According to Pearson, an already existing fiber material called M5 would be sufficiently strong to build a lunar space elevator [ comment: Moonstalk]. His calculations show that a cable with a lifting capacity of 200 kg (440 lbs) would have a mass of only 6800 kg (15000 lbs).The spool of cable would be large, however. It could be a problem with its size- you have to fit it in a cargo area that would be compatible with an available launch configuration. Since you need 38,000 miles or so of cable, the spool will be large.
The cable would be deployed from L1 until it reaches the surface. From there, it would be anchored down and further strengthened so that it can carry heavier payloads. With a lifting capacity of only 200 kg, this would indicate a need for heavier payloads. It may take multiple cables for that purpose, if that is the idea. It doesn't appear that passengers will be able to use the Moonstalks. They may be very useful in delivering cargo cheaply and efficiently, however.
A couple of Moonstalks, on each of L1 and L2 Lagrange points, would simplify transit between the surface and into space.
In order to colonize the moon, there will need to be some economic reason for its existence. In other words, how do you make money from this enterprise? If income isn't feasible, then how might you save money?
One thing is clear: getting stuff from the lunar surface and back into low Earth orbit should be cheaper than getting it from the ground into LEO. A Moonstalk would make it even more affordable.
One possibility would be solar panels which could be assembled and put into GEO. Once there, it can generate electricity and beam it back toward the ground. The panels can be manufactured on the lunar surface and sent up piece by piece to a station at the L1 Lagrange point.
Or, power could be supplied to spacecraft traversing Cis Lunar space. This would defray expenses in traveling from the Earth and back.
If operating costs were to be diminished enough, small amounts of goods transported from the lunar surface could make the entire enterprise self sufficient.
What goods, though? Some have suggested using lunar water as a fuel supply. This could make a mission to Mars much cheaper. The fuel could be transported from the poles to the Moonstalk, and from there onward to the Lagrange point. It would fuel the spacecraft at that point for its journey to Mars.
Furthermore, lunar water could be useful in growing food. Not only food to sustain a crew on the moon, but food for Mars missions. A substantial portion of food supplies from the moon could save a lot of money for Mars missions.
A more ambitious possibility is manufacturing stuff for use in space. Let's say you could build rocket engines and launch them from the lunar surface. Or build them piece by piece, send them up the Moonstalk, and assemble them at a Lagrange point. Together with being supplied by lunar fuel, a lot of the cost of the Martian expedition could be taken care of by the lunar colony itself.
In reference to the need for an anchor in space of over 6000 tons, the following source is cited.