How much? A lot more than you could afford, and probably more than the government could afford. The most effective climate dimming agent is said to be sulphur dioxide,sprayed into the upper atmosphere, where it reflects the sun's rays back into space. Smoke and dust particles also have a dimming effect if there is enough of them. We get both of these effects when there is a massive volcanic eruption like Pinatubo in the 1980s, or better still, Tambora in 1815.
The trouble is that the effect doesn't last very long. Pinatubo had a very slight effect for about a year, Tambora (the most massive eruption in historical times) a more dramatic effect for several years, but global warming persists for centuries. The dust eventually falls to earth, the SO2 becomes acid rain and wreaks havoc with buildings and non-resistant structures on the ground. If you were an eccentric billionaire and wanted to do it, you wouldn't be allowed to. It wouldn't achieve the effect you wanted in any case, but if you went ahead regardless and the expense of the project didn't bankrupt you, the law suits by people damaged by your pollution would.
As you say, pollution inhibits plant growth, which is the opposite of what we need because plant growth reduces atmospheric CO2.