Golden Rule savings rate

In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state level or growth of consumption, as for example in the Solow growth model. Although the concept can be found earlier in John von Neumann and Maurice Allais's works, the term is generally attributed to Edmund Phelps who wrote in 1961 that the Golden Rule "do unto others as you would have them do unto you" could be applied inter-generationally inside the model to arrive at some form of "optimum", or put simply "do unto future generations as we hope previous generations did unto us."
In the Solow growth model, a steady state savings rate of 100% implies that all income is going to investment capital for future production, implying a steady state consumption level of zero. A savings rate of 0% implies that no new investment capital is being created, so that the capital stock depreciates without replacement. This makes a steady state unsustainable except at zero output, which again...