Some environmental policies focus on emissions intensity rather than total emissions, or they try to mitigate the regulatory impact on the final product market. To analyze the effects of these policies, or to evaluate the distributional effects of any regulation on consumers and producers, output must be incorporated explicitly into an economic model of abatement, separately from the emissions variable. This provides two options. Traditionally, total emissions and output are the independently controlled variables, leaving emissions intensity as endogenously determined. Alternatively, one can make emissions intensity and output the control variables, leaving total emissions as the endogenously determined variable. One is the dual of the other and the problems are equivalent, but the latter method offers more transparency for examining intensity-based policies. This note shows how the intensity-based model fits into the traditional context.