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Load-based trading of CO2 places responsibility for reducing emissions upon retail suppliers of electricity by requiring them to buy energy from a mix of sources so that their weighted emissions do not exceed a given standard. It has been argued that load-based trading would solve the problem of emissions leakage, cost consumers less, and provide more incentive for energy efficiency than traditional source-based cap-and-trade programs. Because pure load-based trading would complicate the operation of spot power markets, variants of load-based trading (the GEAC and CO2RC proposals) that separate emissions attributes from energy have also been proposed. We present models of the pure load-based and source-based trading that calculate equilibrium prices, along with consumer costs for the case in which these systems cover essentially all producers and consumers in a market. We show that load-based programs are equivalent to source-based trading in which emissions allowances are allocated by various rules, and have no necessary cost advantages over traditional cap-and-trade systems. As avoided costs of energy under pure load-based trading are the same as in source-based trading, the former provides no additional incentive for energy efficiency. However, load-based programs impose additional administrative costs, so source-based trading programs are to be preferred to load-based trading.