We develop an economic partial equilibrium model for energy supply and demand with capital and labor as production factors, and endogenous technological change through learning by research and learning by doing. Our model reproduces the learning curve typical for (bottom-up) energy system models. The model also produces an endogenous S-curved transition from fossil fuel energy sources to carbon-free energy sources over the coming two centuries. We use the model to study changes in fossil fuel and carbon-free energy use and carbon dioxide emissions induced by carbon taxes. It is shown that induced technological change accelerates the substitution of carbonfree energy for fossil fuels substantially, and can increase by factor 5 the cumulative emission reductions achieved through a carbon tax over the period 2000-2100.