What is the prescription of Ramsey capital taxes for heterogeneous-agent incomplete-market economy in the long run? Aiyagari (1995) addressed the question and showed that a positive capital tax should be imposed to implement the steady-state allocation that satisfies the so-called modified golden rule. In his analysis of the Ramsey problem, a critical assumption made is the existence of optimal steady-state allocations. This paper revisits the issue and finds sharply different results. We demonstrate the optimal Ramsey allocation may feature no steady state. The key to our results is embedded in the hallmark of incomplete-market model that the risk-free rate is lower than the time discount rate in the steady state of competitive equilibrium.