Elasticity (economics)

In economics, elasticity is the ratio of the incremental percentage change in one variable with respect to an incremental percentage change in another variable. Elasticity is usually expressed as a positive number (i.e., an absolute value) when the sign is already clear from context.

One typical application of the concept of elasticity is to consider what happens to consumer demand for a good (for example, a product) when prices increase. As the price of a good rises, consumers will usually demand less of that good, perhaps by consuming less, substituting other goods, and so on. The greater the extent to which demand falls as price rises, the greater is the price elasticity of demand. However, there may be some goods that consumers require, cannot consume less of, and cannot find substitutes for even if prices rise (for example, certain prescription drugs). For such goods, the price elasticity of demand might be considered inelastic.

Further, elasticity will normally be different in the short term and the long term. For example, for many goods the supply can be increased over time by locating alternative sources, investing in an expansion of production capacity, or developing competitive products which can substitute. One might therefore expect that the price elasticity of supply will be greater in the long term than the short term for such a good, that is, that supply can adjust to price changes to a greater degree over a longer time

This applies to the demand side as well. For example, if the price of gasoline rises, consumers will find ways to conserve their use of the resource. However, some of these ways, like finding a more fuel-efficient car, take time. So consumers as well may be less able to adapt to price shocks in the short term thsn in the long term.

The concept of elasticity has an extraordinarily wide range of applications in economics. In particular, an understanding of elasticity is useful to understand the dynamic response of supply and demand in a market, in order to achieve an intended result or avoid unintended results. For example, a business considering a price increase might find it lowers their profits if demand is highly elastic, as sales would fall sharply. Similarly, a business considering a price cut might find that it does not increase sales, if demand for the product is price inelastic.

A real world example of how elasticity can be useful in business situations can be shown by the equation MR = P * (1+E)/E where MR is marginal revenue, P is price of the good, and E is the own price elasticity of demand for the good. Notice that when E is between negatative infinity and negative one, demand is elastic. When E is between negative one and zero, demand is inelastic. And at E=-1, demand is unitary elastic (thus MC=MB and MNB=0).

Generalized cases

Keeping in mind the example of price elasticity of demand, these figures show x = Q horizontal and y = P vertical.

Figure 1: Illustrations of perfect elasticity and perfect inelasticity.

In this example the demand curve (D₁) is perfectly elastic.

In this example the demand curve (D₂) is perfectly inelastic.

Mathematical definition

Unit elasticity for a supply line passing through the origin.

The general formula for elasticity (the "y-elasticity of x") is:

$E_{x,y}={\Big |}{\frac {{\rm {percent\ change\ in}}\ x}{{\rm {percent\ change\ in}}\ y}}{\Big |},$

or, more formally,

$E_{x,y}={\Big |}{\frac {\partial \ln x}{\partial \ln y}}{\Big |}={\Big |}{\frac {\partial x}{\partial y}}\cdot {\frac {y}{x}}{\Big |}$.

The solution of $E_{x,y}={\frac {1}{\alpha }}$ (constant elasticity) is $y={\frac {1}{\alpha }}x^{\alpha }$.

A common mistake for students of economics is to confuse elasticity with slope. (Case & Fair, 1999: 108, 109). Elasticity is the slope of a curve on a loglog graph only, not on a regular graph (taking into account whether the independent variable is on the horizontal or the vertical axis). Consider the information in figure 2. This is a special case which illustrates that slope and elasticity are different. In the above example the slope of S₁ is clearly different from the slope of S₂, but since the rate of change of P relative to Q is always proportionate, both S₁ and S₂ are unit elastic (i.e. E = 1).

Importance

Elasticity is an important concept in understanding the incidence of indirect taxation, marginal concepts as they relate to the theory of the firm, distribution of wealth and different types of goods as they relate to the theory of consumer choice and the Lagrange multiplier. Elasticity is also crucially important in any discussion of welfare distribution: in particular consumer surplus, producer surplus, or government surplus.

The concept of elasticity was also an important component of the Singer-Prebisch thesis which is a central argument in dependency theory as it relates to development economics.

See also

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

References

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