Arc Elasticity of Demand

When changes in price are very small, the mathematical formula of the Flux Method gives satisfactory indicator of the price elasticity of demand. But when price change is large or substantial, it is better to use the Arc Method. This is because, the use of Flux Method gives one figure of price elasticity when the price rises, and another figure when the price falls even when we use the same set of prices. This can be understood from the following example of price – demand relationship in case of goods A:

When price falls from $ 5 to $ 3, price elasticity of demand is
E_P = - ∆Q / ∆P. P₀/Q₀ where
∆Q = 2,500
= 2,500 /-2 x 5 / 2,000 ∆P₀ = - 2
 P₀ = 5
= - (- 3.12) = 3.12  Q₀ = 2,000

And when price rises from $ 3 to $ 5, price elasticity of demand is
E_P = - ∆Q / ∆P. P₀/Q₀ where
∆Q = 2,500
= -2,500 /2 x 3 / 4,500 ∆P = 2
P₀ = 3
= - (- 0.83) Approx. Q₀ = 4,500
  = 0.83 Approx.

Now in the first case, demand is quite elastic while in the second case, its elasticity is very low. Thus, for the same set of prices we have two quite different results. This has happened because the change in price is quite large, it is 40 per cent when the price falls and 66 per cent when the price rises. Corresponding to such large changes in price, the changes in quantity demanded are also substantial which make the P/Q ratio change markedly for the same amount of price rise and price fall.

Another way of looking at this that when price falls from $ 5 to 3 and quantity changes from 2,000 to 4,500, the change in quantity (∆Q) is 2,500 and change in price the original quantity Q which was 2,000 when price fell from $ 5 to 3, becomes 4,500 when price rises from $ 3 to 5. Similarly the original price P, which was $ 5 when price fell, now becomes $ 3 when price rises. Thus while ∆Q / ∆ P in the equation remain uncharged there is a change in P/Q ration that changes the coefficient of elasticity of demand.