Policy makers and analysts are often faced with situations where it is unclear whether market-based instruments hold real promise of reducing costs, relative to conventional uniform standards. We develop analytic expressions that can be employed with modest amounts of information to estimate the potential cost savings associated with market-based policies, with an application to the environmental policy realm. These simple formulae can help increase intuition and understanding of the sources of cost savings, and help identify and design instruments that merit more detailed investigation. We illustrate the use of these results with an application to nitrogen oxides control by electric utilities in the United States.