Is there a Halacha on how much profit can a person make on something?
For example, assuming that market forces won't lower the price on a product (I'm a natural monopoly), can I have a 1000% markup?
As far as I'm aware, as long as you haven't violated the prohibition of "אונאה," you're in the clear.
There is a prohibition of "אונאה/overcharging," which is defined as overcharging by more than 1/6 of the market price (see the mishna on Bava Metzia 49b). However, this prohibition doesn't apply to everything; notably, real-estate is exempt from אונאה (Bava Metzia 47b).
Your case would be one where there is no market value:
[...] When there is no existent market for an item then Onaah does not apply (Hilchos Mishpat page 294). [...]
(from the Rabbi Hoffman article)
Since the laws of אונאה are pretty complicated, having a few simanim (chapters) of Shulchan Aruch discussing them (starting at CM 227), it's best to ask a rabbi for the specific halacha in any given case.
I believe there's a Gemara that discusses a maximum of 100% margins on food, though I don't know how actively that's used today. (If I recall there was some fellow who begged the local rabbinate to impose protectionism against a new competitor of his; the rabbinate replied that their attitude until then had been laissez faire; if they were to step in, then they would also enforce the policy of maximum margins, as well as demanding to see his books to determine that in fact the upstart was impinging on his livelihood.
There's an mp3 where Rabbi Yitzchak Breitowitz acknowledges that other than the 100%-on-food comment, there's not traditionally a lot in the literature about this. Ona'ah is the prohibition of mis-representing the going market rate for a product, assuming there is one. (He admitted that by that definition, if several sellers colluded to raise the market rate, there would be a new market rate and ona'ah wouldn't apply.) We're dealing with much bigger businesses than those in Talmudic times; thus, some local rabbinates will choose to apply other controls in the best interest of consumers.
We also have the Gemara in Pesachim where there was a town whose practice was to buy new clay pots after Pesach (as the chametz pots were deemed not kosher). The new rabbi in town told the pottery sellers that if they marked up their prices, he would respond with halachic policy by pronouncing that the buy-new-pots practice wasn't necessary. (Similarly, it's said that ... was it the Baal Shem Tov or the Baal HaTanya? told his followers to stop buying fish before Shabbos, as the fishmongers were making the Friday prices far too high.)