How does a neoclassical growth model fail in a non-classical world?

A neo-classical growth model assumes that income growth is primarily determined by output supply constraints, in the form of limits on capital, labour, and other factor inputs. Income distribution and macroeconomic flows are not generally modelled. Its predictions come under stress in today's economy where growth seems to be influenced by these factors, both domestically and internationally.

A neoclassical model may have a production function of the form y=A.k^b where y is output per person, k is capital per person, and A and b are constants. The production function is not the neoclassical part, having been used in Keynesian models and saying nothing about the flow of income. It is the other equations expressing dynamics which characterise the model as neoclassical or not. A neoclassical growth model may have dk/dt = s.y where t is time and s is a constant, so capital accumulation is independent of everything apart from the previous production. On differentiating the production function with respect to time we get dy/dt.df/dy = dk/dt.A.b.k^(b-1), and we can then substitute dk/dt and k from the production function and accumulation function to get dy/dt in terms of y alone.

We can alternatively posit an accumulation function dk/dt = s.y.I(y < c) for an indicator function I equal to one if y is less than a constant c and zero otherwise. We may be trying to capture a demand effect, where people only want or can afford goods up to a certain level of production, and then stop buying so companies in response stop accumulating (k is assumed to be the only factor of production here). Under this accumulation equation, we would have an identical growth equation up to y=c, then suddenly the neo-classical equation for dy/dt in terms of y would stop working.

One could find other examples.