As antibiotic consumption grows, bacteria are becoming increasingly resistant to treatment. Antibiotic resistance undermines much of modern health care, which relies on access to effective antibiotics to prevent and treat infections associated with routine medical procedures. The resulting challenges have much in common with those posed by climate change, which economists have responded to with research that has informed and shaped public policy. Drawing on economic concepts such as externalities and the principal-agent relationship, we suggest how economics can help to solve the challenges arising from increasing resistance to antibiotics. We discuss solutions to the key economic issues, from incentivizing the development of effective new antibiotics to improving antibiotic stewardship through financial mechanisms and regulation.