In the short run, the supply curves of two goods are identical (although one has a more elastic demand curve). However, with a reduction in taxes on these two goods, both suppliers and consumers gain a shared benefit.
What changes (if any) to these benefits will occur if we consider the long run (perfect competition)?
I'm not sure, but I think the demand curve will turn horizontal, and producers benefit more than consumers (in terms of surplus) in the long run?
Over time, both supply and demand will likely become more elastic (Added: although there's no reason to think either one will become perfectly elastic without more information), as producers have the opportunity to change investment patterns and consumers can substitute into other goods if they wish. Drawing the graphs should give you some idea how consumer and producer surplus change over time as this happens. You should notice that the tax becomes less of a burden over time.
Hope that helps!
An example of this might be whale oil. Consumers have found superior and cheaper substitutes for whale oil, so you might say they are extremely price sensitive. Judging by the amount they consume (zero), price elasticity of demand must be perfectly elastic and somewhere below what it would cost to produce it.
Producers would produce whale oil if consumers were willing to pay what it would cost to make it (and if whaling weren't illegal... but, hey, I'm trying to make an economic point here ). But they aren't. So producers have a perfectly elastic supply curve that is somewhere above consumers' demand curve.