Most AC units now-a-days have a power saving mode. This cools up to a certain temperature and then turns the AC off when it has reached the specific temp. I think running the fan is going to run about the same amount of power as running the cool setting. Try updating your AC unit and it'll save you money in the long run.

The compressor inside the unit is what uses the most electricity. You will be consuming a lot less power with the fan on by itself.

Running your fan on continuous during the summer heat will help save you money because it will avoid air stratification . Since cold air is heavier than warm air it will settle in the lower part of the house ( basement) and the warmer air will rise to the upper rooms . By running your blower motor on continuous , the colder basement air will mix with the upper warmer air and keep a more even temp throughout your home and therefore shortening the running time of your power eating A/C outside.Also ceiling fan on the upper level of the house will help in controlling this phenomenon.