Marginal productivity theory remains at the core of mainstream distribution and production theory. However, marginal productivity can be adjusted for imperfect competition to yield, what might be called, adjusted marginal products. Thereafter, things remain analytically very similar and those adjusted marginal products then determine the stock demand for capital and drive long-run capital accumulation.
The imperfect competition model of so-called New Keynesians continues to assert price and nominal wage flexibility would restore full employment. In a financialized economy with massive inside debts, that strikes me as an implausible proposition.Both require to be solved and provide a real alternative that the notion of the natural rate is abandoned. Note that this would strengthen Wren-Lewis and other New Keynesian arguments.