Elasticity (economics)

# Elasticity (economics)

Overview
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, elasticity is the measurement of how changing one economic variable affects others. For example:
Discussion

Encyclopedia
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, elasticity is the measurement of how changing one economic variable affects others. For example:
• "If I lower the price of my product, how much more will I sell?"
• "If I raise the price, how much less will I sell?"
• "If we learn that a resource is becoming scarce, will people scramble to acquire it?"

In more technical terms, it is the ratio of the percentage change in one variable to the percentage change in another variable. It is a tool for measuring the responsiveness of a function to changes in parameters in a unitless way. Frequently used elasticities include price elasticity of demand
Price elasticity of demand
Price elasticity of demand is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price...

, price elasticity of supply
Price elasticity of supply
Price elasticity of supply is a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good or service to a change in its price....

, income elasticity of demand, elasticity of substitution
Elasticity of substitution
Elasticity of substitution is the elasticity of the ratio of two inputs to a production function with respect to the ratio of their marginal products . It measures the curvature of an isoquant and thus, the substitutability between inputs , i.e...

between factors of production
Factors of production
In economics, factors of production means inputs and finished goods means output. Input determines the quantity of output i.e. output depends upon input. Input is the starting point and output is the end point of production process and such input-output relationship is called a production function...

and elasticity of intertemporal substitution
Elasticity of intertemporal substitution
Elasticity of intertemporal substitution is a measure of responsiveness of the growth rate of consumption to the real interest rate...

.

Elasticity is one of the most important concepts in neoclassical economic theory. It is useful in understanding the incidence of indirect taxation, marginal concepts
Marginal concepts
In economics, marginal concepts are associated with a specific change in the quantity used of a good or service, as opposed to some notion of the over-all significance of that class of good or service, or of some total quantity thereof.- Marginality :...

as they relate to the theory of the firm
Theory of the firm
The theory of the firm consists of a number of economic theories that describe the nature of the firm, company, or corporation, including its existence, behavior, structure, and relationship to the market.-Overview:...

, and distribution of wealth
Distribution of wealth
The distribution of wealth is a comparison of the wealth of various members or groups in a society. It differs from the distribution of income in that it looks at the distribution of ownership of the assets in a society, rather than the current income of members of that society.-Definition of...

and different types of goods as they relate to the theory of consumer choice. Elasticity is also crucially important in any discussion of welfare
Welfare economics
Welfare economics is a branch of economics that uses microeconomic techniques to evaluate economic well-being, especially relative to competitive general equilibrium within an economy as to economic efficiency and the resulting income distribution associated with it...

distribution, in particular consumer surplus, producer surplus, or government surplus.

In empirical work an elasticity is the estimated coefficient in a linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...

equation where both the dependent variable and the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

are in natural logs. Elasticity is a popular tool among empiricists because it is independent of units and thus simplifies data analysis.

Generally, an elastic variable is one which responds a lot to small changes in other parameters. Similarly, an inelastic variable describes one which does not change much in response to changes in other parameters. A major study of the price elasticity of supply
Price elasticity of supply
Price elasticity of supply is a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good or service to a change in its price....

and the price elasticity of demand
Price elasticity of demand
Price elasticity of demand is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price...

for US products was undertaken by Hendrik S. Houthakker and Lester D. Taylor.

## Mathematical definition

The definition of elasticity is based on the mathematical notion of point elasticity.

In general, the "x-elasticity of y", also called the "elasticity of y with respect to x", is:

The approximation becomes exact in the limit as the changes become infinitesimal in size.

The absolute value operator is for simplicity – generally the sign of the elasticity is understood as being always positive or always negative. However, sometimes the elasticity is defined without the absolute value operator, when the sign may be either positive or negative or may change signs. A context where this use of a signed elasticity is necessary for clarity is the cross-price elasticity of demand — the responsiveness of the demand for one product to changes in the price of another product; since the products may be either substitutes
Substitute good
In economics, one way we classify goods is by examining the relationship of the demand schedules when the price of one good changes. This relationship between demand schedules leads economists to classify goods as either substitutes or complements. Substitute goods are goods which, as a result...

or complements
Complement good
A complementary good, in contrast to a substitute good, is a good with a negative cross elasticity of demand. This means a good's demand is increased when the price of another good is decreased. Conversely, the demand for a good is decreased when the price of another good is increased...

, this elasticity could be positive or negative.

### Elasticities of demand

Price elasticity of demand
Price elasticity of demand measures the percentage change in quantity demanded caused by a percent change in price. As such, it measures the extent of movement along the demand curve. This elasticity is almost always negative and is usually expressed in terms of absolute value (i.e. as positive numbers) since the negative can be assumed. In these terms, then, if the elasticity is greater than 1 demand is said to be elastic; between zero and one demand is inelastic and if it equals one, demand is unit-elastic. A perfectly elastic demand curve is horizontal (with an elasticity of infinity) whereas a perfectly inelastic demand curve is vertical (with an elasticity of 0).

Income elasticity of demand
Income elasticity of demand measures the percentage change in demand caused by a percent change in income. A change in income causes the demand curve to shift reflecting the change in demand. IED is a measurement of how far the curve shifts horizontally along the X-axis. Income elasticity can be used to classify goods as normal or inferior. With a normal good demand varies in the same direction as income. With an inferior good demand and income move in opposite directions.

Cross price elasticity of demand
Cross price elasticity of demand measures the percentage change in demand for a particular good caused by a percent change in the price of another good. Goods can be complements, substitutes or unrelated. A change in the price of a related good causes the demand curve to shift reflecting a change in demand for the original good. Cross price elasticity is a measurement of how far, and in which direction, the curve shifts horizontally along the x-axis. A positive cross-price elasticity means that the goods are substitute good
Substitute good
In economics, one way we classify goods is by examining the relationship of the demand schedules when the price of one good changes. This relationship between demand schedules leads economists to classify goods as either substitutes or complements. Substitute goods are goods which, as a result...

s.

Cross elasticity of demand between firms
Cross elasticity of demand for firms, sometimes referred to as conjectural variation, is a measure of the interdependence between firms. It captures the extent to which one firm reacts to changes in strategic variables (price, quantity, location, advertising, etc.) made by other firms.

Elasticity of intertemporal substitution
Combined Effects
It is possible to consider the combined effects of two or more determinant of demand. The steps are as follows: PED = (∆Q/∆P) x P/Q. Convert this to the predictive equation: ∆Q/Q = PED(∆P/P) if you wish to find the combined effect of changes in two or more determinants of demand you simply add the separate effects: ∆Q/Q = PED(∆P/P) + YED(∆Y/Y)[12]
Remember you are still only considering the effect in demand of a change in two of the variables. All other variables must be held constant. Note also that graphically this problem would involve a shift of the curve and a movement along the shifted curve.

### Elasticities of supply

Price elasticity of supply
The price elasticity of supply measures how the amount of a good firms wish 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 movement along the supply curve. If the price elasticity of supply is zero the supply of a good supplied is "inelastic" and the quantity supplied is fixed.

Elasticities of scale
Elasticity of scale or output elasticities measure the percentage change in output induced by a percent change in inputs. A production function
Production function
In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs...

or process is said to exhibit constant returns to scale if a percentage change in inputs results in an equal percentage in outputs (an elasticity equal to 1). It exhibits increasing returns to scale if a percentage change in inputs results in greater percentage change in output (an elasticity greater than 1). The definition of decreasing returns to scale is analogous.

## Applications

The concept of elasticity has an extraordinarily wide range of applications in economics. In particular, an understanding of elasticity is fundamental in understanding the response of supply and demand
Supply and demand
Supply and demand is an economic model of price determination in a market. It concludes that in a competitive market, the unit price for a particular good will vary until it settles at a point where the quantity demanded by consumers will equal the quantity supplied by producers , resulting in an...

in a market.

Some common uses of elasticity include:
• Effect of changing price on firm revenue. See Markup rule
Markup rule
The Markup rule is used in economics to explain firm pricing decisions. It states that the price a firm with market power will charge is equal to a markup over the firm's marginal cost, equal to one over one minus the inverse of the price elasticity of demand....

.
• Analysis of incidence of the tax burden and other government policies. See Tax incidence
Tax incidence
In economics, tax incidence is the analysis of the effect of a particular tax on the distribution of economic welfare. Tax incidence is said to "fall" upon the group that, at the end of the day, bears the burden of the tax...

.
• Income elasticity of demand can be used as an indicator of industry health, future consumption patterns and as a guide to firms investment
Investment
Investment has different meanings in finance and economics. Finance investment is putting money into something with the expectation of gain, that upon thorough analysis, has a high degree of security for the principal amount, as well as security of return, within an expected period of time...

decisions. See Income elasticity of demand.
In international economics and international trade, terms of trade or TOT is /. In layman's terms it means what quantity of imports can be purchased through the sale of a fixed quantity of exports...

effects. See Marshall–Lerner condition and Singer–Prebisch thesis.
• Analysis of consumption
Consumption (economics)
Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally, consumption is defined in part by comparison to production. But the precise definition can vary because different schools of economists define production quite differently...

and saving behavior. See Permanent income hypothesis
Permanent income hypothesis
The permanent income hypothesis is a theory of consumption that was developed by the American economist Milton Friedman. In its simplest form, the hypothesis states that the choices made by consumers regarding their consumption patterns are determined not by current income but by their longer-term...

.