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It's all very variable.Drillers. They have a minimum at what they need to sell it at. And that price is a select few. So if refiners no longer needed the quantity that they needed it at now, price would go up for refiners?
Economics of exploring for oil in the first place come down to multiple factors. Cost of that exploration which is location dependent. Quantity of oil realistically likely to be found and what it would cost to extract it and get it to a customer. Price of oil (revenue from selling it). Government fees, taxes etc.
Economics of developing a well where the oil is known to exist also highly variable. Cost to get a contractor to drill it (or for major companies, cost of continuing to employ your own crews, maintain your own equipment etc). Cost of roads, pipelines, power and anything else you'll need to build to facilitate it. Government charges and tax. And a really big one - return on capital.
What happens with interest rates has a huge influence over the economics of an oil field. Something that's hugely profitably in world of 1% rates could be too expensive for anyone to be even remotely interested in if interest rates were 10%.
That's the bit proponents of "Peak Oil" missed. They correctly identified geology, they're geologists after all so that's not surprising, and they correctly identified that the best oil is used first (pick the lowest hanging fruit) and so on. They also correctly identified that many individual fields and entire countries, including Australia, have indeed seen a peak and decline of their oil production.
What they missed was interest rates. They simply didn't consider that anyone would ever invest in something with the expectation of a 5%, or heaven forbid 1%, return on capital. They were thinking of rates very much higher than that, since that's what was normal at the time, and hence did their calculations on that basis.
Apply 1980's or even 1990's rates of return and lending standards and the US shale oil industry's completely unviable. Not a bit of a loss maker but rather something that's not even remotely close to being a viable business and which no bank would go anywhere near. Drop the rates low enough though and that changes everything.
So the answer to what price oil needs to be in order to be profitable depends on other things basically. That is, is a 1% return per annum considered profitable? Or are we talking about 20% being required? That makes a massive difference.