Growth, Poverty Trap and Escape

The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction $s$ of the output of a production function and the technology efficiency parameter $A$, appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital $k_p$. We derive analytically the steady state probability distribution $P(k_p)$ and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, $P(k_p)$ is bimodal with the twin peaks corresponding to states of poverty and well-being respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of $A$. We identify a critical value of $A_c$ below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at $A_c$. The economic model, with conceptual foundation in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.