Price Elasticity of Demand

What is Price Elasticity of Demand?

•Price elasticity of demand (PED) is defined as the measure of responsiveness in the quantity demanded for a commodity as a result of change in price of the same commodity. It is a measure of how consumers react to a change in price. In other words, it is percentage change in 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 of demand refers to the way prices change in relationship to the demand, or the way demand changes in relationship to pricing. Price elasticity can also reference the amount of money each individual consumer is willing to pay for something. People with lower incomes tend to have lower price elasticity, because they have less money to spend. A person with a higher income is thought to have higher price elasticity, since he can afford to spend more. In both cases, ability to pay is negotiated by the intrinsic value of what is being sold. If the thing being sold is in high demand, even a consumer with low price elasticity is usually willing to pay higher prices.
Elasticity implies stretch and flexibility. The flexibility or the price elasticity of demand will change based on each item. Changing nature of both price and demand are affected by a number of factors.
Generally, goods or services offered at a lower price lead to a demand for greater quantity. If you can get socks on sale you might buy several pairs or several packages, instead of just a pair. This means that though the seller offers the socks at a lower price, he usually ends up making more money, because demand for the product has increased. However if the price is set too low, the retailer may lose money by selling too many pairs of socks at a reduced rate.

Price elasticity of demand evaluates how change in price influences demand. In certain circumstances, demand remains inelastic, despite higher prices. This is true of a number of medications that are available to treat certain conditions, where there is no substitute. Demand remains constant in spite of high prices.

In simpler words, demand for a product can be said to be very inelastic if consumers will pay almost any price for the product, and very 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 (high or low prices with relatively equivalent quantity demanded), so it is not elastic. On the other hand, demand for sugar is very elastic because as the price of sugar increases, there are many substitutions which consumers may switch to.

A price fall usually results in an increase in the quantity demanded by consumers. 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 substitutes 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.
Various research methods are used to calculate price elasticity:
Test markets
Analysis of historical sales data
Conjoint analysis

Price Elasticity of Demand
Elasticity of demand (Ped) = % change in demand of good X / % change in price of good X
•If the PED is greater than one, the good is price elastic. Demand is responsive to a change in price. If for example a 15% fall in price leads to a 30% increase in quantity demanded, the price elasticity = 2.0
•If the PED is less than one, the good is inelastic. Demand is not very responsive to changes in price. If for example a 20% increase in price leads to a 5% fall in quantity demanded, the price elasticity = 0.25
•If the PED is equal to one, the good has unit elasticity. The percentage change in quantity demanded is equal to the percentage change in price. Demand changes proportionately to a price change.
•If the PED is equal to zero, the good is perfectly inelastic. A change in price will have no influence on quantity demanded. The demand curve for such a product will be vertical.
•If the PED is infinity, the good is perfectly elastic. Any change in price will see quantity demanded fall to zero. This demand curve is associated with firms operating in perfectly competitive markets

Factors that determine the value of price elasticity of demand
1. Number of close substitutes within the market - The more (and closer) substitutes available in the market the more elastic demand will be in response to a change in price. In this case, the substitution effect will be quite strong.
2. Luxuries and necessities - Necessities tend to have a more inelastic demand curve, whereas luxury goods and services tend to be more elastic. For example, the demand for opera tickets is more elastic than the demand for urban rail travel. The demand for vacation air travel is more elastic than the demand for business air travel.
3. Percentage of income spent on a good - It may be the case that the smaller the proportion of income spent taken up with purchasing the good or service the more inelastic demand will be.
4. Habit forming goods - Goods such as cigarettes and drugs tend to be inelastic in demand. Preferences are such that habitual consumers of certain products become de-sensitised to price changes.
5. Time period under consideration - Demand tends to be more elastic in the long run rather than in the short run. For example, after the two world oil price shocks of the 1970s - the "response" to higher oil prices was modest in the immediate period after price increases, but as time passed, people found ways to consume less petroleum and other oil products. This included measures to get better mileage from their cars; higher spending on insulation in homes and car pooling for commuters. The demand for oil became more elastic in the long-run
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.)
This simple formula has a problem, however. It yields different values for Ed depending on whether Qd and Pd are the original or final values for quantity and price. This formula is usually valid either way as long as you are consistent and choose only original values or only final values. (note that a percentage change is always calculated with the initial value in the denominator; if you are to use your final value in the denominator then you must treat that value as the initial value in the numerator. i.e. if price increases from $5 to $10, then the percentage increase is calculated as: ((10 − 5)/5)*100 = 100%. If price decreases from 10 to 5, the percent decrease = ((5 − 10)/10))*100 = −50%. If you throw 10 into the denominator without switching the terms in the numerator your product's price will appear to increase by 50% which is simply not true.)
Or, using the differential calculus form:

This can be rewritten in the 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

Point-price elasticity
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. "Q" means 'Quantity' and "P" means 'Price'.
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.