Arc elasticity of demand calculates the elasticity between two points on a curve by using the midpoint between the two curves.

(OR)

The arc elasticity of demand evaluates the sensitivity of demand to the midpoint rather than the initial point. It delivers the same value for equal-amount price hikes and reductions.

(OR)

If the size of the price shift is minimal, whether arc elasticity or price elasticity is employed to determine price increases or decreases is less important.

Arc elasticity is used in non-uniform pricing to quantify demand elasticity and price items to optimum profitability. Arc elasticity is useful for larger price changes.

It provides the same absolute elasticity measure when prices rise and fall.

(OR)

The elasticity of one variable with respect to another between two locations is defined as arc elasticity. When there is no universal function to define the relationship between the two variables, it is employed.

The elasticity of a curve changes depending on where you are on most curves. As a result, elasticity must be measured in a specific area of the curve.

To determine the arc elasticity of demand, we first find the midpoint.

                              Q ₁ + Q ₂

Midpoint Q = _____________

                                     2

                           P₁ + P₂

Midpoint P = __________

                                  2

Arc Elasticity of demand (PED) =   (Q ₂ – Q₁)/2

                                                           __________

                                                               (P₂ – P₁)/2

(OR)

Arc Elasticity of demand (PED) = Percentage change in quantity of demand/Percentage change in price

                                                        = %ΔQd/%ΔP

One problem with the price elasticity of demand formula is that it produces different results depending on whether the price rises or declines. If you change the start and end points in our example above, assuming the price rises from $8 to $10 and the quantity required falls from 60 to 40, the Ped will be:

% change in quantity demanded = (40 – 60) / 60 = -0.33

% change in price = (10 – 8) / 8 = 0.25

PE_d = -0.33 / 0.25 = 1.32, which is much different from 2.5

The arc elasticity can be employed to solve this problem. By employing a midpoint between two points on the demand curve, arc elasticity evaluates elasticity at the midpoint between the two points. The demand arc elasticity may be computed as follows:

• Arc E_d = [(Qd₂ – Qd₁) / midpoint Qd] ÷ [(P₂ – P₁) / midpoint P]

Let’s calculate the arc elasticity following the example presented above:

• Midpoint Qd = (Qd₁ + Qd₂) / 2 = (40 + 60) / 2 = 50
• Midpoint Price = (P₁ + P₂) / 2 = (10 + 8) / 2 = 9
• % change in qty demanded = (60 – 40) / 50 = 0.4
• % change in price = (8 – 10) / 9 = -0.22
• Arc E_d = 0.4 / -0.22 = 1.82

When using arc elasticities, you don’t have to worry about which point is the beginning and which point is the ending point because the arc elasticity delivers the same elasticity number whether prices grow or fall. When there is a significant fluctuation in price, the arc elasticity is more useful than the price elasticity.

Key point:

1) In the idea of arc elasticity, elasticity is assessed on a graph over the arc of the demand curve.

2) Arc elasticity computations use the midpoint between two locations to calculate elasticity.

3) The arc elasticity is more effective for greater price fluctuations since it produces the same elasticity result whether the price falls or rises.