Question

Analyzing Data In May, Montclair Electronics sold 100 portable DVD players at \(\$ 150\) each. High consumer demand at the start of the summer travel season increased the price to \(\$ 180 .\) In June, the store sold 115 DVD players at the higher price. Is the supply of DVD players elastic or inelastic? Show your math calculations to support your answer

Short answer

The supply of DVD players is inelastic, with an elasticity of 0.75.

Step-by-step solution

Understanding the Concept of Elasticity

Elasticity of supply measures how responsive the quantity supplied is to a change in price. If the supply is elastic, suppliers can increase the quantity supplied significantly with a price increase. If it's inelastic, the quantity supplied doesn't change much with price changes.

Calculate Percentage Change in Quantity Supplied

First, find the initial and final quantities. The initial quantity supplied is 100 DVD players, and the final quantity is 115 DVD players. The percentage change in quantity supplied is calculated as follows: \[ \frac{\text{Final Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}} \times 100 = \frac{115 - 100}{100} \times 100 = 15\% \]

Calculate Percentage Change in Price

Now, calculate the percentage change in price. The initial price is \\(150 and the final price is \\)180. \[ \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 = \frac{180 - 150}{150} \times 100 = 20\% \]

Compute the Elasticity of Supply

The elasticity of supply is calculated by dividing the percentage change in quantity supplied by the percentage change in price:\[ \text{Elasticity of Supply} = \frac{\text{Percentage Change in Quantity}}{\text{Percentage Change in Price}} = \frac{15\%}{20\%} = 0.75 \]

Determine the Elasticity Type

Since the elasticity of supply (0.75) is less than 1, the supply is considered inelastic. This means that suppliers are relatively unresponsive to price changes, and the quantity supplied doesn't increase significantly when the price increases.

Key concepts

Elasticity of Supply Calculations

Elasticity of supply is a key economic concept that measures how much the amount of a good that suppliers are willing to sell changes in response to a change in price. Essentially, it is a ratio: the percentage change in quantity supplied versus the percentage change in price. The formula is given by: \[ \text{Elasticity of Supply} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}} \]This calculation helps determine whether a good is elastic or inelastic in terms of supply. If the ratio is greater than 1, the supply is elastic, indicating suppliers are highly responsive to price changes. On the other hand, if the ratio is less than 1, as seen in our original exercise with an elasticity of 0.75, the supply is considered inelastic.

Percentage Change in Quantity

Understanding how to calculate the percentage change in quantity helps in evaluating the elasticity of supply. The percentage change in quantity is calculated by taking the difference between the final quantity and the initial quantity, divided by the initial quantity, and then multiplied by 100 to convert it into a percentage. This can be expressed as: \[ \text{Percentage Change in Quantity} = \frac{\text{Final Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}} \times 100 \]For the DVD player example, the initial quantity was 100 units, and the final quantity was 115 units. Therefore, the percentage change in quantity is:- \[ \frac{115 - 100}{100} \times 100 = 15\% \]This 15% increase in quantity signals how much more suppliers were willing to supply when the price changed.

Percentage Change in Price

The percentage change in price is a crucial factor in determining elasticity. It tells us how significantly the price of a product has changed over a certain period. This is calculated similarly to the change in quantity by using the initial and final prices: \[ \text{Percentage Change in Price} = \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 \]Applying this to the original problem where the price of DVDs increased from \(150 to \)180:- \[ \frac{180 - 150}{150} \times 100 = 20\% \]Thus, the price change was 20%, reflecting the increasing consumer demand during the summer travel season. In elasticity calculations, understanding both this percentage and its counterpart in quantity is essential to determining supply responsiveness.