When the demand curve is relatively inelastic, consumers pay.
When the demand curve is relatively elastic, producers pay.
When the supply curve is relatively inelastic, producers pay.
When the supply curve is relatively elastic, consumers pay.
When the curves are unit elastic, producers and consumers pay 50/50.
The taxation of elastic goods is not profitable because as the price increases, the quantity decreases substantially.
This is why governments ususally target inelastic goods for taxation, compared to elastic ones. Tax incidence is the analysis of the effect of a particular tax on the distribution of economic welfare.