Elasticity (economics)
In economics, elasticity measures the responsiveness of one economic variable to a change in another. For example, if the price elasticity of the demand of a good is −2, then a 10% increase in price will cause the quantity demanded to fall by 20%. Elasticity in economics provides an understanding of changes in the behavior of the buyers and sellers with price changes. There are two types of elasticity for demand and supply, one is inelastic demand and supply and the other one is elastic demand and supply.
Introduction
The concept of price elasticity was first cited in an informal form in the book Principles of Economics published by the author Alfred Marshall in 1890. Subsequently, a major study of the price elasticity of supply and the price elasticity of demand for US products was undertaken by Joshua Levy and Trevor Pollock in the late 1960s.Elasticity is an important concept in neoclassical economic theory, and enables in the understanding of various economic concepts, such as the incidence of indirect taxation, marginal concepts relating to the theory of the firm, distribution of wealth, and different types of goods relating to the theory of consumer choice. An understanding of elasticity is also important when discussing welfare distribution, in particular consumer surplus, producer surplus, or government surplus.
Elasticity is present throughout many economic theories, with the concept of elasticity appearing in several main indicators. These include price elasticity of demand, price elasticity of supply, income elasticity of demand, elasticity of substitution between factors of production, cross-price elasticity of demand, and elasticity of intertemporal substitution.
In differential calculus, elasticity is a tool for measuring the responsiveness of one variable to changes in another causative variable. Elasticity can be quantified as the ratio of the percentage change in one variable to the percentage change in another variable when the latter variable has a causal influence on the former and all other conditions remain the same. For example, the factors that determine consumers' choice of goods mentioned in consumer theory include the price of the goods, the consumer's disposable budget for such goods, and the substitutes of the goods.
Within microeconomics, elasticity and slope are closely linked. For price elasticity, the relationship between the two variables on the x-axis and y-axis can be obtained by analyzing the linear slope of the demand or supply curve or the tangent to a point on the curve. When the tangent of the straight line or curve is steeper, the price elasticity is smaller; when the tangent of the straight line or curve is flatter, the price elasticity is higher.
ratio, independent of the type of quantities being varied. An elastic variable responds more than proportionally to changes in other variables. A unit elastic variable responds proportionally to changes in other variables. In contrast, an inelastic variable changes less than proportionally in response to changes in other variables. A variable can have different values of its elasticity at different starting points. For example, for the suppliers of the goods, the quantity of a good supplied by producers might be elastic at low prices but inelastic at higher prices, so that a rise from an initially low price might bring on a more-than-proportionate increase in quantity supplied. In contrast, a raise from an initially high price might bring on a less-than-proportionate rise in quantity supplied.
In empirical work, an elasticity is the estimated coefficient in a linear regression equation where both the dependent variable and the independent variable are in natural logs. Elasticity is a popular tool among empiricists because it is independent of units and thus simplifies data analysis.
Definition
The elasticity of a variable with respect to a change in variable is defined as follows:.
When the changes are infinitesimal we can define the elasticity of with respect to as follows:
.
That is, the elasticity is the measure of the sensitivity of one variable to another. A highly elastic variable will respond more dramatically to changes in the variable it is dependent on.
In economics, the common elasticities all have the same form:
| elastic | Q changes more than P | |
| unit elastic | Q changes like P | |
| inelastic | Q changes less than P |
Suppose price rises by 1%. If the elasticity of supply is 0.5, quantity rises by.5%; if it is 1, quantity rises by 1%; if it is 2, quantity rises by 2%.
Special cases:
Example of calculation
Suppose the demand curve is.Then
The price-elasticity of demand will be:
Maximizing revenue
Seller revenue is maximized when because at that point a change in price is exactly cancelled by the quantity response, leaving the total revenue unchanged. To maximize revenue, a firm must increase price if demand is inelastic: and decrease price if demand is elastic:As the total revenue is unchanged, we have that
So
The cancellation of the 's is justified by the fact that both time differentials are non-zero and the same.
The elasticity of demand is different at different points of a demand curve, so for most demand functions, including linear demand, a firm following this advice will find some price at which and further price changes would reduce revenue.
Types of elasticity
Price elasticity of demand
measures sensitivity of demand to price. Thus, it measures the percentage change in demanded quantity for a good in response to a change in its own price. More precisely, it gives the percentage change in quantity demanded in response to a one per cent change in price. Expressing this mathematically, price elasticity of demand is calculated by dividing the percentage change in the quantity demanded by the percentage change in the price.If price elasticity of demand is calculated to be less than 1, the good is said to be inelastic. An inelastic good will respond less than proportionally to a change in price; for example, a price increase of 40% that results in a decrease in demand of 10%.
Goods that are inelastic often have at least one of the following characteristics:
- Few, if any, available substitutes
- Essential goods
- Addictive goods
- Bought infrequently or a small percentage of income
Example: In the above graphical representation which shows an effect of prices on demand. If the price of the pizza is $20 at which the quantity demanded is 5, if there is an increase in price of pizza to $30 it will lead to decrease in quantity demanded to 3 which shows that small changes in the price of pizza lead to higher changes in quantity demanded.
Price elasticity of supply
The price elasticity of supply measures how the amount of a good that a supplier wishes to supply changes in response to a change in price. In a manner analogous to the price elasticity of demand, it captures the extent of horizontal movement along the supply curve relative to the extent of vertical movement. If supply elasticity is zero, the supply of a good supplied is "totally inelastic", and the quantity supplied is fixed. It is calculated by dividing the percentage change in quantity supplied by the percentage change in price.The supply is said to be inelastic when the change in the prices leads to small changes in the quantity of supply. Whereas the elastic supply means the changes in prices causes higher changes in the quantity supplied.
Income elasticity of demand
is a measure used to show the responsiveness of the quantity demanded of a good or service to a change in the consumer income. Mathematically, this is calculated by dividing the percentage change in the quantity demanded by the percentage change in income. Generally, a higher income will increase quantity demanded as consumers will be willing to spend more.Cross-price elasticity of demand
measures the sensitivity between the quantity demanded in one good when there is a change in the price of another good. As a common elasticity, it follows a similar formula to price elasticity of demand. Thus, to calculate it the percentage change in the quantity of the first good is divided by the percentage change in price in the second good. The related goods that may be used to determine sensitivity can be complements or substitutes. Finding a high-cross price elasticity between the goods may indicate that they are more likely substitutes and may have similar characteristics. If cross-price elasticity is negative, the goods are likely to be complements.Real-world examples of cross-price elasticity:
| Product Under Investigation | Comparison Product | Price Elasticity |
| US Domestic Tuna | Imported Tuna | 0.45 |
| US Domestic Tuna | Bread | -0.33 |
| US Domestic Tuna | Ground Meat | 0.3 |
| Beer | Wine | 0.2 |
| Beer | Soft Drinks | 0.3 |
| Transit | Automobiles | 0.85 |
| Transportation | Recreation | -0.05 |
| Food | Recreation | 0.15 |
| Clothing | Food | -0.18 |