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Milds # Elasticity (economics)

In economics, elasticity refers to the measurement of a percentage change of one economic variable in response to a change in another.

## 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.

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.

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 arise from an initially low price might bring on a more-than-proportionate increase in quantity supplied. In contrast, arise 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. 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.

## 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: $\varepsilon ={\frac {\partial y/y}{\partial x/x}}$ 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: $\varepsilon ={\frac {\partial Q/Q}{\partial P/P}}$ if continuous, or $\varepsilon ={\frac {\frac {Q_{2}-Q_{1}}{Q_{1}}}{\frac {P_{2}-P_{1}}{P_{1}}}}={\frac {\%\ {\mbox{change in quantity Q}}}{\%\ {\mbox{change in price P}}}}$ if discrete.
 $|\varepsilon |>1$ elastic Q changes more than P $|\varepsilon |=1$ unit elastic Q changes like P $|\varepsilon |<1$ 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: $\varepsilon \rightarrow \infty$ ; quantity has an infinite response to even a small price change. For example, there is a company which has occoured some financial problem, and the company would like to increase the price of apple from $0.5/kg to$0.55/kg. Obviously consumers will not purchase apple from this company because there are many companies which sell apple to consumers with lower price.
perfectly inelastic: $\varepsilon =0$ ; quantity does not respond at all to a price change.For example, the ticket price of Justin Bieber’s concert has changed from the original 150 US dollars to 200 US dollars, then the die-hard fans of Justin Bieber are still willing to pay a higher price to listen to Justin Bieber live or even see Justin Bieber

Seller revenue (or, alternatively, consumer expenditure) is maximized when $\varepsilon =-1$ (unit elasticity) because at that point a change in price is exactly cancelled by the quantity response, leaving $PQ$ unchanged. To maximize revenue, a firm must: Relatively Elastic Demand: increase price if demand is inelastic: $|\varepsilon |<1$ reduce price if demand is elastic: $|\varepsilon |>1$ 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 $|\varepsilon |=1$ and further price changes would reduce revenue. (This is not true for some theoretical demand functions: $Q^{d}=3P^{-.5}$ has an elasticity of -.5 for any value of $P$ , 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. 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.

### Price Elasticity of Supply

Main Article: Price elasticity of supply

Calculating 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.

### Income Elasticity of Demand

Main Article: 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. Generally, a higher income will increase quantity demanded as consumers will be willing to spend more.

### Cross-Price Elasticity of Demand

Main Article: Cross elasticity of demand

Basic Formula for Cross-Price Elasticity

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. 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 it 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

### 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. 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.

## 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. 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 there were many substitutions exist in the market, consumer would have more choices and the elasticity of demand would be higher (elastic). In contrast, if there were few substitutions exist in the market, consumers then have less choices and no little to no available substitutes which means elasticity of demand would be lower (inelastic).

If a product is a necessity to the survival or daily life of a consumer, it is likely to be inelastic. 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.

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. 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.

### 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.

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.

## 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.

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.

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.