We consider discrete-time optimal growth models without discounting. Specifically, we analyze unitelastic models with utility function $\ln c_t$ and production function $k^a_t$ , where the discount factor is 1. We define the Ramsey Gap as the summation of steady-state utility minus the utility achieved at each period (Equation (9), in the text), and define the Ramsey-optimal paths as feasible paths which minimize the Ramsey Gap. Here we take the steady-state utility level as the level to be compared to, while Ramsey (1928) himself takes the so-called Bliss level. We show that a Ramsey-optimal path exists in our model. Also, the value of Ramsey Gap of the Ramsey-optimal path in our model is shown to be $(a/(1-a))(\ln a^{1/(1-a)} - \ln k_0 )$, when the initial stock of capital is $k_0$ (Equation (12)). This approach may be regarded as a method which can be used to analyze optimal growth models when discount factor is 1.