Price_elasticity_of_demand

In economics and business studies, the price elasticity of demand (PED) is an elasticity that measures the nature and degree of the relationship between changes in quantity demanded of a good and changes in its price.

Contents 1 Introduction 2 Interpretation of elasticity 3 Mathematical definition 4 Elasticity and revenue 5 Point-price elasticity 6 See also 7 External links 8 References 8.1 Notes 8.2 General references

Introduction

Interpretation of elasticity

Value	Meaning
n = 0	Perfectly inelastic.
0 < n < 1	Relatively inelastic.
n = 1	Unitary elastic.
1 < n < ∞	Relatively elastic.
n = ∞	Perfectly elastic.

For all normal goods and most inferior goods, a price drop results in an increase in the quantity demanded by consumers. The demand for a good is relatively inelastic when the quantity demanded does not change much with the price change. 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.

Inelastic demand is commonly associated with "necessities," although there are many more reasons a good or service may have inelastic demand other than the fact that consumers may "need" it. Demand for salt, for instance, at its modern levels of supply is highly inelastic not because it is a necessity but because it is such a small part of the household budget. (Technology has increased the supply of salt modernly and reduced its historically high price.) Demand for water, another necessity, is highly inelastic for similar supply side reasons. Demand for other goods, like chocolate, which is not a necessity, can be highly elastic.

Substitution serves as a much more reliable predictor of elasticity of demand than "necessity." For example, few substitutes for oil and gasoline exist, and as such, demand for these goods is relatively inelastic. However, products with a high elasticity usually have many substitutes. For example, potato chips are only one type of snack food out of many others, such as corn chips or crackers, and predictably, consumers have more room to turn to those substitutes if potato chips were to become more expensive.

It may be possible that quantity demanded for a good rises as its price rises, even under conventional economic assumptions of consumer rationality. Two such classes of goods are known as Giffen goods or Veblen goods. Another case is the price inflation during an economic bubble. Consumer perception plays an important role in explaining the demand for products in these categories. A starving musician who offers lessons at a bargain basement rate of $5.00 per hour will continue to starve, but if the musician were to raise the price to $35.00 per hour, consumers may perceive the musician\'s ability to charge higher prices for lessons as an indication of higher quality, thus increasing the quantity of lessons demanded.

PED is determined by a number of factors that essentially all fall under the umbrella of "choice". By choice we mean the power of choice that the consumer of a given good holds to give up the consumption of said good. The greater this choice the more price elastic the good will be and, by contrast, as the balance of this power falls in favour of the supplier the more inelastic the good will be. This is due to the consumer\'s "Perceived Value". A good which is difficult to replace or give up consuming will have a higher perceived value than that which is more easily replaced thus the consumer will be willing to pay more for such a good. Perceived Value represents the absolute maximum price a consumer is willing to pay for a good. When the price exceeds this level, the consumer will give up consumption of this good.

1. Availability of Good Quality Substitutes: Easily substitutable goods will enable buyers to switch to an alternative good and thus such goods will exhibit greater elasticity than goods that do not have substitutes available, ceteris paribus (assuming all other variables are equal). It is important to understand that a given good is in essence unique and thus the comparability of the available substitute(s) in terms of quality to the original good is an important sub-variable. The better the substitute(s) can replace the original good in terms of desirability, affordability, practicality etc. the more elastic the good will become. For example, a commuter taking the train to work could switch to taking the bus if faced with rising train fares. However, this may mean more inconvenience and/or longer journey time for example and thus will form part of his consideration before switching that mode of transport and it may take a certain price difference before he will resort to this option representing the substitute\'s quality. A contrasting inelastic good would be water which is arguably insubstitutable so a local community faced with rising water costs will be left with little choice but to pay the increased costs forming a price inelastic good.
2. Whether the good is habit forming or obligatory: Addictive drugs, whether psychologically addictive or physically addictive, and other goods where dependency plays a key role will naturally exhibit inelastic properties. At aggregate level, rising costs of such goods are unlikely to reduce demand significantly. Classic examples of such goods would be alcohol and tobacco or in an extreme case, heroin. A heroin addict will virtually go to any length to achieve the next fix irrespective of cost. Governments often place taxes on these types of goods, namely alcohol, tobacco and fuel because of their highly inelastic demand since consequently such goods are assured revenue generators for the treasury.
3. The proportion of the consumer\'s income the good represents: Goods which typically make up a small proportion of people\'s income will exhibit inelastic qualities. Conversely, goods which form a large proportion of people\'s income will cause greater responses in demand to comparable % increases or decreases in price. For example, if cinema ticket costs rise by 20%, decreases in demand are unlikely to be pronounced. However a 15% drop in a "luxury" good such as a car or LCD Television changes in demand are likely to be relatively greater.
4. How closely the good is defined: Taking our example from (2), cigarettes in general are, as discussed, an inelastic good. However a particular brand of cigarettes will exhibit far more elastic properties if its price rises. In general therefore, the exact type of good will affect its PED properties.
5. How closely the consumer (end-user) is defined?: This is an important factor intrinsically related to most of the preceding variables. "Choice" is very subjective and factors 1,2 and 3 vary relative to the individual consumer because every single consumer can potentially have a different Perceived Value of a good. A good that is easily replaceable or habit forming or expensive for one person may well not be for another and thus how well the consumer is defined will affect the PED. At nationwide level, if the cost of butter rises significantly consumers can choose to consume margarine instead but a shop who makes and sells butter cookies will not have this option and thus the PED will be far more inelastic in the latter case. A driver faced with rising petrol bills may opt to switch to using the train. However an airline company has no choice but to absorb rising fuel costs and will according have a much more inelastic demand curve for essentially the same good.
6. How closely the time period is defined: Generally the greater the time period, the more possible it may be for a good to be replaced with a substitute. Using home energy as an example, a gas user faced with rising gas bills will unlikely be able to switch to electric alternatives overnight due to possibly contractual tie-ins and time needed to change a stove to electric hob for example. However over three months, a switch is far more viable and the PED will be accordingly more elastic. Likewise, prices are dynamic. Over short time periods, prices of substitutes maybe static, over longer periods, the price of substitutes may drop, making them more appealing. [Puiatti, 18:36 10-Nov-07]

Various research methods are used to calculate price elasticity:

• Test markets
• Analysis of historical sales data
• Conjoint analysis

Mathematical definition

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

$E\_d\; =\; \backslash frac\{\backslash \%\backslash \; \backslash mbox\{change\; in\; quantity\; demanded\}\}\{\backslash \%\backslash \; \backslash mbox\{change\; in\; price\}\}\; =\; \backslash frac\{\backslash Delta\; Q\_d/Q\_d\}\{\backslash Delta\; P\_d/P\_d\}$

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.

A more elegant and reliable calculation uses a midpoint calculation, which eliminates this ambiguity. Another benefit of using the following formula is that when E_d = 1, it means there will be no change in revenue when the price changes from P₁ (the original price) to P₂.

Q_av means the average of the original and final values of quantity demanded, and likewise for P_av.

$\backslash begin\{align\}$

E_d &= \frac{\Delta Q_d/Q_{av}}{\Delta P_d/P_{av}} \\

   &= \frac{(Q_2 - Q_1)\ /\ [(Q_1 + Q_2)/2]}{(P_2 - P_1)\ /\ [(P_1 + P_2)/2]} \\
   &= \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1+P_2}{Q_1+Q_2} \end{align}

Or, using the differential calculus:

$E\_d=\backslash frac\{dQ\}\{dP\}\backslash frac\{P\}\{Q\}$

This can be rewritten in the form:

$E\_d=\{\{\backslash partial\; \backslash ln\; (Q)\}\backslash over\{\backslash partial\; \backslash ln\; (P)\}\}$

Elasticity and revenue

See also: Total revenue test

A set of graphs shows the relationship between demand and total revenue. As elasticity decreases in the elastic range, revenue increases, but in the inelastic range, revenue decreases.

When the price elasticity of demand for a good is inelastic (|E_d| < 1), the percentage change in quantity 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 (|E_d| > 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) (|E_d| = 1), the percentage change in quantity is equal to that in price.

When the price elasticity of demand for a good is perfectly elastic (E_d 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 (E_d = 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).

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
Demand curve: Q = 1,000 - 0.6P
a.) Given this demand curve determine the point price elasticity of demand at P = 80 and P = 40 as follows.
i.) obtain the derivative of the demand function when it\'s expressed Q as a function of P.
$\{\{\backslash partial\; Q\}\backslash over\{\backslash partial\; P\}\}\; =\; -0.6$
ii.) next apply the above equation to the sought ordered pairs: (40, 976), (80, 952)
$E\_p=\{\{\backslash partial\; Q\}\backslash over\{\backslash partial\; P\}\}\{P\; \backslash over\; Q\; \}$
e = -0.6(40/976) = -0.02
e = -0.6(80/952) = -0.05

See also

• Supply and demand
• Elasticity
• Price elasticity of supply
• Income elasticity of demand
• Cross elasticity of demand
• Arc elasticity
• Yield elasticity of bond value

External links

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

References

Notes

General references

• Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.

This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia