This contribution1 introduces a sectoral supply functions approach of equilibrium dynamics in the context of a simple model of overlapping generations with heterogeneous goods. The class of preferences that is here considered hinges upon an endogenous leisure motive and an elementary savings behaviour, that comes as a simpler alternative to the Diamond tradition in the benchmark contributions about the properties of overlapping generations economies with two industries. The presence of some institution making possible intergenerational transfers is shown to influence both the equilibrium aggregate factors shares and elasticity of substitution along a stationary equilibrium. Both Wealth-to-Capital and Golden Rule steady state equilibria being considered, the economies are categorised, either as Samuelsonian or classical, according to the sign of the transfers between generations at the Golden Rule steady state. The local stability properties of the various types of equilibria are successively investigated, the elasticities of substitution between the two inputs being emphasised to play a key-role for that purpose. Interestingly, the smoothing properties of factors substitution and their respective contribution to the obtention of the local uniqueness property may differ between the Samuelsonian and classical economies.