Learning by doing, endogenous discounting and economic development

In this paper, we focus on a growth model where the discount rate is decreasing in capital accumulation and endogenous growth is made possible through learning by doing, knowledge accumulation being a by-product of gross investment. In such a model, the utility function has to be restricted to take positive values implying that the elasticity of marginal utility is lower than one. The presence of endogenous discounting generates a steady-state of stagnation which can be saddle-path stable or unstable depending on the marginal productivity of knowledge. In the case of long run growth, the fact that the elasticity of marginal utility is lower than one implies the existence of two asymptotic balanced growth paths: the one with the higher growth rate being a saddle point while the one with the lower growth rate not being a saddle point. We also study the optimal solution which is characterized by a unique balanced growth path. The policy consists as usual in subsidizing investment in order to internalize the externality.