Information about Price Elastic
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.
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.
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.
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 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 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:
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.
Or, using the differential calculus:
Interestingly, repeated use of the chain rule reveals that:
From the following process:
Note:
Further Note:
Implying:
Substitution reveals:
When the price elasticity of demand for a good is inelastic (|Ed| < 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 (|Ed| > 1), the percentage change in quantity 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. Hence, when the price is raised, the total revenue remains unchanged. The demand curve is a rectangular hyperbola.
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 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 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.
ii.) next apply the above equation to the sought ordered pairs: (40, 976), (80, 952)
e = -0.6(40/976) = -0.02
e = -0.6(80/952) = -0.05
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
| Value | Meaning |
|---|---|
| n = 0 | Perfectly inelastic. |
| 0 < n < 1 | Relatively inelastic. |
| n = 1 | Unit elastic. |
| 1 < n < 8 | Relatively elastic. |
| n = 8 | 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.
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 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 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:
- 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
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.
Or, using the differential calculus:
Interestingly, repeated use of the chain rule reveals that:
From the following process:
Note:
Further Note:
Implying:
Substitution reveals:
Elasticity and revenue
- See also:
)
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 elastic (|Ed| > 1), the percentage change in quantity 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. Hence, when the price is raised, the total revenue remains unchanged. The demand curve is a rectangular hyperbola.
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 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
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.
ii.) next apply the above equation to the sought ordered pairs: (40, 976), (80, 952)
e = -0.6(40/976) = -0.02
e = -0.6(80/952) = -0.05
See also
- Supply and demand
- Price elasticity of supply
- Income elasticity of demand
- Cross elasticity of demand
- Arc elasticity
- Yield elasticity of bond value
External links
References
Notes
General references
- Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.
Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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In economics, elasticity is the ratio of the proportional change in one variable with respect to proportional change in another variable. Price elasticity, for example, is the sensitivity of quantity demanded or supplied to changes in prices.
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antibiotic is a chemotherapeutic agent that inhibits or abolishes the growth of micro-organisms, such as bacteria, fungi, or protozoans. The term originally referred to any agent with biological activity against living organisms; however, "antibiotic" now is used to refer to
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In economics, one kind of good (or service) is said to be a substitute good for another kind insofar as the two kinds of goods can be consumed or used in place of one another in at least some of their possible uses.
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potato chip or crisp is a thin slice of potato, deep fried or baked until crisp. Potato chips serve as an appetizer, side dish, or snack. Commercial varieties are packaged for sale, usually in bags.
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A corn chip is a snack food made from corn (maize) meal that has been processed into a particular shape, typically a small scoop.
A similar snack is the tortilla chip, which is made from fried corn tortilla wedges or strips.
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A similar snack is the tortilla chip, which is made from fried corn tortilla wedges or strips.
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cracker is a dry, thin, crispy, and usually savory biscuit that developed from military hardtack and nautical ship biscuits.
In 1801 Josiah Bent began a baking operation in Milton, Massachusetts, selling "water crackers" or biscuits made of flour and water that would not
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In 1801 Josiah Bent began a baking operation in Milton, Massachusetts, selling "water crackers" or biscuits made of flour and water that would not
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Homo economicus, or Economic man, is the concept in some economic theories of man (that is, a human) as a rational and self-interested actor who desires wealth, avoids unnecessary labor, and has the ability to make judgments towards those ends.
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A Giffen good is an inferior good for which a rise in its price makes people buy even more of the product as a consequence of the income effect. Evidence for the existence of Giffen goods is limited, but there is an economic model that explains how such a thing could exist.
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Veblen goods if people's preference for buying them increases as a direct function of their price.
It is claimed that some types of high-status goods, such as expensive wines or perfumes, are Veblen goods, in that decreasing their prices decreases
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It is claimed that some types of high-status goods, such as expensive wines or perfumes, are Veblen goods, in that decreasing their prices decreases
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economic bubble (sometimes referred to as a "speculative bubble", a "market bubble", a "price bubble", a "financial bubble", or a "speculative mania") is “trade in high volumes at prices that are considerably at variance from intrinsic values”.
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Market research is broader in scope and examines all aspects of a business environment. It asks questions about competitors, market structure, government regulations, economic trends, technological advances, and numerous other factors that make up the business environment.
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Conjoint analysis is a statistical technique used in market research to determine how people value different features that make up an individual product or service.
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In calculus, the chain rule is a formula for the derivative of the composite of two functions.
In intuitive terms, if a variable, y, depends on a second variable, u, which in turn depends on a third variable, x, then the rate of change of
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In intuitive terms, if a variable, y, depends on a second variable, u, which in turn depends on a third variable, x, then the rate of change of
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Good may refer to:
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- Good and evil, in religion, ethics, and philosophy
- Good (economics and accounting), a useful object or service
- Good Technology, a company which sells Push e-mail products for mobile phones
- Form of the Good in Platonic philosophy
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hyperbola (Greek ὑπερβολή literally 'overshooting' or 'excess') is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves
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supply and demand describe market relations between prospective sellers and buyers of a good. The supply and demand model determines price and quantity sold in the market.
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In economics, the price elasticity of supply is defined as a numerical measure of the responsiveness of the quantity supplied of product(A) to a change in price of product (A) alone.
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In economics, the income elasticity of demand measures the responsiveness of the quantity demanded of a good to the change in the income of the people demanding the good. It is calculated as the ratio of the percent change in quantity demanded to the percent change in income.
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In economics, the cross elasticity of demand and cross price elasticity of demand measures the responsiveness of the quantity demand of a good to a change in the price of another good.
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Arc elasticity is the elasticity of one variable with respect to another between two given points.
The y arc elasticity of x is defined as:
where the percentage change is calculated relative to the midpoint
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The y arc elasticity of x is defined as:
where the percentage change is calculated relative to the midpoint
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Yield elasticity of bond value is the percentage change in bond value divided by a one per percentage change in the yield to maturity of the bond. This is equivalent to saying the derivative of value with respect to yield times the (interest rate/value).
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