2.6.1 Price elasticity of supply (PES) Notes

Price elasticity of supply is defined as the percentage change in quantity supplied divided by the percentage change in price:

$$ \mathrm{PES} = \frac{\%\Delta Q_s}{\%\Delta P}$$

Where:

• $\%\Delta Q_s$ = Percentage change in quantity supplied
• $\%\Delta P$ = Percentage change in price

Therefore, using the above formulas, PES can be written as:

$$ \mathrm{PES} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}\times 100}{\frac{P_{new}-P_{old}}{P_{old}}\times 100} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}}{\frac{P_{new}-P_{old}}{P_{old}}}=\frac{\frac{\Delta Q}{Q_{old}}}{\frac{\Delta P}{P_{old}}} $$

As observed above, it is almost identical to $PED$ but rather focuses on the quantity supplied.

As we can see, the price elasticity of supply is positive.

• This is due to the law of supply, where the percentage change of quantity supplied will be in the same direction as that of price.
• Therefore PES is mathematically always positive.

Degrees of PES: Theoretical Range of Values

PES values help classify supply into different categories.

Relative PES cases

Price Inelastic

1. When $0 < PES < 1$, the supply is called price inelastic.
2. Here, the percentage change in quantity supplied is less than the percentage change in price
3. Therefore $PES$ is smaller than 1 and the quantity supplied is greatly unresponsive

Price Elastic

1. When $1 < PES < \infty$, the supply is called price elastic.
2. Here, the percentage change in quantity supplied is more than the percentage change in price.
3. Therefore $PES$ is greater than 1 and the quantity supplied is greatly responsive.

Example Diagrams

The figure above shows the supply curve of a good that has a high PES or in other words, is elastic.

• There is a higher increase in quantity supplied compared to the change in price.
• The curve is relatively flatter and starts from the y axis.

The figure above shows the supply curve of a good that has a low PES or in other words, is inelastic.

• There is a lower increase in quantity supplied compared to the change in price.
• The curve is relatively steeper and starts from the x axis.

Usually, the flatter curve represents a high elasticity and the curve that is steeper represents a low elasticity (inelasticity).

Special Cases where PES is constant

Unit Elastic

1. When $PES = 1$, the supply is called unit price elastic (Unitary PES).
2. Here, the percentage change in quantity supplied is equal to the percentage change in price.
3. Therefore the quantity supplied is exactly as responsive to the price.

Perfectly Inelastic

1. When $PES = 0$, the supply is called perfectly price inelastic.
2. Here, the percentage change in quantity supplied is always 0 regardless of what happens to the price.
3. Therefore the quantity supplied is perfectly unresponsive to the price.

Perfectly Elastic

1. When $PES = \infty$, the supply is called perfectly price elastic.
2. Here, the percentage change in quantity supplied can be of any magnitude even if the price doesn't change.
3. A small price increase causes producers to produce an infinite amount, and a small price fall causes producers to produce nothing as the point of production will not be at the line of production (elastic line).
4. Therefore $PES$ is infinity and the quantity supplied is perfectly responsive.

Determinants of PES

Many goods and services can have ranges of different values of PES.

Time

The length of time available to producers makes them more responsive to price changes.

1. If they have limited time, it may be difficult for firms to change their inputs to produce more or less goods, hence the supply is price inelastic.
2. However, with more time, they can adjust their inputs and (factors of) production much easier, making them more responsive and thus supply more elastic.

Mobility of Factors of Production

The easier it is to move factors of production from one area of production to another, the more elastic the supply.

1. If factors are easy to move, then firms can easily move factors to the production of goods where prices increase (more responsive)
2. If factors are more fixed, then firms can't easily respond to price changes.

Unused Capacity

Sometimes firms have unused capacity of certain factors of production as they may not exhaust all factors at all times.

1. If the firm has used a lot of its capacity, then even with a price increase it would be difficult for the producers to respond as they have no spare available
2. However, if the firm has spare capacity available, then it can easily allocate this capacity for the production of the good whose price increased, making them more responsive.

Ability to store stocks

Firms that can store a larger capacity of produced goods likely have a higher elasticity in supply.

1. A higher storage capacity means producing extra is possible as there are more storage options and hence are more responsive.
2. However, a lack of storage means the producers need to be careful and not overproduce and thus are less responsive.

Rate of Cost Increase

If the cost of producing an extra unit rises faster, then expanding production would be difficult.

1. If costs increase at a fast rate, then even with increases in the price of the goods, the producers may not increase production by much, thus having inelastic supply.
2. If costs increase relatively slow then it would be easy for producers to take advantage of higher prices and thus have elastic supply.