If we assume that the "law" of supply and demand holds then prices go up when demand increases, but how much they rise is unspecified by any theory. One can draw a line ex post facto, but that's not a theory.
Something has happened in the oil market over the past decade or so which none of us understand, including the "experts". Look at all the theories: speculation, hoarding, the rise of demand in China, etc. What these theories all have in common is a lack of actual data.
Just looking at other markets in history, it is usually the case that a sharp rise in prices is related to a speculative fever. This has been true for everything from tulips to US homes. It seems highly likely that oil is another instance of this.
Now what is missing is any indication of who the speculative players are. I would guess that they are to be found in the oil producing states and connected with the government in some manner. The lack of reliable reserve and production figures makes manipulation of markets easier.
Oil will rise again when the alternative energy suppliers have been driven out of business or, at least, severely weakened. There is already an economic collapse going on in the Canadian oil tar fields with thousands of workers being laid off. The low prices don't support the cost of extraction.
As with any monopolist enterprise driving the competition out by using low prices gets followed by a return to fixed markets. Jerome is right, just wait awhile. Policies not Politics ---- Daily Landscape
It may be that unusual swings in prices are normally associated with speculation, but it's also true that a swing of $140/barrel to $40/barrel is not an extraordinarily big swing for a commodity market. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.
The shape is not specified by any generic theory, of course, because a generic theory must accommodate a wide range of supply conditions, but the generic theory does specify the determinants of the shape of the supply curve. Under the Peak Oil theory of oil supply, from the neighborhood of the oil peak onwards, the supply curve is:
... which is to say, marginal cost of production for existing fields, then transitioning to a bidding war allocation at the production maximum. Over time, exhaustion of the lowest cost of production fields will lead to the supply curve shifting up and in. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.