Price elasticity of demand

Price elasticity of demand (PED) is defined as the responsiveness of the quantity demanded of a good or service to a change in its price.

In other words, it is percentage change of quantity demanded by the percentage change in price of the same commodity. In economics and business studies, the price elasticity of demand is a measure of the sensitivity of quantity demanded to changes in price. It is measured as elasticity, that is it measures the relationship as the ratio of percentage changes between quantity demanded of a good and changes in its price. Price elasticity is almost always negative, although analysts tend to ignore the sign. Only goods which do not conform the law of demand, such as Veblen and Giffen goods, have a positive PED.

In simpler words: demand for a product can be said to be very inelastic if consumers will pay almost any price for the product, while demand for a product may be elastic if consumers will only pay a certain price, or a narrow range of prices, for the product. Inelastic demand means a producer can raise prices without much hurting demand for its product, and elastic demand means that consumers are sensitive to the price at which a product is sold and will not buy it if the price rises by what they consider too much. Drinking water is a good example of a good that has inelastic characteristics - in that people will pay anything for it. On the other hand, demand for sugar is very elastic because as the price of sugar increases there are many substitute goods which consumers may switch to.

Various research methods are used to calculate price elasticity, including test markets, analysis of historical sales data and conjoint analysis.

Determinants

A number of factors can affect the elasticity of a good:

Substitutes: The more substitutes, the higher the elasticity, as people can easily switch from one good to another if a minor price change is made

Percentage of income: The higher the percentage that the product's price is of the consumer's income, the higher the elasticity, as people will be careful with purchasing the good because of its cost

Necessity: The more necessary a good is, the lower the elasticity, as people will attempt to buy it no matter the price, such as the case of insulin for those that need it.

Duration: The longer a price change holds, the higher the elasticity, as more and more people will stop demanding the goods (i.e. if you go to the supermarket and find that blueberries have doubled in price, you'll buy it because you need it this time, but next time you won't, unless the price drops back down again)

Breadth of definition: The broader the definition, the lower the elasticity. For example, Company X's fried dumplings will have a relatively high elasticity, whereas food in general will have an extremely low elasticity.

Mathematical definition

The formula used to calculate coefficients of price elasticity of demand for a given product is

Conventions differ regarding the minus sign, considering remarks like "price elasticity of demand is usually negative". (The sign of the coefficient should actually be determined by the directions in which price and quantity change; i.e. if the price increases by 5% and quantity demanded decreases by 5%, then the elasticity at the initial price and quantity = −5%/5% = −1. Note, however, that many economists will refer to price-elasticity of demand as a positive value although it is generally negative due to the negative relationship between price and quantity demanded, as denoted by the law of demand.)

Or, using the differential calculus form:

On the graduate level, Mas-Colell, Winston, and Green (1995) defines elasticity of demand with respect

to price as follows. Let be the demand of goods as a function of parameters

price and wealth, and let be the demand for good . The elasticity of demand with respect to price pk is

Elasticity and revenue A set of graphs shows the relationship between demand and total revenue. As price decreases in the

elastic range, revenue increases, but in the inelastic range, revenue

decreases.

A firm considering a price change must know what effect the change in price will have on total revenue. Generally any change in price will have two effects:

the price effect: an increase in unit price will tend to increase revenue, while a decrease in price will tend to decrease revenue.

the quantity effect: an increase in unit price will tend to lead to fewer units sold, while a decrease in unit price will tend to lead to more units sold.

Because of the inverse nature of the demand relationship the two effects are offsetting. The firm needs to know what the net effect will be. Elasticity provides the answer.

When the price elasticity of demand for a good is inelastic (|Ed| < 1), the percentage change in quantity demanded is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa.

When the price elasticity of demand for a good is elastic (|Ed| > 1), the percentage change in quantity demanded is greater than that in price. Hence, when the price is raised, the total revenue of producers falls, and vice versa.

When the price elasticity of demand for a good is unit elastic (or unitary elastic) (|Ed| = 1), the percentage change in quantity is equal to that in price.

When the price elasticity of demand for a good is perfectly elastic (Ed is undefined), any increase in the price, no matter how small, will cause demand for the good to drop to zero. Hence, when the price is raised, the total revenue of producers falls to zero. The demand curve is a horizontal straight line. A banknote is the classic example of a perfectly elastic good; nobody would pay £10.01 for a £10 note, yet everyone will pay £9.99 for it.

When the price elasticity of demand for a good is perfectly inelastic (Ed = 0), changes in the price do not affect the quantity demanded for the good. The demand curve is a vertical straight line; this violates the law of demand. An example of a perfectly inelastic good is a human heart for someone who needs a transplant; neither increases nor decreases in price affect the quantity demanded (no matter what the price, a person will pay for one heart but only one; nobody would buy more than the exact amount of hearts demanded, no matter how low the price is).

Note that a firm would never operate within the inelastic range of its demand curve since by raising prices the firm would assure not only an increase in revenue but also an increase in profits.

Interpreting coefficients

Perfectly inelastic demand

Perfectly elastic demand

Value Meaning

Ed = 0 Perfectly inelastic.

- 1 < Ed < 0 Relatively inelastic or inelastic demand.

Ed = - 1 Unit (or unitary) elastic.

-∞ < Ed < - 1 Relatively elastic or elastic demand.

Ed = -∞ Perfectly elastic.

A price fall usually results in an increase in the quantity demanded by consumers, per the law of demand. The demand for a good is relatively inelastic when the change in quantity demanded is less than change in price. Goods and services for which no substitute goods exist are generally inelastic. Demand for an antibiotic, for example, becomes highly inelastic when it alone can kill an infection resistant to all other antibiotics. Rather than die of an infection, patients will generally be willing to pay whatever is necessary to acquire enough of the antibiotic to kill the infection.

Point-price elasticity

Something not immediately evident is that PED is not constant, and varies over the demand curve, due to its percentage nature. This can be demonstrated either via a set change at different points, or through the more abstract use of point-price elasticities. For any point on the demand curve, a point-price elasticity can be calculated.

Point elasticity = (% change in Quantity) / (% change in Price) Point elasticity = (∆Q/Q)/(∆P/P) Point elasticity = (P ∆Q) / (Q ∆P) Point elasticity = (P/Q)(∆Q/∆P)

Note: In the limit (or "at the margin"), "(∆Q/∆P)" is the derivative of the demand function with respect to P.

Worked example

Suppose a certain good (say, laserjet printers) has a demand curve Q = 1,000 − 0.6P. We wish to determine the point-price elasticity of demand at P = 80 and P = 40. First, we take the derivative of the demand function Q with respect to P:

Next we apply the equation for point-price elasticity, namely:

to the ordered pairs (40, 976) and (80, 952). We have:

at P=40, point-price elasticity e = −0.6(40/976) = −0.02. at P=80, point-price elasticity e = −0.6(80/952) = −0.05.

Disclaimer: these are not my original notes, I have copied them from net and then prepared.