Whereas Carbon Nanotechnology will be needed to create a tether on an Earth-bound elevator, a Lunar elevator is possible with current technology using high-strength commercially available materials such as Kevlar, Spectra or M5 Fibre according to https://en.wikipedia.org/wiki/Lunar_space_elevator
There are two points in space where an elevator's docking port could maintain a stable, lunar-synchronous position: the Earth-Moon Lagrange points L1 and L2. L1 is 56,000 km away from the Earth-facing side of the Moon, (at the lunar equator) and L2 is 67,000 km from the center of the Moon's far side, in the exact opposite direction. At these points, the effect of the Moon's gravity and the effect of the centrifugal force resulting from the elevator system's synchronous, rigid body rotation cancel each other out. The gravitational stability of these Lagrange points are not permanent, (L1 and L2 are in unstable equilibrium along a straight line between Earth and Moon,) but so long as small inertial adjustments are made to account for minor gravitational perturbations, any object positioned there can remain stationary.
Both of these positions are substantially farther up than the 36,000 km from Earth to geostationary orbit. Furthermore, the weight of the limb of the cable system extending down to the Moon would have to be balanced by the cable extending further up, and the Moon's slow rotation means the upper limb would have to be much longer than for an Earth-based system, or be topped by a much more massive counterweight. To suspend a kilogram of cable or payload just above the surface of the Moon would require 1,000 kg of counterweight, 26,000 km beyond L1. (A smaller counterweight on a longer cable, e.g., 100 kg at a distance of 230,000 km — more than halfway to Earth — would have the same balancing effect.) Without the Earth's gravity to attract it, an L2 cable's lowest kilogram would require 1,000 kg of counterweight at a distance of 120,000 km from the Moon. The average Earth-Moon distance is 384,400 km.
As a comparison, an elevator's journey from Earth will be around 96,000 kilometers, or about 59,651 miles, well beyond geostationary orbit (which is roughly 35,800 km altitude).
An estimated price tag for an Earth elevator is \$6 billion to \$20 billion USD using nanotechnology that still needs improvements due to length manufacturing limitations.
If you figure a low ball of \$6 billion for about 96,000 kilometers of materials give us around \$62,500 * 120,000 to a figure of around 7.5 billion
using a high tech solution estimate that is not needed.
A closer estimate would be approximately \$1.8 billion according to:
And the publication they got their numbers from,
Other interesting links: