Question

If the quantity of dental services demanded increases by 10 percent when the price of dental services falls by 10 percent, is the demand for dental services inelastic, elastic, or unit elastic?

Short answer

The demand for dental services is unit elastic.

Step-by-step solution

Understand the Problem

First, understand the question: We need to determine the price elasticity of demand based on the given percentage changes in quantity demanded and price.

Define Elasticity of Demand

The price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Set Up the Formula

The formula for price elasticity of demand is: \[ \text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \]

Insert Given Values

We are given that the quantity demanded increases by 10 percent and the price falls by 10 percent. Plug these values into the formula: \[ \text{PED} = \frac{10\text{\textpercent}}{-10\text{\textpercent}} \]

Calculate the Elasticity

Calculate the value of PED: \[ \text{PED} = \frac{10}{-10} = -1 \]. Since we are looking at the magnitude, we take the absolute value: \[ |\text{PED}| = 1 \]

Interpret the Result

Compare the value of PED to 1: An elasticity of 1 indicates unit elasticity, meaning the percentage change in quantity demanded is exactly equal to the percentage change in price.

Conclusion

Since the absolute value of the price elasticity of demand is 1, the demand for dental services is unit elastic.

Key concepts

Elasticity

Elasticity in economics refers to how much the quantity demanded or supplied of a good responds to changes in price. It's a measure of sensitivity or responsiveness. This concept is crucial because it helps businesses and policymakers understand how changes in price influence supply and demand.
There are several types of elasticity, but here we focus on price elasticity of demand (PED).
The formula for PED is simple:
\[\text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}\]\
Depending on the absolute value of PED, demand can be classified as elastic, inelastic, or unit elastic.
* **Elastic demand**: When PED > 1. A small change in price leads to a larger change in quantity demanded.
* **Inelastic demand**: When PED < 1. A change in price causes a smaller change in quantity demanded.
Understanding elasticity helps businesses set optimal pricing strategies and allows governments to predict the effects of taxation and regulation.

Demand Responsiveness

Demand responsiveness measures how much consumers change their buying patterns in response to price changes.
When a product's price drops significantly and consumers buy much more of it, the product is said to have a highly responsive (elastic) demand. Conversely, if a price drop doesn't significantly increase demand, the product's demand is inelastic.
Factors that influence demand responsiveness include:
* **Substitute availability**: If there are good substitutes available, demand tends to be more elastic.
* **Necessity vs. luxury**: Necessity goods generally have inelastic demand, while luxury goods tend to have more elastic demand.
* **Proportion of income**: Expensive items that take up a large portion of income typically have more elastic demand.
For our dental services example, the demand is responsive (elastic) if a price cut leads to a large change in the quantity demanded. Since both the percentage change in price and quantity demanded are equal, taking their absolute values gives us a unit elastic demand.

Unit Elastic

If the absolute value of the price elasticity of demand is exactly 1, the demand is said to be unit elastic.
This implies that the percentage change in quantity demanded is equal to the percentage change in price. For instance, in our exercise on dental services:
* A 10% reduction in price leads to a 10% increase in quantity demanded.
This balance means that total revenue (price multiplied by quantity) remains unchanged when price changes. Businesses can use this information to predict how price adjustments might impact their total revenue.
Factors leading to unit elasticity include balanced shifts in consumer need and price preference and a roughly equal availability of substitutes.
Understanding unit elasticity helps businesses and economists predict more accurately and design better pricing strategies that neither waste resources nor lose revenue.