Because of the risk of breaking a cable due to micrometeorite impacts cables are not the way to go. In the space elevator games ribbons are used. The idea is to use a ribbon that is about 50 cm wide and x micrometer thick.

For those interested a few links:

euspec.warr.de/

www.spaceward.org/

liftport.com/



And for those in Europe who have a receiver that can receive 143.050 MHz in SSB.
This frequency is used by a radar located in Graves, France to determine satellite orbits. It also gives you and me the possibilty to hear meteors entering the Earth's atmosphere!
The meteor creates ionized air when it burns up high in the atmosphere and radiowaves are reflected off of that ionized trail the meteor leaves behind which you can hear with a radio.

charlesfradley wrote: The quantity of Zylon required for the 55,000 km elector [it is actually longer] is surprisingly modest, about 30 tons, which is less than one year's production of the fiber. Remember it is very thin, about 0.2 mm.

It would make a cheap practice run for when we build one on Earth. Obviously the greater lengthand the atmosphere will make things a little different., However, but building one on the Moon first some of the more basic issues can be resolved before we build the "Big One".