The first sections of this paper represent an interesting contribution to the weak turnpike property in connection with the standard dynamic (periodic) model of Ramsey equilibrium and possible inefficiency of such equilibria and give a good overview about problems and results in this field (especially along Ramsey equilibrium paths). Under `weak turnpike property' the authors understand that eventually the most patient household is never in a no-capital position. Starting with Section 5 of this paper, the authors deal with -- as they say -- the basic unresolved question, whether Ramsey equilibria always satisfy the weak turnpike property. As an answer they construct under special conditions an example of a Ramsey equilibrium (period-three Ramsey equilibrium cycle) in which the most patient household reaches a no-capital position infinitely often (in fact periodically) and the Ramsey equilibrium is inefficient. By the way, the authors mention a recent paper by Mitra and Sorge, where for a continuous-time version of the considered model the most patient household owns the entire capital stock of the economy after some finite time in every Ramsey equilibrium.