Oil (and gas) depletion is theoretical. If (this is within any forecastable period – ie not 2 centuries from now) oil production depletes, prices will rise dramatically. This will make oil financially infeasible as an energy source long before actual physical depletion.
Road transportation accounts for 2/3rds (approx) of oil use with around 2/3rds (approx) used for cars/motor vehicles. It is likely that most of that goes away. Jet fuel accounts for another 12% and this would likely reduce significantly once price increases.
Although it isn’t as cheap (today), it is also possible to make hydrocarbon feedstock from things like coal (which is far more abundant) or biomass (mostly renewable).
Far more of a problem is that gas prices would also rise significantly along with oil. Gas is not only used for energy but a lot of it is used to make fertilizer. Running out of cheap fertilizer means global food insecurity rises exponentially. Rich countries can probably afford it (although with far higher food costs) but poorer countries and countries with poor soil would starve.
Brazil, India, China, Indonesia (and a big bunch of other smaller countries) might have a huge problem because they use 2x to 3x the amount of fertilizer per acre of arable land compared to countries that have better soil. These four countries alone account for over 40% of the world’s population.
In short, plastics manufacturing would be the least of the problems should we run out of cheap oil.
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