Human capital and welfare

We introduce the Human Development Index (HDI) in a growth model to show that if households cared about human capital, even if infinitesimally, then human capital would increase forever protecting economies indirectly. Here, human capital will have an additional positive effect on social welfare through the quality of individual health and education. In a simple economy with a Cobb-Douglas technology and logarithmic preferences, we provide the explicit trajectories for human capital, consumption, and the HDI, which correspond to the balanced growth path (BGP). Using a two-step maximization strategy, we compute the optimal initial value of the control variable, in this case, the initial optimal labour supply. In other words, we prove the optimality of the BGP. We highlight a HDI crossing property: the propensity to consume has a positive effect on the HDI in the short run, but negative in the long run.