Charles Talleyrand wrote:

What's the cheapest cost to orbit a chemical rocket is likely to
yield in the next fifty years? Will we see $100/pound to orbit?
How about $10/pound? And what underlying technology will
this rocket use?

Depends on what you're planning to send. For example, if your payload is
capable of withstanding, say, 50 gravities, you could launch via a railgun
(a la Jules Verne). You'd only need a 60 km long rail. Cost to orbit
would be just about nothing; the main expense would be amortizing the
railgun cost, and the technology is basically "off the shelf." There's
been talk of building a prototype along Mauna Loa (nice, tall mountain near
the equator and in the middle of the ocean so neighbor's don't complain
about the noise).

You could use the railgun to cheat a little; at a modest 3 gravities, that
60 km railgun would get you up to about 2 km/sec. Not sure how much that
would cut your cost-to-orbit, but it would probably be a significant
amount.

Jeffs