Recall that Shell (or any one company) is just a part of the fuel market. By boycotting one company for a day, a week, or a month, you're not changing any market factor. You're simply shifting demand from one producer to the other, which in turn, would raise the product prices from the producers from which you ARE buying. So the price of Shell gas might then be lower than Exxon...but it won't be because Shell dropped their prices -- it'll be because Exxon raised theirs.

The only way to lower your expenditure on petroleum is to use less of it.