological level

The Solow model is a fundamental tool of neoclassical economics for explaining economic growth. However, its classical variant, which assumes exponential growth of both the labor force and the level of technology, does not accurately reflect real-world demographic and technological dynamics. This thesis analyzes an alternative version of the Solow model, where both the labor force and the technological level grow logistically. It is shown that this system possesses two asymptotically stable equilibria, although under realistic initial conditions, only one of them is attained. Under these conditions, the capital function exhibits at most one extremum, specifically a minimum. In the second part of the thesis, a stochastic variant of the model based on the birth and death processes is introduced, offering insights into the behavior of the economy under uncertainty. Simulations suggest the existence of a quasi-stationary distribution for the modeled variables of capital and economic output. Subsequent statistical tests confirmed that the estimated means of these stationary distributions coincide with the corresponding asymptotic equilibrium values of the deterministic model.