I look at using chemical vapor deposition (and welding) to build a mono-crystalline, mono-molecular carbon space elevator over at The Space Review. Surprisingly, it will cost about what Brad Edwards budgeted for single-walled carbon nanutube (CNT) manufacturing.
If space elevators cost $25,000/kg and space delivery after the elevator’s up cost $10-$800/kg, then the second space elevator probably should be built out of less expensive, less exotic materials. If Kevlar is only 2% as strong as carbon nanotubes, you can still afford 50 kg of Kevlar for the price of 1 kg of diamonds at delivery costs and purchase prices less than $500 if elevator-quality CNT cost at least as much as bulk purchases of pure synthetic diamonds wholesale. One wouldn’t use Kevlar further down the elevator because then there would be a multiplier because we would need more Kevlar to hold the Kevlar and it would go up by a factor of e50 or so. But that doesn’t apply right at the base–it’s pretty much linear there.
Another issue I may explore is that if a Mars elevator can be 6 tons or less, it might weigh less than the fuel needed to take off from Mars or even the fuel and aerobrake to get from Mars geosynchronous orbit to the surface. Mars exploration economics change a lot if return oxygen can be carted up from the surface by elevator. Note that one would not necessarily need laser or microwave power to power a climber on Mars. Solar power for a climber would have it climb slower, but it would still climb.
A great place to work the kinks out of space elevator technology is the Moon. A Lunar space elevator going from a little ways Earthward of Earth-Moon L-1, would not need materials as strong as a space elevator for the Earth’s surface. If successful, it would allow much more mass to go down to the surface and much more return mass than the 46 metric tons of LSAM ascender and descender. A 7-ton Lunar elevator and some climbers powered from Earth would provide as much cargo capacity as Edwards’s starter elevator on Earth. Since Lunar exploration doesn’t really begin in earnest until late next decade according to the current (perhaps overly optimistic) vision, it might be worth doing some thought experiments about saving mass on the very first sortie to the Moon by using a Lunar space elevator. Pearson advocated this using M5 fiber to make a 7,000 kg Lunar elevator with 200 kg capacity a few years back. Forget thought experiments, launch the @$%#! elevator.