"The most oft-quoted pricetag for Mir was $4.3 billion. That's just to build it (not sure if it includes the cost for putting it into orbit). Then you got to have the infrastructure to support it, both with round-the-clock ground control and monitoring, satellites, relay stations, and frequent resupply flights, which the Russians have quoted as $250 million per year. It was up there for 12 years... $7 billion total.

Any way you cut it, $7B is no small chunk of change. :-)

Based on that, I think that building and then maintaining a moon base, even a modest one, would cost far more than $10B."

With a moonbase, you could put one on the Moon and forget it was there for 20 years, and "maintain" the base. Or you could send crew every month to your lunar base for next the 20 years.
Maintaining the building on the Moon isn't a significant cost, unlike space station which at least needs to maintain it's orbit.

Nor does a moonbase need to be as complex as a station in orbit. Having some gravity changes how you design this thing.
You don't need to dock a spacecraft to a moonbase. The moonbase doesn't need the ability fly in a 3 dimensional space. It's basically a house which can maintain atmospheric pressure and has a airlock. It could be a shack, a cabin, a two bedroom apartment, office space, lab, warehouse, workshop, all of the above, or something else. It could be an inflatable shack, it could be a sealed cave (or lava tube), it could be a rigid dome, it could be made of lunar material, it could be merely a parked spacecraft.

Keeping a crew of 2 or 4 on the moon for long periods of time could pretty expensive. If all China wanted to do was keep a crew of 2 on the moon and say rotate them out with new crew every 6 months for 10 years- this could easily cost them more than 10 billion.

I think it would interesting to know the total amount of rocket fuel that Mir used throughout it's lifetime.
The total mass of rockets to put it into orbit and the total mass of rockets required to reboosted throughout the years.
I don't think this would equal placing Mir's mass on the Moon, but I think you could lift a prefabricated moonbase "similar" to Mir but which was designed for lunar living, oppose to living in zero gee.
-gb