Evidence from the PJM and New England electricity markets illustrates the benefit of using observed bid data to better understand the strong relationships between fundamental supply and demand factors and power prices. Exploiting the high correlation between movements of bids and fuel prices, we propose a parametric form for the bid stack function in order to construct a fundamental model for spot power prices. This approach allows for the investigation of possible merit order changes and fuel switching, which are considered key factors impacting prices of carbon emissions allowances. We therefore adapt the model to construct an equilibrium carbon price model, which can begin to capture the important but complicated dependence structure between CO2, electricity and other energy prices.