The main objective of this work is to study the influence of population-economic relations to the atmospheric carbon cycle. It describes a conceptual model based on a fertility endogenous approach. Changes in the dynamic of population and economy modify the energy consumption and the amount of anthropogenic carbon emissions emitted to the air. The impact of the calculated global carbon emissions on the atmospheric CO2 concentrations is estimated through a carbon flux or carbon budget model. The model is organized in two modules: the first, computes population and macroeconomic variables as GDP, GDP per capita, energy consumption and carbon emissions. The second module calculates the carbon budget cycle (stocks and fluxes) through the atmosphere, ocean, soil and vegetation. This model shows that in the long run population decline will produce a decrease in GDP growth, which will contribute to a stabilization or reduction in the energy consumption and carbon emissions, associated to reductions in carbon and energy intensities. Nevertheless, due to accumulation process in the atmosphere, the atmospheric carbon concentration will not stabilize or decline in the next 100 years. Moreover this rate may change due to saturation processes modifying the amount of carbon exchanged between ocean and atmosphere, delaying a stabilization of the CO2 concentrations in the atmosphere variables.