Does anyone know what a stairlift costs?

dtripli, before installing a stairlift, see if you can find one for a test drive.

If you are getting one for someone else, make sure they are comfortable with using it. It's better to know now then spending time and money having one installed... it is used once.... then never used again.

Yes--ask lots of questions about why you want to install a stairlift! I found that talking through this issue with several people led me to thinking of options I hadn't considered and making very different--and better--decisions. I tend to want to hurry up and get whatever's needed--or seems to be needed--asap. This experience taught me to slow down. :-)

l did a DIY installation of an Ameriglide stair which cost $2500 delivered. That was for a straight run interior stair about 9 foot height. The exterior stair, also a straight run, was installed by a local company and is a higher quality (Bruno Elite) and cost about $5500 installed. The first time we installed an exterior stairlift we chose a used unit they had removed from somewhere else after one years use, but I don’t think the money saved was worth it in our case. We had to replace it after about 5 years. We live at the beach and anything metal corrodes quickly in the salt air.

They're more expensive for curved staircases or one with a landing where it has to make a U-turn.

Contact a store where you can buy medical equipment, and chances are good you can buy a refurbished, used one. They're sold by sections of track, so the price is going to vary depending on the length and shape of your staircase.

We bought a used one for my mother (straight stairs) for about $3000, then after she moved out, we sold it back to the same medical supply store for about $300. I considered it a rental, and it was well-worth the cost.

we have about 15 steps going straight up to the 2nd floor it was$3,200.

Don't hold me to this - because I don't have a lot of actual experience - my FIL's stairlift was paid in full by the VA (thank goodness). When my mom priced one for their split level home for my dad, it was going to be in excess of $15,000 to install (this was approximately 8 years ago) - I believe because it was going to have to go from the garage up 7 stairs and then turn a corner and up 7 more stairs so that he could have access to the main floor and the second story (so essentially they would need two I think is how it broke out because the corner turn would block egress for others). Eventually it was easier (albeit more expensive up front) for her to build an addition to their house that was ground level access with a handicap accessible bathroom that dad could literally just roll right into with the walker or wheelchair and have an accessible shower as well and that would also see her into her golden years as well. (and this also added to the value of the house, while the stair lift would just have to be removed when getting ready to sell).

Why is it whenever you ask about the cost of something people will tell you "it's expensive!" or "they're not cheap!"....those terms are meaningless because what is considered expensive by one person may be well within the range expected by another.
It's been a while since I did any research on this so I can't quote a price, but I do know that things like the curves mentioned by Tynagh bump the price up exponentially. I also know that simple straight systems can be found used through resale sites or from the dealers, you ability to take advantage of that would depend on whether you have DIY abilities.
Also another forum member likes to caution people considering stair lifts to try one out first, it's a big expense if someone is too frightened or is cognitively unable to use it!

Yes, aren't cheap and hard to sell because they are custom fitted.

It is not cheap. I purchased a used one that had to be worked into a curve to allow the "rider" to stay seated while on a landing. It cost about $8K.

The only way you would know for sure for YOUR cost is to call several places in your area that sell and install them.
I would think that each would be different depending on complexity of the stairway and how long of a run would have to be installed.
I would also suggest that you ask about USED ones that they may have removed after they were no longer used.
NOW...
Please think ahead on this. Is there a possibility that other adaptations could be made so that installing a stair lift would not be necessary.
I am going to assume that in time stairs will not be the only change that might have to be made.
Is there a bathroom on the floor that this person will be using that will accommodate the use of equipment to make bathing/showering safer? Are the halls wide enough and door ways wide enough for equipment.
Will a hospital bed be able to be placed in the room that is used to make caring for this person safer?
Is there an area on the main floor that would be able to be used as a bedroom that will eventually make taking care of this person easier on the caregiver(s).
A main floor room will also make it easier to keep this person engaged with the family not isolated on another floor.