Using elasticity: revenue, taxes and subsidies

Total revenue = price × quantity sold. Watch what happens to it when price changes:

With inelastic demand, a firm can raise its price and earn more revenue, because sales fall only a little. Examples: petrol, electricity, a medicine with no substitute.
With elastic demand, a firm should think about cutting its price: the extra sales more than make up for the lower price. Examples: one brand of crisps, a particular airline on a busy route.
Revenue is not profit: extra sales also add to costs.

Governments often put indirect taxes on goods with inelastic demand, such as fuel, alcohol and tobacco. People keep buying them after the tax pushes the price up, so the tax raises a lot of revenue.
The same fact means a tax on an inelastic good does not cut consumption much: if the aim is to reduce smoking, the tax must be large, or combined with other policies such as bans on advertising.
With inelastic demand, firms can pass most of a tax on to consumers as a higher price. With elastic demand they cannot, so producers bear more of it.
A subsidy lowers the price. It raises consumption a lot when demand is elastic, for example a subsidy on bus fares where people can choose to drive instead, and only a little when demand is inelastic.

In a recession, incomes fall: firms selling luxuries (YED above 1) see sales fall sharply, and those selling inferior goods (negative YED) may gain.
When incomes rise, governments can expect more tax from luxuries, and firms can plan which products to expand.