Parametric combination

Growth Scenario

(a) $\alpha +\beta <1$ and $x=0$

No perpetual growth, steady state exists

(b) $\alpha +\beta <1$ and $x>0$

Pure exogenous growth

(c) $\alpha +\beta =1$ and $x=0$

Strict endogenous growth

(d) $\alpha +\beta =1$ and $x>0$

Co-existence of endogenous and exogenous growth