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In economics and business studies, the
price elasticity of demand (PED) is an
elasticity (economics) that measures the nature and degree of the relationship between changes in quantity demanded of a good and changes in its price.
Introduction
When the price of a good falls, the quantity consumers demand of the good typically rises; if it costs less, consumers buy more. Price elasticity of demand measures the responsiveness of a change in quantity demanded for a good or service to a change in price.
Mathematically, the PED is the ratio of the relative (or percent) change in quantity demanded to the relative change in price. For most goods this ratio is negative, but in practice the elasticity is represented as a positive number and the minus sign is understood. For example, if for some good when the price
decreases by 10%, the quantity demanded
increases by 20%, the PED for that good will be two.
When the PED of a good is greater than one in absolute value, the demand is said to be
elastic; it is highly responsive to changes in price. Demands with an elasticity less than one in absolute value are
inelastic; the demand is weakly responsive to price changes.
Interpretation of elasticity
{| class="wikitable"|-! Value! Meaning|-| n = 0| Perfectly inelastic.|-| 0 < n < 1| Relatively inelastic.|-| n = 1| Unit elastic.|-| 1 < n < ∞| Relatively elastic.|-| n = ∞| Perfectly elastic.|}
For all Normal_good and most
Inferior_good, 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.
Price elasticity of demand is rarely constant throughout the ranges of quantity demanded and price. A good or service can have relatively inelastic demand up to a certain price, above which demand becomes elastic. Even if automobiles, for example, were extremely inexpensive, parking or other related ownership issues would presumably keep most people from owning more than some "maximum" number of automobiles. For these and other reasons, elasticity of demand remains valid only over a specific (and small) range of price. Demand for cars (as well as other goods and services) is not elastic or inelastic for all prices. Elasticity of demand can change dramatically across a range of prices.
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
substitute good. For example, potato chips are only one type of snack food out of many others, such as corn chips or cracker (food), 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 good 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 lessons ability to charge higher prices as an indication of higher quality, thus increasing the quantity of lessons demanded.
Various research methods are used to calculate price elasticity:
Mathematical definition
The formula used to calculate the coefficient 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}
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.
A more elegant and reliable calculation uses a midpoint calculation, which eliminates this ambiguity. Another benefit of using the following formula is that when
Ed = 1, it means there will be no change in revenue when the price changes from
P1 (the original price) to
P2.
Qav means the average of the original and final values of quantity demanded, and likewise for
Pav.
\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=\frac{dQ}{dP}\frac{P}{Q}
Interestingly, repeated use of the chain rule reveals that:
E_d={{\partial \ln (Q)}\over{\partial \ln (P)-->
From the following process:
Note:
{{\partial \ln (Q)}\over{\partial \ln (P)-->={{\partial \ln (Q)}\over{\partial Q-->\times{{\partial Q}\over{\partial \ln (P)-->={{1}\over{Q-->\times{{\partial Q}\over{\partial \ln (P)-->
Further Note:
{{\partial Q}\over{\partial P-->={{\partial \ln (P)}\over{\partial P-->\times{{\partial Q}\over{\partial \ln (P)-->={{1}\over{P-->\times{{\partial Q}\over{\partial \ln (P)-->
Implying:
{{\partial Q}\over{\partial \ln (P)-->={P}\times{{\partial Q}\over{\partial P-->
Substitution reveals:
{{\partial \ln (Q)}\over{\partial \ln (P)-->={{1}\over{Q-->\times{{\partial Q}\over{\partial P-->\times{P}=E_d
Elasticity and revenue
When the price elasticity of demand for a
good is
inelastic (].
When the price elasticity of demand for a good is
perfectly elastic (Ed is
Infinity#Mathematical infinity), 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 bill, 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 effect 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.
{{\partial Q}\over{\partial P--> = -0.6
ii.) next apply the above equation to the sought ordered pairs: (40, 976), (80, 952)
E_p={{\partial Q}\over{\partial P-->{P \over Q }
e = -0.6(40/976) = -0.02
e = -0.6(80/952) = -0.05
See also
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.
In economics and business studies, the price elasticity of demand (PED) is an elasticity (economics) that measures the nature and degree of the relationship between changes in quantity demanded of a good and changes in its price.
Introduction
When the price of a good falls, the quantity consumers demand of the good typically rises; if it costs less, consumers buy more. Price elasticity of demand measures the responsiveness of a change in quantity demanded for a good or service to a change in price.
Mathematically, the PED is the ratio of the relative (or percent) change in quantity demanded to the relative change in price. For most goods this ratio is negative, but in practice the elasticity is represented as a positive number and the minus sign is understood. For example, if for some good when the price decreases by 10%, the quantity demanded increases by 20%, the PED for that good will be two.
When the PED of a good is greater than one in absolute value, the demand is said to be elastic; it is highly responsive to changes in price. Demands with an elasticity less than one in absolute value are inelastic; the demand is weakly responsive to price changes.
Interpretation of elasticity
{| class="wikitable"|-! Value! Meaning|-| n = 0| Perfectly inelastic.|-| 0 < n < 1| Relatively inelastic.|-| n = 1| Unit elastic.|-| 1 < n < ∞| Relatively elastic.|-| n = ∞| Perfectly elastic.|}
For all Normal_good and most Inferior_good, 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.
Price elasticity of demand is rarely constant throughout the ranges of quantity demanded and price. A good or service can have relatively inelastic demand up to a certain price, above which demand becomes elastic. Even if automobiles, for example, were extremely inexpensive, parking or other related ownership issues would presumably keep most people from owning more than some "maximum" number of automobiles. For these and other reasons, elasticity of demand remains valid only over a specific (and small) range of price. Demand for cars (as well as other goods and services) is not elastic or inelastic for all prices. Elasticity of demand can change dramatically across a range of prices.
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 substitute good. For example, potato chips are only one type of snack food out of many others, such as corn chips or cracker (food), 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 good 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 lessons ability to charge higher prices as an indication of higher quality, thus increasing the quantity of lessons demanded.
Various research methods are used to calculate price elasticity:
Mathematical definition
The formula used to calculate the coefficient 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}
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.
A more elegant and reliable calculation uses a midpoint calculation, which eliminates this ambiguity. Another benefit of using the following formula is that when Ed = 1, it means there will be no change in revenue when the price changes from P1 (the original price) to P2.
Qav means the average of the original and final values of quantity demanded, and likewise for Pav.
\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=\frac{dQ}{dP}\frac{P}{Q}
Interestingly, repeated use of the chain rule reveals that:
E_d={{\partial \ln (Q)}\over{\partial \ln (P)-->
From the following process:
Note:
{{\partial \ln (Q)}\over{\partial \ln (P)-->={{\partial \ln (Q)}\over{\partial Q-->\times{{\partial Q}\over{\partial \ln (P)-->={{1}\over{Q-->\times{{\partial Q}\over{\partial \ln (P)-->
Further Note:
{{\partial Q}\over{\partial P-->={{\partial \ln (P)}\over{\partial P-->\times{{\partial Q}\over{\partial \ln (P)-->={{1}\over{P-->\times{{\partial Q}\over{\partial \ln (P)-->
Implying:
{{\partial Q}\over{\partial \ln (P)-->={P}\times{{\partial Q}\over{\partial P-->
Substitution reveals:
{{\partial \ln (Q)}\over{\partial \ln (P)-->={{1}\over{Q-->\times{{\partial Q}\over{\partial P-->\times{P}=E_d
Elasticity and revenue
When the price elasticity of demand for a good is inelastic (].
When the price elasticity of demand for a good is perfectly elastic (Ed is Infinity#Mathematical infinity), 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 bill, 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 effect 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.
{{\partial Q}\over{\partial P--> = -0.6
ii.) next apply the above equation to the sought ordered pairs: (40, 976), (80, 952)
E_p={{\partial Q}\over{\partial P-->{P \over Q }
e = -0.6(40/976) = -0.02
e = -0.6(80/952) = -0.05
See also
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.
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