Abstract: The coming peak of fossil fuels may cause shortages in the energy supply and major disturbances on the global economy. The forecasts for the future of our way of life are very divergent depending on the prediction used for the future human access to energy. Steady-state or collapse seems to be the two most probable scenarios for society after the fossil fuel peak and exhaustion of mineral resources that the new energetic mix will require. The LINEX production function, which is dependent on the energy input is used to model the gross domestic product (GDP) of a western economy in several different energetic scenarios after the fossil fuel peak. A future steady-state economy with zero population growth appears as the best possible scenario. Some of the implications and challenges derived from this steady-state economy are discussed.