As an economist, I'm certain that the more expensive something becomes, the less demand there will be for it.
Is it an effective way? It is certainly an effective way. I'd say it's not the only way. As all people in the field know, there's also regulation. That's one way, and subsidies are another way, but generally speaking, the consensus among economists is that a broad-based price on carbon is the least disruptive way to reduce greenhouse gas emissions.