The goal of the paper is to present an alternative version of the Ramsey-Cass-Koopmans model, standing as an application of the formalised theory. Indeed, the main general reflections of these authors (in 1928 for F.Ramsey, and in 1965 for D.Cass and TC.Koopmans), give place to a theoretical application model presented in the literature, which encounters problems of insolvency of the differential system rising from the optimisation program. This one does not allow to end up with an analytical solution for the optimal path leading to the steady state of an economy, and needs therefore to be completed by some numerical methods. However, it is known from TC.Koopmans that a major part of the problem in optimal growth is centred on the determination of a maximising criterion, for which he suggests a choice according to the results of its application. The presented theoretical model uses a criterion different from the usually assumed ‘CRRA’ function, associated with some particularities in the resolution of the program (using the Hamiltonian algorithm). The paper shows for result, a complete and different example for optimal growth with a formalised expression for the saddle path. The model which is also supported by a generated numerical example, is analysed and compared to the other version with a particular attention to the golden rule path, discussed for instance by E.Phelps (in 1961).