Price Elasticity of Supply
This is a measure of the responsiveness of the quantity supplied to changes in price. In other words, it is the percentage change in the quantity supplied as a result of a given percentage change in price. It is calculated as the percentage change in the quantity supplied divided by the percentage change in price. This elasticity is usually positive, as an increase in price is an incentive to increase production.
Determinants of Supply Elasticity
The price elasticity of supply depends on the flexibility producers have to change the quantity they produce. The supply of available construction land is hardly alterable, while in manufactured goods, companies can expand their production capacity in response to a price increase.
In most markets, supply is more elastic in the long term compared to the short term. This is because, in the short term, producers' response is limited. They can partially alter production capacity in existing factories, but in the short term, it is not possible to change factory sizes to increase or reduce capacity. On the contrary, in the long term, companies can build new factories or close old ones. Additionally, new companies can enter the market, or some existing ones can exit. Therefore, the time horizon in which supply elasticity is measured significantly affects the outcome.
How to Calculate Price Elasticity of Supply?
The price elasticity of supply is defined as:
\[ E_{s} = \frac{\text{Percentage change in the quantity supplied}}{\text{Percentage change in price}} \]
The change in the quantity supplied (\(\Delta Q_s\)) and the change in price (\(\Delta P\)) are calculated as the difference between initial and final values, that is:
\[ \Delta Q_s = Q_s^{\text{final}} - Q_s^{\text{initial}} \]
\[ \Delta P = P^{\text{final}} - P^{\text{initial}} \]
This leads to the following expression in terms of absolute changes:
\[ E_{s} = \frac{\frac{\Delta Q_s}{Q_s}}{\frac{\Delta P}{P}} \]
By multiplying both sides of the original equation by \(\frac{P}{\Delta P}\), the result is:
\[ \left( E_{s} \cdot \frac{\Delta P}{P} \right) = \left( \frac{\Delta Q_s}{Q_s} \cdot \frac{P}{\Delta P} \right) \]
Now, we can see that the multiplication of \(\frac{\Delta P}{P}\) with \(\frac{P}{\Delta P}\) simplifies, canceling out terms as:
\[ \frac{\Delta P}{P} \cdot \frac{P}{\Delta P} = 1 \]
This leaves us with the equation:
\[ E_{s} = \frac{\Delta Q_s}{\Delta P} \cdot \frac{P}{Q_s} \]
Where:
- \(\Delta Q_s\) = change in the quantity supplied (final value minus initial value)
- \(\Delta P\) = change in price (final value minus initial value)
- \(P\) = initial price
- \(Q_s\) = initial quantity supplied
This formula is useful for calculating the price elasticity of supply using data on changes in quantities and prices.
Example of Calculating Price Elasticity of Supply
Let us consider a specific example to calculate the price elasticity of supply.
Suppose that:
- Initial quantity supplied (\(Q_s^{\text{initial}}\)): 100 units
- Final quantity supplied (\(Q_s^{\text{final}}\)): 140 units
- Change in the quantity supplied (\(\Delta Q_s\)): \(Q_s^{\text{final}} - Q_s^{\text{initial}} = 140 - 100 = 40\) units
- Initial price (\(P^{\text{initial}}\)): 20 monetary units
- Final price (\(P^{\text{final}}\)): 30 monetary units
- Change in price (\(\Delta P\)): \(P^{\text{final}} - P^{\text{initial}} = 30 - 20 = 10\) monetary units
Substituting these values into the formula:
\[ E_{s} = \frac{\Delta Q_s}{\Delta P} \cdot \frac{P}{Q_s} \]
Substituting the values:
\[ E_{s} = \frac{40}{10} \cdot \frac{20}{100} \]
We calculate each part:
- \(\frac{40}{10} = 4\)
- \(\frac{20}{100} = 0.2\)
Now, multiply both results:
\[ E_{s} = 4 \cdot 0.2 = 0.8 \]
Therefore, the price elasticity of supply is 0.8, indicating that a 1% increase in price results in a 0.8% increase in the quantity supplied.
Elastic, Inelastic, and Unit Elastic Supply
When the quantity supplied responds with a proportionally greater change than the change in price, the supply is said to be elastic. If the response of the quantity supplied is proportionally smaller to price changes, the supply is inelastic. Finally, when a percentage change in price results in an equal percentage change in the quantity supplied, the supply is unit elastic. To summarize:
Elasticity of supply is classified as follows:
- Perfectly inelastic: \(E_s = 0\) - The quantity supplied does not change with price changes. The supply curve is vertical.
- Inelastic: \(0 < E_s < 1\) - The quantity supplied changes less than proportionally to price changes. A price increase results in a less than proportional increase in quantity supplied.
- Unit elastic: \(E_s = 1\) - The quantity supplied changes in the same proportion as the price change. A price increase results in an equal increase in quantity supplied.
- Elastic: \(E_s > 1\) - The quantity supplied changes more than proportionally to price changes. A price increase results in a more than proportional increase in quantity supplied.
- Perfectly elastic: \(E_s = \infty\) - The quantity supplied changes infinitely with a small price change. The supply curve is horizontal.