Price Elasticity of Demand

The law of demand holds that there is an inverse relationship between price and quantity demanded. When price rises, quantity demanded falls. However, it is also useful to know by how much quantity demanded will fall. On one hand, consumers might react strongly to an increase in price and curtail their purchases. Conversely, it is possible that consumers may not adjust their purchasing behavior at all when price rises. The price elasticity of demand is a measure of how responsive the quantity demanded of a good is to changes in its price, all other factors held constant. The price elasticity of demand (E_D) is the percentage change in the quantity demanded (Q_D) divided by the percentage change in price (P). In other words, price elasticity of demand equals the percentage change in quantity of demand divided by the percentage change in price. For example, suppose that the price of a brand of shampoo decreases by 10%. This is the percentage change in price. With this price decrease, consumers respond by buying more of the shampoo. The resulting demand for the shampoo increases by 15%. This is the percentage change in quantity of demand. Thus, the price elasticity of demand is calculated as $15\%/10\%=1.5$.

The price elasticity of demand will always be less than or equal to zero because of the inverse relationship between price paid and quantity demanded. An absolute value is used when calculating the price elasticity of demand because it is a measurement of the amount (or the "size") of the responsiveness. The number itself is unitless—it indicates by what percentage the quantity demanded changes for a 1% change in price. For example, if the demand for pizza has an elasticity of 2.5, the quantity demanded of pizza will fall by 2.5% if the price of pizza rises by 1%.

The midpoint formula is used to calculate elasticity. The midpoint formula is used to calculate the percentage change in a variable by dividing the change in the variable by the average of the the initial and final values. The midpoint formula is given as where $A_{1}$ is the first value of the first variable, $A_{2}$ is the second value of the first variable, $B_{1}$ is the first value of the second variable, and $B_{2}$ is the second value of the second variable. In the case of economics, the first variable is price and the second variable is quantity. This formula is often preferred by economists because the change over time is taken into account when calculating elasticity. Suppose the price (P) of a T-shirt rises from $10 to $15, and this causes the quantity demanded (Q) to fall from 4,500 to 3,500. To be able to estimate the elasticity, the percentage changes in these variables must first be calculated. According to the midpoint formula, the change in each variable is divided by the midpoint between the original and new values. Therefore, the percentage change in price is $5/12.5=40\%$. The percentage change in quantity demanded is $1\text{,}000/4\text{,}000=25\%$. With this information, the price elasticity of demand can be calculated: $25\%/40\%=0.625$.

Demand can be classified as elastic or inelastic. Elastic demand is demand in which the percentage of the quantity demanded changes more than the percentage that the price changes. Inelastic demand is demand in which the quantity of a good or service that consumers demand is relatively insensitive to changes in price; the percentage change in price is larger than the percentage change in quantity demanded. The size of the elasticity (large or small) determines whether demand is elastic or inelastic. When the absolute value of the price of elasticity demand is greater than 1 ($\lvert \text{E}_{\text{D}}\rvert \gt 1$), it is elastic. When the absolute value of the price of elasticity demand is less than 1 ($\lvert \text{E}_{\text{D}}\rvert\lt 1$), it is inelastic.

When demand is elastic, consumers are highly responsive to changes in price. Small changes in price cause large changes in demand. In this situation, the change in quantity demanded outweighs the change in price, so the numerator of the equation is larger than the denominator. Therefore, when the absolute value of the price elasticity of demand is greater than 1, demand is elastic. For example, if the price of oranges decreases by 20% and in response the demand for oranges increases by 30%, then demand for oranges is considered elastic.

Conversely, when demand is inelastic, consumers are relatively insensitive to changes in price. In this case, the percentage change in price is larger than the percentage change in quantity demanded, so the numerator of the elasticity formula is smaller than the denominator; the absolute value of the price elasticity of demand is less than 1.

For example, a shirt company may experiences a price elasticity of demand of 0.625 at a particular price. Therefore the demand for T-shirts is considered inelastic at that particular price. If the price of T-shirts were to increase by 40%, the quantity demanded would fall by only 25%. Consumers are not very responsive to the large change in the price of T-shirts.

A third case occurs when the absolute value of the price elasticity of demand is equal to 1. This is a unit elastic demand. This occurs only when the percentage change in quantity demanded is equal to the percentage change in price.

There are five primary factors that determine whether consumers are responsive (elastic) or insensitive (inelastic) to price changes: the number of substitutes available, whether the good is a necessity or a luxury, the time frame considered, how broadly the market is defined, and the proportion of a consumer's budget accounted for by the good.

When the price of the good or service changes, what other options does a consumer have? For example, are close substitutes, equivalent or almost equivalent replacements, available? If the price of oranges rises, a consumer can choose to purchase another type of fruit, such as tangerines. When close substitutes are available, consumers will likely be more sensitive to changes in price, and the demand for the good will be relatively elastic. In contrast, if a good or service has no close substitutes (such as insulin), consumers will be unable to react strongly to changes in price, and demand for the product will be relatively inelastic.

A related consideration is whether the good or service is a necessity or a luxury. Consumers are much more responsive to changes in the prices of luxury items, such as a pair of designer sunglasses if a person already owns basic sunglasses, because they can always choose to not purchase them at all. Therefore the demand for luxury goods is often elastic. However, when the price of a necessity rises, consumers may try to purchase slightly less of it but cannot reduce their consumption too much because they need to purchase the good. This is applicable to things such as food and gas. This makes demand for necessities inelastic.

Another important issue is the amount of time available to make a purchasing decision. If the price of gasoline rises overnight, many consumers already have plans the following day to drive to work or to school. It is not easy to adjust those plans quickly, so the good is still purchased. However, if the price of gasoline remains high, over time people may look for alternative transportation, carpool with others, or find ways to reduce their commuting time. This means that in the long run, demand will be more elastic than in the short run.

The fourth determinant of the price elasticity of demand is how broadly the market is defined. This is somewhat related to the availability of substitutes. For example, the demand for ice cream in general is less elastic than the demand for a particular brand of ice cream. Many different brands of ice cream are available. Therefore, consumers will respond more to a change in the price of a specific brand than they will to a change in the overall price of ice cream. The broader the definition of the market, the less elastic demand will be.

The fifth factor is the proportion of consumers' budgets that is accounted for by a good. A 1% decrease in the price of a car will have a much larger impact on consumers than a 1% decrease in the price of paper towels. Although both may be important to consumers, the demand for cars will be more responsive and therefore more elastic.