# arc elasticity

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## Arc Elasticity

A variable's elasticity (or relative stability of a variable with respect to another variable's change) when the two variables are between two given points. One calculates the arc elasticity by dividing the percentage change of one variable by the percentage change of the other. This is used to find a more accurate measure of the price elasticity of demand.
Fig. 8 Arc elasticity.

## arc elasticity

a rough measure of the responsiveness of DEMAND or SUPPLY to changes in PRICE, INCOME, etc. In the case of PRICE ELASTICITY OF DEMAND, it is the ratio of the percentage change in quantity demanded (Q) to the percentage change in price (P) over a price range such as P0 to P1 in Fig. 8. Arc elasticity of demand is expressed notationally as:

where P0 = original price, Q0 = original quantity, P1 = new price, Q1 = new quantity. Because arc elasticity measures the elasticity of demand (e) over a price range or arc of the demand curve, it is only an approximation of demand elasticity at a particular price (POINT ELASTICITY). However, the arc elasticity formula gives a reasonable degree of accuracy in approximating point elasticity when price and/or quantity changes are small. See also ELASTICITY OF DEMAND.

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In particular, we compute arc elasticity around the equilibrium market price for each hour.
As outlined by Vazquez (2008), discussion and debate on the accuracy and applicability of Allen's arc elasticity has a long history, dating back to the 1930s and continuing into the 1980s, 1990s, and 2000s (e.
He further argues that a geometric mean calculation of the arc elasticity formula retains the positive attributes of Allen's analysis and provides instructors and practitioners with the flexibility of choosing from among at least three approaches: the conventional percentage change method, Dalton's upper and lower elasticity measures, or a standardizing ray technique.
The arc elasticity computation (Phelps and Newhouse 1972; Gemmill, Costa-Font, and McGuire 2007) is preferred when only specific points on the demand curve are observed.
In a computation of arc elasticity, it is shown that the demand for camping at the recreational site was relatively inelastic.
In a computation of arc elasticity, the demand for fishing at the site was very inelastic.
Arc elasticity equals the percentage change in energy use relative to the average of the new and old values for both quantity (Q) and price (P), as depicted in the following equation:
For this article elasticity measures were estimated using point elasticities followed by an arc elasticity estimate to account for the endpoints of the income ranges.
Unfortunately, the concept of arc elasticity does not allow for an unambiguous ranking of the two markets: For small price intervals around the kink in the demand curves the arc elasticity ranks the elasticity of the first market lower, but for larger intervals and for intervals that do not contain that price, in particular, for intervals around either of the critical prices at which the firm may consider pricing, the ranking is in line with the results from the use of the more common point elasticity.
In their recent article in this journal, "Restrictions of Allen's Arc Elasticity of Demand; Time to Consider the Alternative?
The critical arc elasticity of demand between the initial price and the monopoly prices is given by 1(r + t/50).
Gould and Ferguson's [1980, 110] formula to calculate the arc elasticity of demand implies that the export demand elasticity over this period was -0.

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