This study compared carbon tax and cap-and-trade systems to reduce pollution and encourage clean innovation. They found that both methods help cut emissions and boost innovation but that cap-and-trade is more effective than a carbon tax. Under a carbon tax system, companies might lose money, but with cap-and-trade, it's less certain and depends on the limits set. The study backs using cap-and-trade to fight climate change, but recommends setting the right emission limits and trading prices for it to work best. Different goals call for different pollution tax policies to be effective.