I. Economic Evaluation of Negative Externalities

This is an economic discussion of carbon taxes and other economic proposals that address negative externalities. That said, why does a carbon tax theoretically reduce the amount of CO₂ emitted into the atmosphere and improve on market outcomes? This discussion requires a clear understanding of economic efficiency and cost minimization. (For example, you could use the equation MP₁/w₁ = MP₂/(w₂ + t), where input 2 is carbon-intensive input, to explain how a carbon tax affects firm production decisions). Moreover, please help me answer the question in-full and provide an in-depth comprehensive explanation along with it.