No one will develop space until it is economically equal or preferable to do things there versus here. If it costs $1million to move a pound of Element X from the moon to Earth, no one is going to mine it until it's comparable to the alternative (mining it here). IF AND ONLY IF Element X reserves on Earth get so depleted that E-X costs ~$1M to find and recover via earth mines, will someone get the capital to go out and get it from the moon.
A space-faring civilization with even a vaguely market economy will be, by its nature, hyper-hyper-inflated compared to ours. Resources will be (no pun) astronomically priced, because no civilization will leave its own world en mass before it has stripped it clean of anything useful.
Until we reach that point, all space expeditions will be for flag planting and science nerds. The sole provinces of governments and non-profits.
Your analysis omitted one factor.
One pound of Element X may be chaper to exploit on Earth than on a near-earth asteroid (for example), but 1 billion pounds of Element x may be cheaper to exploiit on a near-earth asteroid than on Earth.
Because any extraterestrial mining will require a large initial investment (much more than any earth-bound mine). But once the necessary apparatus is in place, it will be much cheaper to dismantle a near-earth asteroid made from Element X and send the bounty to Earth than to dig continuously for scraps (comparatively) of Element X.
In conclusion - on the short-term, extraterestial mining is, indeed, priceier than earth-bound mining. On the long-term, it can be much more profitable.