Understanding the price elasticity of supply is crucial for analyzing how the quantity supplied of a good responds to changes in its price. The price elasticity of supply measures the responsiveness of quantity supplied to price changes, and it is calculated using a formula similar to that of price elasticity of demand, but with quantity supplied in the numerator. The formula can be expressed as:
$$E_s = \frac{\%\ \text{Change in Quantity Supplied}}{\%\ \text{Change in Price}}$$
In this context, the law of supply states that as the price of a good increases, the quantity supplied also increases, leading to a positive elasticity value. This means that the signs of the changes do not affect the calculation, as both the percentage change in quantity supplied and the percentage change in price will yield positive results.
To calculate the price elasticity of supply, follow these steps:
Identify the initial and new prices and quantities supplied. For example, if the price of ice cream rises from $4 to $6 and the quantity supplied increases from 90,000 to 110,000, note these values.
Calculate the change in quantity supplied and the change in price. Here, the change in quantity supplied is:
$$\Delta Q_s = 110,000 - 90,000 = 20,000$$And the change in price is:
$$\Delta P = 6 - 4 = 2$$Find the average quantity supplied and average price:
$$\text{Average Quantity Supplied} = \frac{110,000 + 90,000}{2} = 100,000$$$$\text{Average Price} = \frac{6 + 4}{2} = 5$$Calculate the percentage changes:
$$\%\ \text{Change in Quantity Supplied} = \frac{20,000}{100,000} = 0.2\ \text{or}\ 20\%$$$$\%\ \text{Change in Price} = \frac{2}{5} = 0.4\ \text{or}\ 40\%$$Finally, plug these values into the elasticity formula:
$$E_s = \frac{0.2}{0.4} = 0.5$$
A price elasticity of supply less than 1 indicates that the supply is inelastic, meaning the quantity supplied increases by a smaller percentage than the price increase. In this example, since the price rose by 40% while the quantity supplied only increased by 20%, the supply is considered inelastic.
In summary, the elasticity of supply can be categorized as follows:
Elastic Supply: If \(E_s > 1\), the quantity supplied is highly responsive to price changes.
Inelastic Supply: If \(E_s < 1\), the quantity supplied is less responsive to price changes, as demonstrated in the ice cream example.
Unit Elastic Supply: If \(E_s = 1\), the percentage change in quantity supplied is equal to the percentage change in price.
By mastering these concepts and calculations, you can effectively analyze how supply responds to price fluctuations in various markets.
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