In Solow growth model, if one perturb the saving, there is convergence of old equilibrium capital to new equilibrium capital as investment breaking point capital is attractor.
However, in derivation of convergence, one needs to invoke $a_K$ elasticity of output to capital. Assuming growth in knowledge, growth of population and decay of capital. Then I need $a_K<1$ to guarantee convergence of old equilibrium to new equilibrium. I am assuming Inada condition on output per effective labor and knowledge is only labor augmenting in the model.
Is $a_K<1$ predetermined by Solow growth model or some condition on the model? This discussion does not assume any particular form of production function, in particular, Cobb-Douglas function.
Ref. Romer, Advanced Macroeconomics, Chpt 1, Sec 5 on speed of convergence.