The current jump in price is because one or more suppliers are dropping out. That shifts the supply curve to the left such that for the same demand for oil, the new price is now further up the steeper part of the curve (see the plots below).
The demand for oil will react to that new price, but it takes time.
Sorry that I don't have a more recent supply curve, however below is an old oil supply curve from 2007/2009 data. The numbers aren't exactly the same, but the idea still holds.
From left to right are the suppliers cost, including internal/political cost, plus profit (the gray curve). As you can see, Saudi Arabia's costs are the lowest while the cost for "Marginal Suppliers Level 2" are the highest. When a supplier like Libya drops out, his amount of crude (about 1.XXX million bbl/day) drops out, shifting part of the curve to the left by 1.XXX million bbl/day (the blue curve). If current demand is above that particular supplier such that he is currently supplying oil, when he drops out, price is pushed upward (on the graph, from about 100 USD/bbl to 120 USD/bbl). All remaining suppliers (including "big oil") now make 20 USD/bbl more for their oil. As a result, their profits go up.
The top plot is the complete supply curve. The bottom plot is the same curve, zoomed in to show the price change.
Archival, quoting your statements:
1) ".....Since US oil is higher priced they gain the most?....."
Not true. Explained below.
2) ".....Effectively the "big oil" has the "big market" and hence increases in price will effect them more than Saudi Arabia? If this is true then the big oil companies still have control of their profit and could surely reduce their profit to compensate for the increased in price and keep there total profit about the same? Since Lybia is a short term thing it would pass. I'm not saying a business has to do such a thing but it can....."
Not true, Explained below.
3) "....Suppose "big oil" were to keep there net profit the same this year as, say, last to reduce the price at the pump....."
Go back and look at various "big oil" Net Income Statements. Not every year is a profitable year. If "big oil" becomes unprofitable, we won't be driving what we're currently driving.
4) "....How much will it actually reduce it? Would it be drastically different(say 50c or more) or due to the huge market(millions of buyers) it would just be a few cents?...."
Can't be done. If I (you) was a shareholder, I'd (you'd) sue them into the ground.
Archival, you need to pay attention to how supply and demand works and forget about "fairness theories" and "they should do this.....theories" . If you honestly think "big oil" is making so much money, then couldn't you buy the stock and reap that "big oil money" for yourself? The deeper you get into the numbers, the more you'll realize why it is the way that it is.
I added the following Oil Supply Table to help explain what is going on in the graphs. This table, when plotted, is the supply curve above.
Key Point: On the spot market EVERYONE gets the same selling price. A barrel of WTI oil is a barrel of WTI oil (or Brent, or whatever grade). The Low Cost suppliers get the same price as the High Cost suppliers.
Column I is the name of the country/group, sorted by Cost (the Cost is all production costs plus "enough" profit to sell the oil). The first guy in the list has the lowest production Costs. That Cost shows up as Price in column L. This Price is the MINIMUM price that particular supplier/group would be willing to accept for his oil. Obviously, if the current price is higher, they'll take it, but if it's lower, they'll drop out. Column J tells you how much oil he has for sale, at that price or higher. This means that the Saudis will sell 10248 Thousand bbl/day for a Price of 28.23 USD/bbl or higher (any lower and they're out).
The next guy in the list is Iran at a Price of 28.24 USD/bbl. He'll sell up to 4.0 million bbl/day at his Price (28.24 USD/bbl), bringing the cumulative amount of oil available to 14.3 million bbl/day (column K). So, if demand is between 10.2 and 14.3 million bbl/day, the price would be 28.24 USD/bbl. That's for EVERYONE that is supplying oil, both Saudi Arabia and Iran (again, a barrel of oil is a barrel of oil).
In the above graphs, I started off with Libya still providing oil (the gray curve in both graphs).
In the second graph, I chose 83 million bbl/day as the example Total Demand (the red line in the graph). When you look at column K of the table, ALL SUPPLIERS up to and including the "United States (offshore 26% of total)" will be selling their oil at the going price. That price is somewhere between 93.57 USD/bbl and 115.66 USD/bbl (the graph is drawn with a linear interpolation between prices). From the second graph, on the gray curve, it looks like 100 USD/bbl is the going price.
So, before Libya drops out, to supply 83 million bbl/day of oil, the market (ALL SUPPLIERS up to the required demand) requires about 100 USD/bbl. Whatever "extra" (above "enough") profit they make is the difference in the market price and their Cost. EVERYONE that sells oil into that market gets 100 USD/bbl.
Now, Libya drops out (everything else is the same).
Column N shows what happens to the Cumulative Production when Libya drops out. Everything is the same above the pink line. The cumulative supply available in both column K and N up to Algeria is 78.8 million bbl/day. However, since demand is 83 million bbl/day, more suppliers are required to fulfill demand. With Libya out, you have to go all the way up to "Marginal Suppliers (Level 1)" to fulfill demand. Their Cost is 145 USD/bbl. From the second graph, on the blue curve, due to interpolation, the going price is now about 120 USD/bbl.
So, after Libya drops out, to supply 83 million bbl/day of oil, the market (ALL SUPPLIERS up to the required demand) requires about 120 USD/bbl. Since this is now 20 USD/bbl higher than before, the profits of ALL SUPPLIERS that are selling oil will jump by 20 USD/bbl.
Notice that no one manipulated demand or supply, and that the SAME supply curve was used both times. The only thing that changed was, Libya dropped out.
Now, go back and think about how you would implement ANY kind of "fairness theory" or "they should do this....theory". The supply curve is the supply curve. It depends on the Costs of the suppliers and how many suppliers are available to provide oil. It's that simple.