What is Elasticity?
Elasticity is the sensitivity of quantity of goods demanded or supplied when price changes. It is a measure of the responsiveness of markets.
Theoretically, perfectly inelastic demand means that there is no substitutes for the good. A good approximation is the market for medicine. Therefore the quantity demanded by the consumers will not change no matter how much the price changes.
For perfectly elastic demand, all substitutes are equivalent. A good approximation is the market for sweets. Once the price of a type of sweets changes, the quantity demanded by consumers will change greatly as they will start purchasing sweets from other markets.
Amount of taxes raised from goods depends on the elasticity of the goods. Taxes will raise more money when imposed on inelastic goods, as the quantity of goods transacted will not drop as much. Understanding elasticity will help to formulate policies, such as the appropriate amount of government spending to be allocated to healthcare.
Price Elasticity of Demand
This is affected by two factors. One, the Substitution Effect on the good as price changes, and two, the Income Effect on the good as price changes.
The Substitution Effect is unambiguous on almost all goods. As price of a good increases, consumers will look for substitutes, therefore price and quantity are always negatively related under this effect.
The Income Effect is dependent on the type of goods. Price changes affects the spending power of the consumer as it changes their budget constraint, hence creating an income effect. If it is a Normal Good, then an increase in income will lead to more consumption, but not as much, as compared to a Luxury Good. If it is an Inferior Good, then consumption will decrease instead, as income rises.
(Reference: MIT OCW Principles of Microeconomics)