Question

If a 5 percent reduction in the price of a good produces a 3 percent increase in the quantity demanded, the price elasticity of demand over this range of the demand curve is a. elastic. b. perfectly elastic. c. unitary elastic. d. inelastic. e. perfectly inelastic.

Short answer

The price elasticity of demand is calculated as \(E = \frac{(3)}{(-5)} = -0.6\). Since -1 < E < 0, the demand is inelastic. Therefore, the answer is d. inelastic.

Step-by-step solution

Price Elasticity of Demand Calculation

\(E = \frac{(3)}{(-5)} = -0.6\) #Step 2: Identify the Category of Elasticity# Now, we can determine the nature of the elasticity based on the value of the price elasticity of demand. The categories are as follows: - Elastic, if \(E < -1\) - Perfectly elastic, if \(E = -\infty\) - Unitary elastic, if \(E = -1\) - Inelastic, if \(-1 < E < 0\) - Perfectly inelastic, if \(E = 0\) Our calculated value of E is -0.6, which falls into the inelastic category.

Elasticity Category

The price elasticity of demand is inelastic since -1 < E < 0. So, the correct answer is: d. inelastic.

Key concepts

Price Elasticity Calculation

Understanding the price elasticity of demand is essential for businesses and economists as it measures consumer behavior in response to a change in price. To calculate the price elasticity of demand, we use the formula:

\[\begin{equation}E = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}\end{equation}\]

This formula provides a coefficient, often denoted as 'E,' which represents how sensitive the quantity demanded of a good is to its price change. For example, if a 5 percent decrease in price results in a 3 percent increase in the quantity demanded, the calculation would be:

\[\begin{equation}E = \frac{3}{-5} = -0.6\end{equation}\]

A negative value is expected because the law of demand states that price and quantity demanded move in opposite directions. It's crucial to interpret this value correctly to understand how much the demand for a product might shift with a change in price.

Demand Curve

The demand curve is a graphical representation that shows the relationship between the price of a good and the quantity of that good that consumers are willing to purchase at various prices. It is generally downward sloping from left to right, highlighting the inverse relationship between price and quantity demanded. This relationship is underpinned by the law of demand, which states that, ceteris paribus, as price falls, the quantity demanded rises, and vice versa.

As for the price elasticity of demand, the demand curve can showcase different elasticity behaviors at different points. For instance, a vertical demand curve signifies perfectly inelastic demand, meaning quantity demanded does not change as price changes. Conversely, a horizontal demand curve indicates perfectly elastic demand, where a slight change in price leads to an infinite change in quantity demanded. Understanding the shape of the demand curve is crucial when evaluating how changes in price will impact demand.

Elasticity Categories

Economists classify the price elasticity of demand into several categories to better understand consumer reactions to price changes:

• Elastic Demand: When the absolute value of the elasticity coefficient is greater than one (\[\begin{equation}E < -1\end{equation}\]), the quantity demanded changes by a greater percentage than the price change.
• Perfectly Elastic Demand: Represented by an elasticity coefficient of negative infinity (\[\begin{equation}E = -\infty\end{equation}\]). Consumers are extremely sensitive to price changes, and any increase can lead to zero demand.
• Unitary Elastic Demand: An elasticity coefficient of exactly negative one (\[\begin{equation}E = -1\end{equation}\]) means the percentage change in quantity demanded is equal to the percentage change in price.
• Inelastic Demand: If the elasticity coefficient is between zero and negative one (\[\begin{equation}-1 < E < 0\end{equation}\]), the quantity demanded changes by a smaller percentage than the price change.
• Perfectly Inelastic Demand: An elasticity coefficient of zero (\[\begin{equation}E = 0\end{equation}\]) indicates that the quantity demanded is completely unresponsive to price changes.

In the given exercise, the calculated elasticity coefficient of -0.6 implies an inelastic demand. This suggests that the percentage change in quantity demanded is less than the percentage change in price, and consumers are relatively less sensitive to price changes within this range of the demand curve.