It's inelastic in the short term, because there are limits to what people can do to change: they aren't necessarily able to immediately dump their existing car

It's inelastic in the short term, because there are limits to what people can do to change: they aren't necessarily able to immediately dump their existing car and trade up; they still have to commute to work; cargo still has to be transported to its destination; factories will not replace their inefficient equipment overnight. Costs go up but behavior doesn't change, so an increase in energy costs just replaces spending on other goods, hurting the rest of the economy. Over the longer run, though, if prices have risen significantly and permanently, and that coincides with a point where a consumer decides they need to replace their car, then oil consumption does start becoming more elastic: the consumer is more likely to choose the more fuel efficient vehicle. We've seen some of this in the rise in sales of small vehicles versus trucks and SUVs lately. This is where building a long-term steady upward price trend is important, versus short-term price shocks, since the former allows the economy to react appropriately by increasing efficiency.