You omitted many components that would go into pricing such as your location. "Wall construction" isn't as simple as it sounds. The structural elements of the home will have to be identified to see if the additional load of the wall, although minimal, would be too much for a joist span to support without additional support from below. The electrical and HVAC will needs to be altered and/or added for the new walls, in addition to the cosmetic finishing of them. It could cost anywhere from 2K-10K+ depending on these issues and the quality of materials used.

As a design consideration, small very tall rooms are very very awkward feeling spaces, not very "study" like at all. I'ts a matter of scale, and closing in a large tall room to create two smaller but tall rooms violates that scale. If you are partitioning off this space with a 17' foot ceiling, you might consider also dropping the ceiling and creating a second floor space out of it as well, even if it's just done as additional storage. A 8' tall smaller space plus an 8' second floor space will make a lot more sense than a single 17' tall space. If you used dimensional lumber to support that second floor, you could essentially have the wood subfloor and beams that support that second floor be visible a an architectural element below in the "study".

Imagine a vibe like this with bookcases lining the wall.
{{!gwi}}

It would also make the project a bit simpler from a construction aspect (but not cheaper because of the additional labor and material) to construct two 8' walls and tie the floor/ceiling joists into the existing structure than it would to create a single 17' tall wall.

We thought about adding the second floor, but decided not to do it because of the cost. We'd have to redo the open stairwell.

I know it's possible to do it in our house because it was an option when it was built. The original owners decided on the formal living room instead. Surprisingly, it doesn't look awkward when I see it in other houses with the same floorplan. We don't have to worry about HVAC because there is a vent where the office would be. The dining area has it's own vent, too. So, it should work out in that aspect. I'm thinking the cost will just be the walls in our case.

I would love a drop ceiling, but we can't do it because we have windows near the ceiling. It would look better, but I think I'll put crown about 10-12 feet up and paint the bottom a light color and the top a darker color. It visually brings down the ceiling. We have already done that in the room with very tall wainscotting.

Thanks for the comments because those are important things to consider.

There is a HVAC worry---along with the vent, there has to be an air return for each space as well.

Air return? We only have two air returns. One is downstairs in the family room hall toward the back of the house and one is upstairs. I don't have one in each room. Unless I'm misunderstanding what you mean by air return.

Any room with a HVAC vent---to allow conditioned air into the room, should also have a cold air return.

Without the returns, air cannot be moved efficiently in a closed space.

Many older houses were not built with enough air returns simply because the houses were so unsealed air could move through the cracks. Makes heating/cooling bills MUCH higher and comfort levels much less comfortable.

Adding more walls simply adds more barriers to the air movement.

"Any room with a HVAC vent---to allow conditioned air into the room, should also have a cold air return."

Numerous houses have been built since the start of forced air without per room returns.

We have a newer house. I've never seen a house with an air return in each room. Maybe they are built different regionally?

My house was built in 1965. There are air returns in every room.

It is not a regional thing. It is a proper design thing.

Example: Bedroom. Two exterior walls. North and west exposures. Cold air return down the hall. Close the bedroom door---carpet leaves no gap under door. How is conditioned air going to get into and out of that room?

That is the point---it is not. Stale space, no air flow, room is too cold in winter, too hot in summer simply because air cannot move easily enough to actually condition the space.

Handymac is 100% correct. A proper HVAC design allows for return vents in each room that is served. Anything less than this is not a proper design and is done that way for cost cutting purposes only. The builder cheaped out and the home will suffer from it. A lot of things were done questionably in my 70's era rancher, but thankfully, HVAC design wasn't one of them.

I inspected every house I went in this weekend for air returns, lol. Everyone had one per floor. Considering this is the norm here I'm not concerned.

Any other thoughts on building the walls?

Don't be so prideful in you home's deficiency. The "norm" in a lot of locations included maybe R-19 in your ceilings for insulation for a long time. I wouldn't live in a house that had that mistake either, even if it were the "norm" for the neighborhood. That wouldn't meet code in most locations in the US now, and codes are also becoming more concerned with air distribution through a home as well since home envelopes have tightened up considerably in the last 40 years. Lots of locations have instituted regulations concerning HVAC that include having proper returns, fresh air intake, and makeup air. Be proactive in addressing these issues in your home and you will have a more comfortable environment in which to live.

"Anything less than this is not a proper design and is done that way for cost cutting purposes only. "

And cost cutting is how you make housing available to more people.

Drywall replaced plaster around the 1950s almost completely in many places.
Is was strictly a cost cutting move.

And there was no insulation put in walls because heating was so cheap and there was no air conditioning.

To get efficient room air flow, there has to be a vent for air to be forced into the room and a return for the air to escape.

Basic physics. Like blowing up a balloon. Blow up a balloon in cold weather. The initial air is warm. But, pretty soon, you cannot add enough warm air to keep the balloon warm---simply because there is no way to get the cold air out.

Does it have to be that way? Of course not. You can go back to lath and plaster walls also. And wood stoves. And sweaters in the winter. And hand fans in the summer with the windows wide open---all like we used to do.

I used to live in a 1978 14' by 70' mobile home. I now live in a 1965 three bedroom house with a full basement. Because the house is insulated better---walls and attic----and the HVAC is properly designed, we spend less money yearly heating and cooling the house than we did in the trailer.

My neighbors house, more expensive, but slightly less square footage, and built later had three cold air returns for the entire house. She shuts off the vents in the two unused bedrooms and still has a higher heating/cooling bill than we do.

Adding cold air returns is a rather inexpensive addition---no matter if building or refitting. Really no reason not top do it when changing a furnace.

While I don't doubt that it would be more efficient to have cold air returns in every room, I really don't think that it's an "inexpensive addition" to retrofit that into a house.
A one storey house with an unfinished basement would be easy to retrofit, but almost every other configuration would be a lot more work with the addition of unsightly bulkheads.

For the record, my house only has a cold air return on each floor and I've never seen a house with one in each room.

Why would it need to be a totally separate "return". It seems to me, if there were some sort of wall "vent" it would function the same. Noise would also travel the vent, but noise travels under doors in Leaky houses too. So, for a study, why not consider just putting in a small, through the wall vent?