Tyler Cowen quotes Aaron Hedlund:
The flaw with both of these models, of course, is that they are representative household models where there is no inequality.
Fair point, but I do not see this as a fatal flaw in trying to adapt the Solow growth model to a theory of inequality. Suppose you have two types of representative households–workers and capitalists. The capitalists do all the saving.
The real trick, which is just as tricky in a model with one type of representative household, is to get the capital/worker ratio to rise without the return on capital falling. At most, that can happen for a while–not indefinitely.
As to your last paragraph, fortunately this is not true. The only equality there is, exists in the limited availability of our time. Anchor time use to itself in coordination – not the random nature of capital. Doing so also means independent (time) product creation in services. Treat capital production and services as separate systems. That way, productivity can rise on a regular basis with full employment, and be measured, in both.
A while can be a long, long time though, especially if technology extends the transfer by substituting capital for labor, or if inequality leads to extended rent extraction through government.