Well, here's a breakdown of the basic materials needed to add a simple handrail with balusters and a newel post at the bottom (no runner):
- Newel post (at the bottom end): ~$35-$40
- Wooden pickets (balusters): $5 each, you'll want at least one per stair and maybe two; I count at least 10 stairs that would need balusters so $50-$100
- Handrail: $35 for 8' ($55 for 12'; you'll be cutting it down to fit rather than joining pieces)
- Misc glue, nails, screws to put everything together; paint/stain/finish for raw wood.
So, materials cost would probably run you about $250-$300; the rest of that quote is direct labor and overhead. Not being a GC you can take this next part with a grain of salt, but I would expect this to take two or three guys one day to do, so at $50/hr (that may be high or low as a standard rate for the average construction jack, but for a master tradesman that's about right) you're looking at $800-1200 for the labor. So, I'd more realistically expect a total estimate between $1200-$1500. A $2000 estimate isn't terribly excessive, depending on what your buddy had in mind, but I would get competing bids including a basic design.
The design I'm thinking of for this bid is very simple; put the newel post in at the bottom stair and anchor it in, bring the rail up to the bottom plate of that ceiling-to-wall transition (that has to be pretty darn solid to meet code so there's plenty of lumber to tie into) and then cut and nail the balusters down directly into each stair. The major complication would be the need to pull back the carpet from the outside edge of the stairs to install everything, then cut and re-seam the carpet around each of the balusters. Not impossible, but it adds an extra twist to the job.
If the contractor looking at this wanted to add a runner down the side of the staircase that would form the base for the balusters and the newel post, that's considerably more effort. That requires de-carpeting all the stairs, and possibly building in supports under the outside edge of this staircase for the extra weight, then building the runner, THEN putting in the newel post, handrail and balusters, before recarpeting the stairs. That could easily be a $2000 job.