Stochastic technology shocks in an extended Uzawa-Lucas model: closed-form solution and long-run dynamics

We add stochastic technological progress, modelled as a geometric Brownian motion with drift, to an augmented Uzawa-Lucas growth model. Under a particular combination of parameters we derive a closed form solution to the model and analytical expressions which show that uncertainty reduces the optimal levels of consumption and increases the proportion of human capital devoted to producing new human capital.