Editing Price elasticity of demand (section)

===Arc elasticity===

{{main|arc elasticity}}
Arc elasticity was introduced very early on by Hugh Dalton. It is very similar to an ordinary elasticity problem, but it adds in the index number problem.  A second solution to the asymmetry problem of having an elasticity dependent on which of the two given points on a demand curve is chosen as the "original" point and which as the "new" one is Arc Elasticity, which is to compute the percentage change in P and Q relative to the ''average'' of the two prices and the ''average'' of the two quantities, rather than just the change relative to one point or the other.  Loosely speaking, this gives an "average" elasticity for the section of the actual demand curve—i.e., the ''arc'' of the curve—between the two points. As a result, this measure is known as the ''[[arc elasticity]]'', in this case with respect to the price of the good. The arc elasticity is defined mathematically as:<ref name="Ferguson"/><ref name="wall">Wall, Stuart; Griffiths, Alan (2008). pp.&nbsp;53–54.</ref><ref name="McConnell; Brue">McConnell;Brue (1990). pp.&nbsp;434–435.</ref>

:<math>E_d = \frac{ \left(\frac{P_1 + P_2}2\right) }{\left( \frac{Q_{d_1} + Q_{d_2}} 2 \right)}\times\frac{\Delta Q_d}{\Delta P} = \frac{P_1 + P_2}{Q_{d_1} + Q_{d_2}}\times\frac{\Delta Q_d}{\Delta P}</math>

This method for computing the price elasticity is also known as the "midpoints formula", because the average price and average quantity are the coordinates of the midpoint of the straight line between the two given points.<ref name="Ruffin"/><ref name="McConnell; Brue"/> This formula is an application of the [[midpoint method]]. However, because this formula implicitly assumes the section of the demand curve between those points is linear, the greater the curvature of the actual demand curve is over that range, the worse this approximation of its elasticity will be.<ref name="wall" /><ref>Ferguson, C.E. (1972). p.&nbsp;101n.</ref>