In mathematics and economics, the arc elasticity is the elasticity of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the point elasticity, which is the limit of the arc elasticity as the distance between the two points approaches zero and which hence is defined at a single point rather than for a pair of points.
The y arc elasticity of x is defined as:
where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint:
The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (x1, y1) which is used in almost all other contexts for calculating percentages) was advocated by R. G. D. Allen for use when x refers to the quantity of a good demanded or supplied and y refers to its price, due to the following properties: (1) it is symmetric with respect to the two prices and quantities, (2) it is independent of the units of measurement, and (3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal. [1]
The arc elasticity is used when there is not a general function for the relationship of two variables, but two points on the relationship are known. In contrast, calculation of the point elasticity requires detailed knowledge of the functional relationship and can be calculated wherever the function is defined.
For comparison, the y point elasticity of x is given by
The arc elasticity of quantity demanded (or quantity supplied) Q with respect to price P, also known as the arc price elasticity of demand (or supply), is calculated as [2]
Suppose that two points on a demand curve, and , are known. (Nothing else might be known about the demand curve.) Then the arc elasticity is obtained using the formula
Suppose the quantity of hot dogs demanded at halftime of football games is measured at two different games at which two different prices are charged: at one measurement the quantity demanded is 80 units, and at the other measurement it is 120 units. The percent change, measured against the average, would be (120-80)/((120+80)/2))=40%. If the measurements were taken in reverse sequence (first 120 and then 80), the absolute value of the percentage change would be the same.
In contrast, if the percentage change in quantity demanded were measured against the initial value, the calculated percentage change would be (120-80)/80= 50%. The percent change for the reverse sequence of observations, 120 units to 80 units, would be (80-120)/120 = -33.3%. The midpoint formula has the benefit that a percentage change from A to B is measured in absolute value as the same as one from B to A.
Suppose that the change in the price of hot dogs, which led to this change in quantity demanded from 80 to 120, was from $3 to $1. The percent change in price measured against the midpoint would be (1-3)/2 = -100%, so the price elasticity of demand is 40%/(-100%) or -0.4. It is common to refer to the absolute value of the price elasticity as simply price elasticity, since for a normal (decreasing) demand curve the elasticity is always negative and so the "minus" part can be made implicit. Thus the arc price elasticity demand of the football fans is 0.4.
In economics, elasticity measures the responsiveness of one economic variable to a change in another. For example, if the price elasticity of the demand of a good is −2, then a 10% increase in price will cause the quantity demanded to fall by 20%. Elasticity in economics provides an understanding of changes in the behavior of the buyers and sellers with price changes. There are two types of elasticity for demand and supply, one is inelastic demand and supply and the other one is elastic demand and supply.
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 crosselasticity of demand (XED) measures the effect of changes in the price of one good on the quantity demanded of another good. This reflects the fact that the quantity demanded of good is dependent on not only its own price but also the price of other "related" good.
In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of a derivative instrument such as an option to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters. Collectively these have also been called the risk sensitivities, risk measures or hedge parameters.
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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 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 complementary good is a good whose appeal increases with the popularity of its complement. Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases. If is a complement to , an increase in the price of will result in a negative movement along the demand curve of and cause the demand curve for to shift inward; less of each good will be demanded. Conversely, a decrease in the price of will result in a positive movement along the demand curve of and cause the demand curve of to shift outward; more of each good will be demanded. This is in contrast to a substitute good, whose demand decreases when its substitute's price decreases.
A demand curve is a graph depicting the inverse demand function, a 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. Marginal revenue is the increase in revenue from the sale of one additional unit of product, i.e., the revenue from the sale of the last unit of product. It can be positive or negative. Marginal revenue is an important concept in vendor analysis. 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.
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.
Differential entropy is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. The actual continuous version of discrete entropy is the limiting density of discrete points (LDDP). Differential entropy is commonly encountered in the literature, but it is a limiting case of the LDDP, and one that loses its fundamental association with discrete entropy.
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.
Elasticity of substitution is the ratio of percentage change in capital-labour ratio with the percentage change in Marginal Rate of Technical Substitution. In a competitive market, it measures the percentage change in the two inputs used in response to a percentage change in their prices. It gives a measure of the curvature of an isoquant, and thus, the substitutability between inputs, i.e. how easy it is to substitute one input for the other.
In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable at point a is defined as
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably.
In economics, the income elasticity of demand (YED) 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. For example, if in response to a 10% increase in income, quantity demanded for a good or service were to increase by 20%, the income elasticity of demand would be 20%/10% = 2.0.
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In mathematical economics, an isoelastic function, sometimes constant elasticity function, is a function that exhibits a constant elasticity, i.e. has a constant elasticity coefficient. The elasticity is the ratio of the percentage change in the dependent variable to the percentage causative change in the independent variable, in the limit as the changes approach zero in magnitude.
