Price elasticity of demand
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In economics, the price elasticity of demand (PED) is an elasticity that measures the responsiveness of the quantity demanded of a good to its price.
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Introduction
Price elasticity of demand is measured as the percentage change in quantity demanded that occurs in response to a percentage change in price. For example, if, in response to a 10% fall in the price of a good, the quantity demanded increases by 20%, the price elasticity of demand would be 20%/(− 10%) = −2. (Case & Fair, 1999: 109).
In general, a fall in the price of a good is expected to increase the quantity demanded, so the price elasticity of demand is negative as above. Note that in economics literature the minus sign is often omitted and the elasticity is given as an absolute value. (Case & Fair, 1999: 110). Because both the denominator and numerator of the fraction are percent changes, price elasticities of demand are dimensionless numbers and can be compared even if the original calculations were performed using different currencies or goods.
An example of a good with a highly inelastic demand curve is salt: people need salt, so for even relatively large changes in the price of salt, the amount demanded will not be significantly altered. Similarly, a product with a highly elastic demand curve is red cars: if the price of red cars went up even a small amount, demand is likely to go down since substitutes are readily available for purchase (cars of other colors).
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. The unicist approach to price elasticity solved the problem integrating the demanded quantity, its subjective value and the price.
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 is
- <math>E_d = \left|\frac{\%\ \rm{change}\ \rm{in}\ \rm{quantity}\ \rm{demanded}\ \rm{of}\ \rm{product}\ X}{\%\ \rm{change}\ \rm{in}\ \rm{price}\ \rm{of}\ \rm{product}\ X}\right| = \frac{\Delta Q_d/Q_d}{\Delta P_d/P_d}</math>
Using all the differential calculus:
<math>E_d={P \over Q }{{\partial Q}\over{\partial P}}</math>
where:
- <math>P</math> = price
- <math>Q</math> = quantity
Elasticity and revenue
Image:Price elasticity of demand and revenue.png
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 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 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 = ∞), 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 straght line. A ten-dollar banknote is an example of a perfectly elastic good; nobody would pay $10.01, 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.
See also
References
- Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.de:Preiselastizität
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