To specifically answer your question, the cost of oil will rise as “easy to extract” fields run out and so oil companies develop more “difficult to extract” oil reserves. As oil prices rise, demand for oil drops until supply and demand reach a new equilibrium. All basic economics.
Demand for oil can drop quite easily as people can, for example, drive less and use more efficient cars etc. Just look at the average efficiency of cars in US vs. Europe, which is entirely the result of the higher pump prices of oil products (which itself is due to higher taxes). Consumers can also substitute oil products for other energy sources, such as electricity generated from natural gas, coal, nuclear, solar, wind, hydro etc.
So, in a “peak oil” environment, rich countries will face higher energy costs but will ultimately make a transition to electricity. Poor countries with energy deficits will suffer enormously as higher energy costs (whether from importing more expensive oil or having to rely on more expensive alternatives) will act like a “dead-weight” cost to the economy, slowing down economic growth)ANSWERS： Oil wells will not run out suddenly. What will happen is that the most easily accessible (and cheapest) sources will be consumed first. Then we turn to other more difficult and more expensive sources like offshore oil wells. Once they are gone we go for even harder to get sources like shale oil or making oil from coal.
This is a gradual not a sudden process. But before all that happens, the price of oil will go high and this will make other sources of energy like renewables, fission, etc seem cheap. That will spur their useANSWERS： They aren’t going to run dry all at once, no advance notice, and there are a number of other sources for petroleum than those wells. But, assuming all petroleum production came to a screeching halt. the whole world would be in some serious hurt. Ships at sea could make port, but wouldn’t be able to leave again. Before long, everything that requires petroleum products to move, or to make, will come to a dead halt. There are some petroleum substitutes out there, but nowhere near enough to replace petroleum in all the places it is currently used.ANSWERS： Then the oilsands and shale deposits will become vastly more valuable. There is as much oil in the Athabaska oilsands as there is in all Saudi Arabia. Anyway, oilwells don't suddenly run dry without divine intervention, and if some god or other decides to shut off the flow of oil, humanity will have a lot more to worry about than that…..