We calculate the cost of a carbon dioxide constraint in the production of electricity by modeling the replacement of coal generators with natural gas generators. We find: First, replacing coal generators with natural gas generators is the most economical way to reduce carbon dioxide emissions by 20 percent. Second, replacing existing coal generation capacity with modern coal generation plants can only reduce total carbon dioxide by 5 percent. Third, the distribution of the efficiency of coal generators in the United States restricts the range over which carbon dioxide prices effectively manage the displacement of coal by gas. Fourth, the narrow range for the price of carbon dioxide creates the possibility that a market in carbon dioxide permits will result in high volatility in the market for electricity. Fifth, the carbon prices implied by the transition from coal to gas will have very little impact on transportation fuels.