This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies
exhibits a basic non-convexity. First, we consider the case of strictly
concave utility function: when the discount rate is either low enough or
high enough, there will be one steady state equilibrium toward which
the convergence of the optimal paths is monotone and asymptotic.
When the discount rate is in some intermediate range, we find sufficient conditions for having either one equilibrium or multiple equilibria
steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to
one single appropriate equilibrium steady state. This state might be a
poverty trap with low per capita capital, which acts as the extinction
state encountered in earlier studies focused on S-shapes production
functions. Second, we consider the case of linear utility and provide
sufficient conditions to have either unique or two steady states when
the discount rate is in some intermediate range . In the latter case, we
give conditions under which the above critical value might not exist,and the economy attains one steady state in ?nite time, then stays at
the other steady state afterward.