In the short run, the answer is likely that the price would change quite a bit more than in the longer run. But Jerry Taylor, of the Cato Institute, appears to believe the price elasticity of demand is one in the long run[h/t Cafe Hayek]. Discussing the effects of opening up more wilderness and northern areas for oil exploration and drilling, he says,
By the time those new fields would be producing, global oil production will probably be about 100 million barrels per day. Optimistically, the fields would yield about 3 million more barrels a day - for a long-run cut in the price of crude of about 3 percent.I have no idea where he obtained that estimate for the long-run price elasticity of demand for crude oil, but it is probably not a bad guess. Overall, if in doubt, a guess that the price elasticity of demand for something is about 1 is probably a good starting point, especially in the long run.





In any case, another way of saying PED=1 is saying that expenditures are constant (i.e., PxQ=k). Do we have evidence of this?
2. To the extent that MV=PQ in the aggregate, then under plausible conditions, it's not a bad guess to start with PQ = k and PED = 1, barring any better evidence. Of course this is a prior one might want to hold pretty loosely for specific products, but after all it's just a starting point.