Remember in the current Falcon 9 design, they are only reusing the first stage -- reported to account for 70% of the
cost of the rocket (which is of course different to the retail price of launch service), and attempting to recover and reuse the fairing, an aluminum honeycomb core + carbon fibre sheet enclosure the size of a city bus, which is thought to add a couple million dollars per rocket including capital costs (SpaceX is thought to have limited capacity to produce fairings at a high rate, which is why they're chasing reuse).
They still need to rebuild the entire second stage each launch, and continue to pay the salaries of 4,000+ employees.
If the end-to-end launch service is priced at $60 million, 70% is $42 million, with the other 30% ($18 million) that needs to be paid each launch. Assuming the cost of all re-use is 100% free (gas and go), a full passing on of the savings would mean the second launch (which has a free first stage) could be priced at $18m + ($42m/2) = $39 million.
That's a 35% discount off $60 million. SpaceX haven't proven that reflying a returned booster is safe and reliable. It will take many relaunches to gain statistical knowledge of safety of the fleet they're building.
If SpaceX can reliably relaunch the first stage 5-10 times with minimal refurbishment costs, the amortized costs drop dramatically. During the development of the Merlin 1, testing aimed for 10 full duration (3 minute) test fires. I can see SpaceX aiming for 5-10 flights per booster with the current iteration of Falcon 9 over the longer term.
I encourage anybody interested to play around with this spreadsheet [1]. If the current design can be proven to have say 5 launches per Falcon 9 booster, that's a 65% saving to SpaceX. Falcon 9 is already the cheapest vehicle in its class (though some providers are cost competitive if doing dual launches on say, an Ariane V). The Russia's Proton rockets were reasonably cost competitive, but their reliability has proven to be very low in recent times.
As Amdahl's Law notes, as the number of reliable relaunches per rocket with minimal refurbishment costs increases towards infinity, the total cost will asymptotically approach the currently non-reusable portion of the costs (so in the current design it's the second stage, launch operations, fuel, fairings etc)
In a few decades, SpaceX wants to get airplane like re-use (fully re-usable with thousands of flights per vehicle lifetime), where each passenger pays a marginal cost of roughly the jet fuel cost and inspections and refurbishments don't happen every single flight but at set intervals. That's a probably several design generations away though (human Mars landing will certainly happen first)
[1] https://docs.google.com/spreadsheets/d/144Y_OVmFFYTh_zTiV-FH...