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Elasticity (economics)

In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. It is a tool for measuring the responsiveness of a function to changes in parameters in a relative way. Commonly analyzed are elasticity of substitution, price and wealth. Elasticity is a popular tool among empiricists because it is independent of units and thus simplifies data analysis.

An "elastic" good is one whose price elasticity of demand has a magnitude greater than one. Similarly, "unity elastic" and "inelastic" describe goods with price elasticity having a magnitude of one and less than one respectively.

Mathematical definition

In economics, the definition of elasticity is based on the mathematical notion of point elasticity . Elasticity can be calculated for any function but in empirical work it is commonly used to analyze supply or demand. Let

displaystyle x(p,w)

be the demand (supply) of goods

x_1,x_2,dots,x_L

as a function of parameters price and wealth, and let

displaystyle x_l(p,w)

be the demand for good

displaystyle l

. The general definition, according to Mas-Collel, Winston and Green is:

E_{x_l,p_k} = frac{partial x_l(p,w)}{partial p_k}cdotfrac{p_k}{x_l(p,w)} = frac{partial log x_l(p,w)}{partial log p_k}

Elasticity can be approximated using percent changes:

E_{x_l,p_k} = frac{% Delta x_l}{% Delta p_k},

where

Delta x_l equiv x_{l, 1} - x_{l, 2}

and similarly for

displaystyle Delta p_k

, and

% Delta x_l equiv frac{Delta x_l}{x_l}

Another way to approximate elasticity is using the average value:

Epsilon_{x_l,p_k} = left(frac{x_l^2 - x_l^1}{.5(x_l^1 + x_l^2)} right)/left(frac{p_k^2 - p_k^1}{.5(p_k^1 + p_k^2)} right)

It is typical to represent elasticity as 'E', 'e' or lowercase epsilon, 'ε'.

Applications

As the price of a good rises, consumers will usually demand a lower quantity of that good; they may consume less of that good, substitute it with another product, etc. The greater the extent to which demand falls as price rises, the greater the price elasticity of demand. Conversely, as the price of a good falls, consumers will usually demand a greater quantity of that good: consuming more, dropping substitutes, etc. However, there may be some goods of which consumers cannot consume less or for which adequate substitutes cannot be found. Prescription drugs, fuel, and food are some examples of these. For such goods, demand does not greatly decrease as the price rises, and elasticity of demand can be considered low.

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 petrol 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 than 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 that doing so lowers 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.

An 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 less than negative one, demand is elastic. When E is between negative one and zero, demand is inelastic. And at E=-1, demand is unit elastic (or unitary elastic), and thus MC=MB and MNB=0.

Examples

A common mistake for students and teachers 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 the figure. This is a special case which illustrates that slope and elasticity are different. In the figure to the left 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).

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

Illustrations of perfect elasticity and perfect inelasticity.

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.

Elasticity as described above is necessarily dimensionless -- meaning that it is independent of units of measurement. For example, the value of the price elasticity of demand for gasoline would be the same whether prices were measured in dollars or euros, or quantities in tonnes or gallons. This unit-independence is the main reason why elasticity is so popular a measure of the responsiveness of economic behavior.

A major study of the price elasticity of supply and the price elasticity of demand for US products was undertaken by Hendrik S. Houthakker and Lester D. Taylor.