[loudmax]

Exactly. Overcoming Earth's gravity well is the reason building a space elevator is such an exciting prospect.

The geosynchronous orbit is about a 10th of the way to the moon, so this moon elevator would go 9/10ths of the way toward the Earth. That's significant but it's precisely that remaining 10th of the way where the vast majority of energy expenditure occurs. If you can make it from the surface of the Earth to geosynchronous, then making it to the moon is relatively cheap.

[narag]

Not orbit, the Moon doesn't orbit the Earth in one day, but a month. The cable would be almost stationary compared to orbit. That needs less power.

[peeters]

Less, but not much less. Around 12 km/s instead of 14 km/s.

[narag]

Escape is 11.2 so something must be off.

Edit: actually you don't need any specific speed. Reaching orbit does, around 9 km/s for low orbit, vertical uplift doesn't.