When Does Saving Power Save the Planet?

The computing industry accounts for 2% of the world's emissions. Power-efficient computing is a frequent topic of research, but saving power does not always save the environment. Jevons' paradox states that resource savings from increases in efficiency will be more than compensated for by increased demand by a process called rebound --- making these ineffective ways to decrease emissions. This is not the case for all applications within computing: applications whose demand is inelastic with respect to power consumption can have reduced power consumption. We analyze several large fields within computer science, including ML, the Internet and IoT, and provide directions on where power efficiency savings will help reduce carbon emissions. We present the economic tools needed to decide whether power-efficiency improvements are likely to result in reduced or increased emissions. We conclude that many problems in computer science do have characteristics of rebound, meaning that green energy is the only solution for many fields.