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A carbon tax is a promising tool for discouraging the greenhouse gas emissions that cause climate change. In principle, a well-designed tax could reduce the risk of climate change, minimize the cost of emissions reductions, encourage innovation in low-carbon technologies, and raise new public revenue. But designing a real-world carbon tax poses significant challenges. We analyze those challenges from a public finance perspective, emphasizing three tax policy design issues: setting the tax rate, collecting the tax, and using the resulting revenue. The benefits of a carbon tax will depend on how policymakers address those issues.