Similar to the price elasticity of supply, we define the *price elasticity of demand*. There are several factors that must be taken into account when analyzing it:

- Availability of substitutes - Goods with close substitutes tend to have higher elasticity because consumers can easily switch between goods.
- Necessities v. luxuries - Necessities usually have inelastic demands whereas luxuries have elastic demands. Whether something is a necessity or a luxury depends on the properties of the buyer, it is not some intrinsic property of the good.
- Definition of the market - By “definition”, we mean where we draw the boundaries of the market. Narrowly defined markets such as vanilla ice-cream may be very elastic whereas broadly defined markets such as food are inelastic.
- Time horizon - If we have a longer time to adjust, the demand tends to be more elastic.

How do we calculate the price elasticity of demand/supply? We divide the percentage change in the demand/supply by the percentage change in the price. To bring about symmetry, we take the percentage change about the midpoint. So for demand, the price elasticity between two points \((P_1,Q_1)\) and \((P_2,Q_2)\) is

\[\frac{(Q_2-Q_1)/((Q_1+Q_2)/2)}{(P_2-P_1)/((P_1+P_2)/2)}.\]The price elasticity of supply can be calculated similarly.

The demand is said to be

*perfectly inelastic*if the price elasticity is equal to \(0\),*inelastic*if the price elasticity is between \(0\) and \(1\),*unitary*if the price elasticity is equal to \(1\),*elastic*if the price elasticity is greater than \(1\), and*perfectly elastic*if the price elasticity is infinite (the demand curve is horizontal).

The *total revenue* is equal to the price of the good multiplied by the quantity of the good sold.

The change of the total revenue with price depends on the price elasticity.

Note that in a perfectly inelastic situation, reducing the price results in the total revenue decreasing proportionately.

- If the demand is inelastic, total revenue and price grow together.
- If the demand is elastic, total revenue and price grow against each other.
- If the demand is unitary, the total revenue does not change with price.

If the demand decreases linearly with price, then it goes from elastic to unitary to inelastic as demand increases.

The *income elasticity of demand* measures how much the quantity demanded changes with the income of the consumer. Similar to before, it is calculated by dividing the percentage changes in each. Income elasticity is positive for normal goods and negative for inferior goods.