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For the supply, see Price elasticity of supply.

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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.^[1] 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. 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.

1 Interpretation of elasticity
2 Determinants
3 Elasticity and revenue
4 Mathematical definition
- 4.1 Point-price elasticity
5 See also
6 External links
7 References
- 7.1 Notes
- 7.2 General references

Interpretation of elasticity

Perfectly inelastic demand

Perfectly elastic demand

Value	Meaning
n = 0	Perfectly inelastic.
−1 < n < 0	Relatively inelastic.
n = −1	Unit (or unitary) elastic.
−∞ < n < −1	Relatively elastic.
n = −∞	Perfectly elastic.

A price fall usually results in an increase in the quantity demanded by consumers (see Giffen good for an exception). 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

Determinants

A number of factors determine the elasticity:

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 (see Substitutes, Necessity above)

^[2]^[3]

Elasticity and revenue

Mathematical definition

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

$E_d = \frac{\%\ \mbox{change in quantity demanded}}{\%\ \mbox{change in price}} = \frac{\Delta Q_d/Q_d}{\Delta P_d/P_d}$

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 E_d depending on whether Q_d and P_d 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:

$E_d = - \frac{P}{Q}\frac{dQ}{dP}$

This can be rewritten in the form:

$E_d = - \frac{d \ln Q}{d \ln P}$

On the graduate level, Mas-Colell, Winston, and Green (1995) defines elasticity of demand with respect to price as follows. Let $\displaystyle x(p,w)$ be the demand of goods $x_1,x_2,\dots,x_L$ as a function of parameters price and wealth, and let $\displaystyle x_l(p,w)$ be the demand for good $\displaystyle l$ . The elasticity of demand $\displaystyle x_l(p,w)$ with respect to price $p k$ is

$E_{x_l,p_k} = \frac{\partial x_l(p,w)}{\partial p_k}\cdot\frac{p_k}{x_l(p,w)} = \frac{\partial \log x_l(p,w)}{\partial \log p_k}$

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:
${{\partial Q}\over{\partial P}} = -0.6.$
Next we apply the equation for point-price elasticity, namely
$E_p={{\partial Q}\over{\partial P}}{P \over Q }$
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.

External links

Approx. PED of Various Products (U.S.)

References

Notes

^ Sullivan, arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. pp. 90. ISBN 0-13-063085-3. http://www.pearsonschool.com/index.cfm?locator=PSZ3R9&PMDbSiteId=2781&PMDbSolutionId=6724&PMDbCategoryId=&PMDbProgramId=12881&level=4.
^ Economic Concepts
^ ECO 240 | Tutorial 4a

General references

Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.
Mas-Colell, Andreu, Michael D. Winston, and Jerry R. Green. Microeconomic Theory. Oxford University Press, New York, 1995.

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Price elasticity of demand

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