Solow Model with a Capital Stock Externality Suppose we have the following form of the Solow Model: $$ Y_t=K_t^{a+b} L_t^{1-a} $$ where a,b >0, and a+b&lt;1.

Is it possible to determine the steady state growth rate of k (k=K/L), and the steady state growth rates of MPL and MPK?
There is no steady state in the Solow framework. The system is explosive because $a,b &gt;0 \wedge a+b&lt;1 \Rightarrow a+b + (1-a) &gt; 1$. Thus $(zK_t)^{a+b} (L_tz)^{1-a} = z^{1+b}(K_t)^{a+b} (L_t)^{1-a}$. I.e. this production function has increasing returns to scale. Such capital stock externalities are discussed in the AK-Models.