There are a ton of unknowns. I think the general consensus is that if it works roughly as hoped, we'll see a 30% drop in launch costs almost right away (within 1 year). Over time, that will improve a little (60%?).
The thing though, is that the price of launching a rocket has more to do with insurance, special needs and so forth. So the question depends on who's perspective you are asking.
A big science mission spending 100m on insurance alone and 180m all told getting 10m off won't care much, particularly with a $5BN total mission cost! For them, SpaceX simply having more flights and not exploding will provide the largest price drops. The insurance rates will go down as reliability is proven.
A commsat might care more about timing. 6 months of delay might be worth many millions.
The group that will benefit the most from this are the cheap and often cutting edge projects. So all the crazy ideas out there, asteroid mining, space hotels, cube sats. And all the regular stuff, constellation launches, no rush science missions, LEO deliveries etc.
Reuse is really only one way that SpaceX is cutting costs for customers though. Streamlining the process of prepping a sat, doing the paperwork, and actually launching is huge, and proving reliability is perhaps bigger.
Alternatively, might SpaceX continue to charge close to the current going rate, and simply use re-use as a way to increase their profitability...
No way. SpaceX won't lower prices hard enough to take ALL the flights if they can but literally keeping competitors afloat would be their main reason to not lower prices further. If the US government steps in to keep ULA alive though, expect fairly thin margins. Musk is very much of the belief of "if you build it, they will come". The idea is to get the price SO LOW that new markets form and help sustain them.
Keep in mind that this is a privately held company because a public company would demand SpaceX show profits. The goal is about lowering the barrier of access to space AND to get us to Mars. That is all. If SpaceX goes bankrupt and a Martian civilization is formed, Mission Accomplished.