Peter Swan, president of International Space Elevator Consortium (ISEC), was quoted as saying that an Earth Based Space elevator could cost close to $10 billion to build and could reduce the cost of putting things into orbit from roughly $3,500 per pound today to as little as $25 per pound.
There is some carbon nanotube bundles that would be strong enough at 80 GPA of strength. However, there is less of this material than you would use to floss your teeth.
There will be a space experiment called the Space Tethered Autonomous Robotic Satellite–Mini elevator, or STARS-Me. It was devised by physicists from Japan’s Shizuoka University. They will 10-meter steel tether in space. This is like a toothpick bridge representing a proof of concept for a 100-mile long bridge. Again you do not have the equivalent of the 1000’s of tons of steel and cement.
The elevator car portion has not been proven beyond 1000 meters instead of the 50,000 kilometers.
The elevator cars have to go through the radiation belt.
If a fully reusable SpaceX BFR is built then 100 tons would be launched every time and only the cost of fuel would be needed. This would bring the cost of rockets down to $80 per kilogram launch cost ($32 per pound). A rocket system where construction has started, the engine is almost developed and some level of reusable rockets have been demonstrated has costs that are almost as good as a low-ball price estimate of a system where the technology does not exist.
The cost estimate of $10 billion for something 40,000 miles long. China spent $600 billion on high-speed rail lines using well-known technology and cement and steel from 2013-2017. China built shorter high-speed rail lines than the 40,000 mile length of the proposed space elevator.
No Space Elevator has ever been built and we have almost none of the required construction materials.
A 24-mile bridge was built in China for $2 billion. One mile long bridges in the US can cost $6.5 billion.
The $10 billion cost estimate seems like a silly and insane low-ball guess.
If the nanotechnology advances to make that much super-strong materials then vastly improved reusable rockets could be built or super cheap space planes would become possible that would be even lower cost than the proposed SpaceX BFR. The alternative advanced access to space would be cheaper than the space elevator using technology to make the space elevator possible.
We have the materials to make and deploy a lunar space elevator in one launch but we have not built it.
It seems the space elevator is an inferior design that is barely theoretically possible and which will not be less expensive.