How I understand it is this: Everyone creates 100 units of pollution together, say ten firms producing 10 units each. Then they say, you can only use 90 next

How I understand it is this: Everyone creates 100 units of pollution together, say ten firms producing 10 units each. Then they say, you can only use 90 next year, 70 the next decade, 50 the decade after. Everyone needs to reduce pollution a bit, this is hard. Some have a 50 year investment in a factory that they can't remodel to pollute less. They'd need to shut down. Others are more flexible, they can remodel existing infrastructure, or shut down ones that are near the end of their lifetime. But why would they make investments in something more clean? Trading means one firm producing 10 units can invest in efficiency. Next year it's allowed to produce 9, but its new tech only produces 5. It can sell the other 4 to four factories which couldn't reduce their emissions from 10 to 9. Over time the polluting parties have funded the non-polluting parties' clean technology, while over time the total pollution has gone down. Moreover, it'll incentivise the lowest-hanging fruit approach, i.e. reduce emissions where it's cheapest to do so, first. That's why it's called cap-and-trade, not just trade.