"The market" has nothing to do with that because one single trade isn't a market; if you and I exchange 1g of gold for $1000 that doesn't say "gold is fairly priced at $1000/gram". If many people exchange gold for money, each with different information and desires, over time the gold will go to the people who pay more, sellers will generally trend their sale price down because higher prices won't get buyers, buyers will trend their buying price up because lower offers won't get accepted, and a range of "price gold is being traded at" values emerge, the spread of those values highest to lowest narrows and hones in on, and tracks a dynamic "price of gold" where it's "fairly traded" - not fair in some Deity decreed way, but fair in that if you trade at close to that price, you aren't buying unusually high or selling unusually low, you're getting no better or worse deal than anyone else, so it's not unfair in your favour or unfair against you, so if it's not unfair then it must be fair - you couldn't get a significantly better trade with anyone else.
Anything distorting those conditions - e.g. there's only one seller, only one buyer, a time constraint, a skill constraint, an information disadvantage, will distort the pricing as well. One trade isn't enough information for a market to exist or to settle on a fair price. I agree there that the market has nothing to do with it.
But I disagree with your implication of "the fair price is the one paid" is somehow unfair in an ethical sense. (I also think OP is in no way obliged to be "fair" in any ethical sense to the company, but that's another matter). The company got a $10M contract for $250k, versus losing the contract, is that unfair? If that really was the pivotal factor between losing the contract and not, the company ought to benefit by spending right up to the point where the contract becomes a money loser, to not lose it. Would it be unfair for the company to get an $8M contract by paying $2M? Or a $2M contract by paying $8M? Is OP obliged to help the company make as much profit on the contract as they can, by charging them less for his services?