Question

The table sets out the supply schedule of jeans. $$\begin{array}{cc} \begin{array}{c} \text { Price } \\ \text { (dollars per pair) } \end{array} & \begin{array}{c} \text { Quantity supplied } \\ \text { (millions of pairs per year) } \end{array} \\ \hline 120 & 24 \\ 125 & 28 \\ 130 & 32 \\ 135 & 36 \end{array}$$ a. Calculate the elasticity of supply when the price rises from \(\$ 125\) to \(\$ 135\) a pair. b. Calculate the elasticity of supply when the average price is \(\$ 125\) a pair. c. Is the supply of jeans elastic, inelastic, or unit elastic?

Short answer

The elasticity of supply when price rises from \(\$125\) to \(\$135\) a pair is about \(3.57\). At this average price, supply is elastic.

Step-by-step solution

- Write Down the Formula for Elasticity of Supply

The elasticity of supply formula is given by: \[E_s = \frac{\% \Delta Q_s}{\% \Delta P}\]

- Calculate the Percentage Change in Quantity Supplied

To find \(\% \Delta Q_s\), use: \[\% \Delta Q_s = \frac{Q_2 - Q_1}{Q_1} \times 100\] where \(Q_1\) is the initial quantity and \(Q_2\) is the final quantity. Here, \(Q_1 = 28\) million pairs and \(Q_2 = 36\) million pairs.

- Solve for Percentage Change in Quantity Supplied

Substitute the values into the formula: \[\% \Delta Q_s = \frac{36 - 28}{28} \times 100 = \frac{8}{28} \times 100 \approx 28.57\%\]

- Calculate the Percentage Change in Price

To find \(\% \Delta P\), use: \[\% \Delta P = \frac{P_2 - P_1}{P_1} \times 100\] where \(P_1\) is the initial price and \(P_2\) is the final price. Here, \(P_1 = 125\) dollars and \(P_2 = 135\) dollars.

- Solve for Percentage Change in Price

Substitute the values into the formula: \[\% \Delta P = \frac{135 - 125}{125} \times 100 = \frac{10}{125} \times 100 = 8\%\]

- Plug the values into the Elasticity of Supply Formula

Now substitute the percentage changes into the elasticity formula: \[E_s = \frac{28.57}{8} \approx 3.57\]

- Explanation of Elasticity Computation

The elasticity of supply when the price rises from \(\$ 125\) to \(\$ 135\) a pair is about \(3.57\). Now for the average price.

- Estimate Elasticity at Average Price

The average price formula is: \[\text{Average Price} = \frac{P_1 + P_2}{2}\]. Here, \[\text{Average Price} = \frac{125 + 135}{2} = 130\] dollars per pair.

- Examine Elasticity Value at Price \(130\)

At an average price of \(\$130\), if the elasticity of supply obtained at \(\$130\) is greater than 1, supply is elastic; if less than 1, supply is inelastic; if exactly 1, unit elastic.

- Determine Supply Nature

Since \(E_s = 3.57\), it indicates that supply is elastic.

Key concepts

price elasticity

Price elasticity of supply measures how much the quantity supplied of a good responds to a change in the price of that good. It shows the sensitivity of suppliers to price changes and is calculated using the formula:\[E_s = \frac{\% \Delta Q_s}{\% \Delta P}\]. In simple terms, this formula compares the percentage change in quantity supplied to the percentage change in price. A higher value indicates that producers are very responsive to price changes, whereas a lower value means they are less responsive.

percentage change

Calculating the percentage change is essential for determining elasticity. To find the percentage change in quantity supplied (\text{}\text\% \Delta Q_s\text{}), you use the following formula: \[\% \Delta Q_s = \frac{Q_2 - Q_1}{Q_1} \times 100\], where Q_1\text{} is the initial quantity and Q_2\text{} is the final quantity. Similarly, the formula for the percentage change in price (\text{}\% \Delta P\text{}) is: \[\% \Delta P = \frac{P_2 - P_1}{P_1} \times 100\], where P_1\text{} is the initial price and P_2\text{} is the final price. These calculations are crucial for finding out how much the quantity supplied or price has changed over a period.

quantity supplied

Quantity supplied refers to the amount of a good that producers are willing and able to sell at a particular price. It's important to note that the quantity supplied can vary with price changes. For example, in our scenario, when the price of jeans rises from \(125 to \)135, the quantity supplied increases from 28 million pairs to 36 million pairs. This increase shows that suppliers are more motivated to sell more jeans when the price goes up. Understanding this term is crucial as it helps in assessing the supply chain's responsiveness to market conditions.

elastic, inelastic, unit elastic

Elasticity of supply can fall into one of three categories: elastic, inelastic, or unit elastic.
• **Elastic supply** occurs when a small change in price results in a significant change in quantity supplied. In our example, the elasticity value is approximately 3.57, indicating very responsive or elastic supply.
• **Inelastic supply** means that a price change has little impact on the quantity supplied. If the elasticity is less than 1, the supply is considered inelastic.
• **Unit elastic supply** is when a percentage change in price results in an equal percentage change in quantity supplied, yielding an elasticity of exactly 1. Understanding these categories helps in predicting how changes in market conditions might affect supply.