2.3 Price Elasticity of Demand

What is Price Elasticity of Demand (PED)?

So far, we've discussed how the demand curve is constructed and why it is downward sloping. We've also discussed how it shifts with different external market factors. However, a question that may arise is what does the demand curve tell us about a consumer? All we know right now is that consumers reduce their quantity demanded as price rises, but there's more to uncover. 

The Price Elasticity of Demand (PED) is a measure of a consumer's sensitivity to price changes. For example, suppose we have two consumers, Harry and Sally, in the market for turkey sandwiches. Let's suppose that at a price of $10, both Harry and Sally demand a quantity of 5 sandwiches. Now let's suppose the deli increases the price from$10 to $15 per sandwich, and in response, Harry decreases from 5 sandwiches to 1 sandwich, whereas Sally decreases from 5 sandwiches to 4 sandwiches. We can say that Sally is much less price sensitive, or alternatively, that her demand for turkey sandwiches is less elastic (or more inelastic) than Harry's. This guide will dive deep into price elasticity of demand, how to calculate it, and what it means for different consumers.

Your homework tonight is to watch When Harry Met Sally

Calculating Price Elasticity of Demand

Mathematically, we define price elasticity of demand as the percent change in quantity demanded over the percent change in price. This is notated as:

Ed = %ΔQd / %ΔP

Where Ed is known as the price elasticity of demand coefficient, and the notation of %Δ is shorthand for "percent change in". You may observe that because a price increase will always lead to a negative change in Qd (by the Law of Demand), Ed will always be negative or zero. Oftentimes, we use the absolute value of Ed to make it positive, since we know that there will be a decrease in Qd with an increase in P, so we just view Ed as a measure of sensitivity.

For example, let's calculate Harry's price elasticity of demand coefficient for sandwiches:

Q1 = 5

Q2 = 1

Thus, %ΔQd = (1 - 5) / 5 * 100 = -80%

P1 = 10

P2 = 15

Thus, %ΔP = (15 - 10) / 10 * 100 = 50%

Using these numbers, we find:

Ed = -80 / 50 = -1.6

This tells us that a 50% increase in price corresponds to an 80% decrease in quantity demanded. This is a relatively elastic demand, since we have a higher percent change in quantity than there was price.

Types of Elasticity

There are 5 main types of elasticity based on the value of Ed. These types help us understand a consumer's general sensitivity to price.

Perfectly Inelastic Demand

This type of demand has a price elasticity of demand coefficient of zero, meaning that the quantity demanded does not change regardless of price changes. An example of this type of demand is for necessities such as food, water, and shelter. People will continue to need these things regardless of the price, so there is no change in demand even if the price increases. Another common example is insulin, where regardless of price, people will need to buy the same amount of insulin because if they don't they will not survive.

Relatively Inelastic Demand

Relatively inelastic has a price elasticity of demand coefficient between 0 and 1, meaning that the quantity demanded is only slightly responsive to price changes. An example of this type of demand is for gasoline. While people may cut back on non-essential driving if gasoline prices increase, they will still need to purchase gasoline for daily commuting and essential errands. As such, a price increase in gasoline will lead to a smaller (percentage wise) decrease in gasoline consumption.

Unit Elasticity

This type of demand has a price elasticity of demand coefficient of exactly 1, meaning that the quantity demanded is exactly proportional to price changes. An example of this type of demand is for luxury goods such as designer clothing or high-end electronics. People may be willing to pay more for these items if the price increases, but they will also be less likely to purchase them if the price becomes too high.

Relatively Elastic Demand

This type of demand has a price elasticity of demand coefficient greater than 1 but less than infinity, meaning that the quantity demanded is highly responsive to price changes. An example of this type of demand is for leisure activities such as movies or concerts. People may be willing to pay a higher price for these types of experiences, but they are also likely to cut back on spending if the prices become too high. As such, a price increase in something concert tickets will lead to a greater (percentage wise) decrease in consumption of said tickets.

Perfectly Elastic Demand

This type of demand has an infinite price elasticity of demand coefficient, meaning that the quantity demanded becomes infinite as the price approaches zero and becomes zero as the price increases. An example of this type of demand is for a product with many substitutes, such as generic brands of a certain type of food. If the price of the preferred brand increases, consumers will switch to a substitute that is cheaper, causing the demand for the preferred brand to drop to zero.

It's important to note that perfect inelasticity and perfect elasticity doesn't really exist in the world, but is rather a conceptual idea for items with super high or super low price elasticities of demand.

Here are some visual representations of the 5 types of elasticity:

For a demand curve, price elasticity will differ moving down the curve even if the slope of the demand curve is constant.

The Total Revenue Test

Another way we can tell what type of elasticity a demand curve is is by using the total revenue test. Total reveue is a measure of the amount of money a business brings in and is defined by the equation TR = P * Q.

The total revenue test connects total revenue to price elasticity by defining rules for how total revenue responds to price changes under certain elasticities.

Under elastic demand, an increase in price will lead to a decrease in total revenue and vice-versa. This is because elastic demand is very sensitive to price changes.

Under inelastic demand, an increase in price will lead to an increase in total revenue and vice-versa. This is because inelastic demand isn't very sensitive to price changes.

Under unit elastic demand, an increase or decrease in price has no change on total revenue. This is because price and quantity change proportionally when demand is unit elastic.

• Elastic demand means that consumers are very responsive to price changes (i.e. if the price of a product increases, there will be a large decrease in the quantity demanded).
• Inelastic demand means that consumers are not very responsive to price changes (i.e. if the price of a product increases, there will be a small decrease in the quantity demanded).
• Unit elastic demand occurs when consumers are proportionally responsive to changes in market price (i.e. if there is a 30% increase in price then there will be a 30% decrease in quantity demanded).
• Perfectly elastic means that consumers will only produce one price level.
• Perfectly inelastic means that quantity demanded will not change when price level changes.

Sample Problem

The total revenue test is used to determine the elasticity of demand when we just want to know whether it is elastic, inelastic, or unit elastic and we do not need the actual coefficient. Firms can use this test to determine its pricing strategy. By being aware of how elastic or inelastic a product is, they have better insight on how to maximize their total revenue. The more elastic demand is for a product, the more cautious they need to be about price changes.