# Elasticity (economics)

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In economics, elasticity measures the percentage change of one economic variable in response to a change in another. [1] If a good's price elasticity of demand is -2, a 10% increase in price causes the quantity demanded to fall 20%.

## Introduction

As one of the most important concepts in neoclassical economic theory, elasticity assists in the understanding of various economic concepts. For example: 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. Elasticity is also crucially important in any discussion of welfare distribution, in particular consumer surplus, producer surplus, or government surplus.

Because of its integral part of economics and its coverage through so many economic theories, there are a few main types of elasticity. 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 terms of differential calculus, it 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 later variable has a causal influence on the former and all other conditions remain the same. For instance, 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. [2]

Within microeconomics, elasticity and slope are always regarded as a pair of two closely related concepts. 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 (demand or supply) is smaller; when the tangent of the straight line or curve is flatter, the price elasticity (demand or supply) is more remarkable. [3]

Elasticity has the advantage of being a unitless ratio, independent of the type of quantities being varied. An elastic variable (with an absolute elasticity value greater than 1) responds more than proportionally to changes in other variables. Also, a unit elastic variable (with an absolute elasticity value equal to 1) responds proportionally to changes in other variables. In contrast, an inelastic variable (with an absolute elasticity value less than 1) 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.

The concept of price elasticity was first cited in an informal form in the book named Principles of Economics (Marshall book) published by the author Alfred Marshall in 1890. It is undeniable that Antoine Augustin Cournot expressed some pioneering views on the concept of price elasticity. [4] Besides, 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. [5]

## Definition

High elasticity indicates high responsiveness, the sensitivity of one variable to another. The x-elasticity of y measures the fractional response of y to a fraction change in x, which can be written as

x-elasticity of y: ${\displaystyle \varepsilon ={\frac {\partial y/y}{\partial x/x}}}$

In economics, the common elasticities (price-elasticity of demand), price elasticity of supply, and cross-price elasticity) all have the same form:

P-elasticity of Q: ${\displaystyle \varepsilon ={\frac {\partial Q/Q}{\partial P/P}}}$ if continuous, or ${\displaystyle \varepsilon ={\frac {\frac {Q_{2}-Q_{1}}{Q_{1}}}{\frac {P_{2}-P_{1}}{P_{1}}}}={\frac {\%\ {\mbox{change in quantity Q}}}{\%\ {\mbox{change in price P}}}}}$ if discrete.
 ${\displaystyle |\varepsilon |>1}$ elastic Q changes more than P ${\displaystyle |\varepsilon |=1}$ unit elastic Q changes like P ${\displaystyle |\varepsilon |<1}$ 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:

Perfectly elastic: ${\displaystyle \varepsilon \rightarrow \infty }$; quantity has an infinite response to even a small price change.
Perfectly inelastic: ${\displaystyle \varepsilon =0}$; quantity does not respond at all to a price change.

Seller revenue (or, alternatively, consumer expenditure) is maximized when ${\displaystyle \varepsilon =-1}$ (unit elasticity) because at that point a change in price is exactly cancelled by the quantity response, leaving ${\displaystyle PQ}$ unchanged. To maximize revenue, a firm must:

Relatively Elastic Demand: increase price if demand is inelastic: ${\displaystyle |\varepsilon |<1}$
reduce price if demand is elastic: ${\displaystyle |\varepsilon |>1}$

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 ${\displaystyle |\varepsilon |=1}$ and further price changes would reduce revenue. (This is not true for some theoretical demand functions: ${\displaystyle Q^{d}=3P^{-.5}}$ has an elasticity of -.5 for any value of ${\displaystyle P}$, so revenue rises infinitely as price rises to infinity even though quantity approaches zero. See Isoelastic function.)

## Types of Elasticity

### Price Elasticity of Demand

Price Elasticity of Demand measures sensitivity of demand to price. Thus, it measures the percentage change in demand in response to a change in price. [6] More precisely, it gives the percentage change in quantity demanded in response to a one per cent change in price (ceteris paribus, i.e. holding constant all the other determinants of demand, such as income). 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. [7]

### 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. [8] 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. [9]

### Income Elasticity of Demand

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. [10] Generally, a higher income will increase quantity demanded as consumers will be willing to spend more.

### Cross-Price Elasticity of Demand

Cross Price Elasticity of Demand measures the sensitivity between the quantity demanded in one good when there is a change in price in another good. [11] 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. [11] The related goods that may be used to determine sensitivity can be complements or substitutes. [6] Finding a high-cross price elasticity between the goods may indicate that they are more likely substitutes and may have similar characteristics. [12] If it is negative, the goods are likely to be complements.

Real-world examples of cross-price elasticity: [13]

 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

### Elasticity of Scale

Elasticity of scale or output elasticity measures the percentage change in output induced by a collective percent change in the usages of all inputs. [14] A production function 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. [15] [16] [17] [18]

## Detriments of Elasticity

There are various factors and detriments that may affect elasticity, and these factors differ for the types of elasticity.

### Factors Affecting Price Elasticity of Demand

If a product has various available substitutes that exist in the market, it is likely that it would be elastic. [19] If a product has a competitive product at a cheaper price in the market in which it shares many characteristics with, it is likely that consumers would deviate to the cheaper substitute. Thus, if many substitutions existed in the market, a consumer would have more choices and the elasticity of demand would be higher (elastic). In contrast, if there were few substitutions that existed in the market, consumers will have fewer choices and little to no available substitutes which means elasticity of demand would be lower (inelastic). [19]

If a product is a necessity to the survival or daily life of a consumer, it is likely to be inelastic. [20] This is due to the fact that if a product is so intrinsically important to the daily life of a consumer, a change in price is not likely to affect its demand. [1]

If the price of a product is increasing and it has little available substitutes, it is likely that the consumer will still continue to pay this higher price. [1] The fact that the consumer needs the good in the short-run, means that he is likely to continue this action regardless in the long-run. This shows inelasticity of demand, because even if there is a huge increase of a product's price, there is no reduction of demand. However, if the consumer could not afford the new price of the product, they would likely have to learn to live without it, making the price elastic in the long-run. [19]

### Factors Affecting Price Elasticity of Supply

Like Price Elasticity of Demand, time also affects Price Elasticity of Supply. Though, there are other varying factors that affect this too, such as: capacity, availability of raw materials, flexibility, and the number of competitors in the market. Though, the time horizon is arguably the most influential detriment to price elasticity of supply. [9]

The longer the time horizon, the easier it is for commodity buyers to choose alternative products (substitutes). Further, as the time for suppliers to respond to price changes increases, a given price change will have a more significant impact on supply. However, suppliers can also hire more labour overtime, raise more funds, build more new factories to expand production capacity, and ultimately increase supply. In general, long-term supply is more elastic than short-term supply because producers need some time to adjust their ability to adapt to changes in demand. [21]

## Applications

The concept of elasticity has an extensive range of applications in economics. In particular, an understanding of elasticity is fundamental in understanding the response of supply and demand in a market. [7]

Elasticity is also a relevant concept to enterprises and governments. For enterprises, elasticity is relevant in the calculation of the fluctuation of commodity prices, and its relation to income.

The concept is also relevant to governments through the implementation of taxation. When a government wants to increase taxes on goods, it can use elasticity to judge whether increasing the tax rate will be beneficial. Often, the demand for goods will be significantly reduced when a government increases taxes on them. Whilst a tax increase on inelastic goods will not impact their demand, it may affect goods that are elastic. Aside from taxation, elasticity can also assist in analysing the need for government intervention.

For those goods that are so essential as necessities of life, the government must ensure that they are available to most consumers. Through setting price ceilings and floors, the government is intervening by ensuring that these goods are reasonably available.

As stated by British political economist David Ricardo, luxury goods taxes have certain advantages over necessities taxes. They are usually paid from income and, therefore, will not reduce the country's production capital. For instance, when the price of wine products rises due to increased taxes, consumers can give up drinking wine. [22]

Other common uses of elasticity include:

## Variants

In some cases the discrete (non-infinitesimal) arc elasticity is used instead. In other cases, such as modified duration in bond trading, a percentage change in output is divided by a unit (not percentage) change in input, yielding a semi-elasticity instead.

## Related Research Articles

In microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded will equal the quantity supplied, resulting in an economic equilibrium for price and quantity transacted. It forms the theoretical basis of modern economics.

Deadweight loss, also known as excess burden, is a measure of lost economic efficiency when the socially optimal quantity of a good or a service is not produced. Non-optimal production can be caused by highly concentrated wealth and income, monopoly pricing in the case of artificial scarcity, a positive or negative externality, a tax or subsidy, or a binding price ceiling or price floor such as a minimum wage.

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that lead to the highest profit. Neoclassical economics, currently the mainstream approach to microeconomics, usually models the firm as maximizing profit.

A good's price elasticity of demand is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded. Other elasticities measure how the quantity demanded changes with other variables.

In economics, the cross elasticity of demand or cross-price elasticity of demand measures the percentage change of the quantity demanded for a good to the percentage change in the price of another good, ceteris paribus. In real life, the quantity demanded of good is dependent on not only its own price but also the price of other "related" products.

In microeconomics, two goods are substitutes if the products could be used for the same purpose by the consumers. That is, a consumer perceives both goods as similar or comparable, so that having more of one good causes the consumer to desire less of the other good. Contrary to complementary goods and independent goods, substitute goods may replace each other in use due to changing economic conditions. An example of substitute goods is Coca-Cola and Pepsi; the interchangeable aspect of these goods is due to the similarity of the purpose they serve, i.e fulfilling customers' desire for a soft drink. These types of substitutes can be referred to as close substitutes.

The 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.

In microeconomics, the law of demand is a fundamental principle which states that there is an inverse relationship between price and quantity demanded. In other words, "conditional on all else being equal, as the price of a good increases (↑), quantity demanded will decrease (↓); conversely, as the price of a good decreases (↓), quantity demanded will increase (↑)". Alfred Marshall worded this as: "When then we say that a person's demand for anything increases, we mean that he will buy more of it than he would before at the same price, and that he will buy as much of it as before at a higher price". The law of demand, however, only makes a qualitative statement in the sense that it describes the direction of change in the amount of quantity demanded but not the magnitude of change.

In economics, a demand curve is a graph depicting the relationship between the price of a certain commodity and the quantity of that commodity that is demanded at that price. Demand curves can be used either for the price-quantity relationship for an individual consumer, or for all consumers in a particular market.

Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit. To derive the value of marginal revenue, it is required to examine the difference between the aggregate benefits a firm received from the quantity of a good and service produced last period and the current period with one extra unit increase in the rate of production. Marginal revenue is a fundamental tool for economic decision making within a firm's setting, together with marginal cost to be considered.

The tax wedge is the deviation from the equilibrium price/quantity as a result of the taxation of a good. Because of the tax, consumers pay more for the good than they did before the tax, and suppliers receive less for the good than they did before the tax. Put differently, the tax wedge is the difference between what consumers pay and what producers receive from a transaction. The tax effectively drives a "wedge" between the price consumers pay and the price producers receive for a product.

In economics, the total revenue test is a means for determining whether demand is elastic or inelastic. If an increase in price causes an increase in total revenue, then demand can be said to be inelastic, since the increase in price does not have a large impact on quantity demanded. If an increase in price causes a decrease in total revenue, then demand can be said to be elastic, since the increase in price has a large impact on quantity demanded.

In economics, tax incidence or tax burden is the effect of a particular tax on the distribution of economic welfare. Economists distinguish between the entities who ultimately bear the tax burden and those on whom tax is initially imposed. The tax burden measures the true economic weight of the tax, measured by the difference between real incomes or utilities before and after imposing the tax, taking into account how the tax leads prices to change. If a 10% tax is imposed on sellers of butter, for example, but the market price rises 8% as a result, most of the burden is on buyers, not sellers. The concept of tax incidence was initially brought to economists' attention by the French Physiocrats, in particular François Quesnay, who argued that the incidence of all taxation falls ultimately on landowners and is at the expense of land rent. Tax incidence is said to "fall" upon the group that ultimately bears the burden of, or ultimately suffers a loss from, the tax. The key concept of tax incidence is that the tax incidence or tax burden does not depend on where the revenue is collected, but on the price elasticity of demand and price elasticity of supply. As a general policy matter, the tax incidence should not violate the principles of a desirable tax system, especially fairness and transparency. The concept of tax incidence is used in political science and sociology to analyze the level of resources extracted from each income social stratum in order to describe how the tax burden is distributed among social classes. That allows one to derive some inferences about the progressive nature of the tax system, according to principles of vertical equity.

In economics, demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given period of time. The relationship between price and quantity demand is also called the demand curve. Demand for a specific item is a function of an item's perceived necessity, price, perceived quality, convenience, available alternatives, purchasers' disposable income and tastes, and many other options.

In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual. Supply can be in produced goods, labour time, raw materials, or any other scarce or valuable object. Supply is often plotted graphically as a supply curve, with the price per unit on the vertical axis and quantity supplied as a function of price on the horizontal axis. This reversal of the usual position of the dependent variable and the independent variable is an unfortunate but standard convention.

In economics, derived demand is demand for a factor of production or intermediate good that occurs as a result of the demand for another intermediate or final good. In essence, the demand for, say, a factor of production by a firm is dependent on the demand by consumers for the product produced by the firm. The term was first introduced by Alfred Marshall in his Principles of Economics in 1890. Demand for all factors of production is considered as derived demand.

In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable at point a is defined as

In economics, the income elasticity of demand is the responsivenesses of the quantity demanded for a good to a change in consumer income. It is measured as the ratio of the percentage change in quantity demanded to the percentage change in income. If a 10% increase in Mr. Ruskin Smith's income causes him to buy 20% more bacon, Smith's income elasticity of demand for bacon is 20%/10% = 2.

Total revenue is the total receipts a seller can obtain from selling goods or services to buyers. It can be written as P × Q, which is the price of the goods multiplied by the quantity of the sold goods.

A monopoly price is set by a monopoly. A monopoly occurs when a firm lacks any viable competition and is the sole producer of the industry's product. Because a monopoly faces no competition, it has absolute market power, and thereby has the ability to set a monopoly price that will be above the firm's marginal (economic) cost. Since marginal cost is the increment in total required to produce an additional unit of the product, the firm would be able to make a positive economic profit if it produced a greater quantity of the product and sold it at a lower price.

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