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Price elasticity of supply refers to the percentage change in quantity supplied of a good or service in response to a 1% change in its price, all other factors remaining constant. It reflects the responsiveness of producers to changing prices and helps us understand how a change in price affects the supply behavior of producers.

Price elasticity of supply (PES) can be calculated using the following formula: \[PES = \frac{\% \hspace{1mm} Change \hspace{1mm} in \hspace{1mm} Quantity \hspace{1mm} Supplied}{\% \hspace{1mm} Change \hspace{1mm} in \hspace{1mm} Price}\] Alternatively, this can also be expressed as: \[PES = \frac{(\Delta Q/Q)}{(\Delta P/P)}\] Here, \(\Delta Q\) is the change in quantity supplied, \(Q\) is the original quantity supplied, \(\Delta P\) is the change in price, and \(P\) is the original price.

The value of PES can be interpreted as follows: 1. If \(PES > 1\), the supply is price elastic, meaning the quantity supplied is very responsive to changes in price. A small increase (decrease) in price leads to a large increase (decrease) in the quantity supplied. This usually happens when producers have the flexibility to easily increase or decrease production, such as industries with excess capacity or easily accessible resources. 2. If \(PES = 1\), the supply is unitary elastic. In this case, a 1% change in price results in a 1% change in quantity supplied. 3. If \(0 < PES < 1\), the supply is price inelastic, meaning the quantity supplied is not very responsive to changes in price. A large increase (decrease) in price only leads to a small increase (decrease) in the quantity supplied. This is often found in industries with limited resources or that are difficult to adjust quickly, such as agriculture, mining, or specialized manufacturing. 4. If \(PES = 0\), the supply is perfectly inelastic. The quantity supplied remains constant regardless of the price. This situation is very rare but can occur in the case of a completely fixed supply, such as a unique piece of art or certain natural resources.

Understanding price elasticity of supply enables businesses, governments, and policymakers to make informed decisions. For example, if the government wants to encourage the production of a particular good, they can consider lowering taxes or providing subsidies to reduce production costs. If the supply is elastic, this may lead to a significant increase in the quantity supplied, benefiting both consumers and producers. On the other hand, if the supply is inelastic, such efforts may not have a significant effect on the quantity supplied.