Arc Elasticity

What Is Arc Elasticity?

Arc elasticity is the elasticity of one variable with respect to one more between two given points. It is utilized when there is no broad function to characterize the relationship between the two variables.

Arc elasticity is likewise defined as the elasticity between two points on a curve. The concept is utilized in both science and economics.

The Formula for the Arc Price Elasticity of Demand Is

$PE_d = \dfrac{\text{% Change in Qty}}{\text{% Change in Price}}$

Instructions to Calculate the Arc Price Elasticity of Demand

In the event that the price of a product diminishes from $10 to $8, leading to an increase in quantity demanded from 40 to 60 units, then, at that point, the price elasticity of demand can be calculated as:

% change in quantity demanded = (Qd₂ - Qd₁)/Qd₁ = (60 - 40)/40 = 0.5
% change in price = (P₂ - P₁)/P₁ = (8 - 10)/10 = - 0.2
Along these lines, PEd = 0.5/ - 0.2 = 2.5

Since we're worried about the absolute values in price elasticity, the negative sign is overlooked. You can reason that the price elasticity of this great, when the price diminishes from $10 to $8, is 2.5.

What Does Arc Elasticity Tell You?

In economics, there are two potential approaches to ascertaining elasticity of demand — price (or point) elasticity of demand and arc elasticity of demand. The arc price elasticity of demand measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a specific point on the demand curve, or between two points on the curve.

Arc Elasticity of Demand

One of the problems with the price elasticity of demand formula is that it gives various values depending on whether price rises or falls. If you somehow managed to utilize different beginning and end points in our model above — that is, on the off chance that you accept the price increased from $8 to $10 — and the quantity demanded diminished from 60 to 40, the Pe_d will be:

% change in quantity demanded = (40 - 60)/60 = - 0.33
% change in price = (10 - 8)/8 = 0.25
PEd = - 0.33/0.25 = 1.32, which is vastly different from 2.5

To dispense with this problem, the arc elasticity can be utilized. Arc elasticity measures elasticity at the midpoint between two chose points on the demand curve by utilizing a midpoint between the two points. The arc elasticity of demand can be calculated as:

Arc Ed = [(Qd₂ - Qd₁)/midpoint Qd] \u00f7 [(P₂ - P₁)/midpoint P]

How about we work out the arc elasticity following the model introduced previously:

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 Ed = 0.4/ - 0.22 = 1.82

Whenever you use arc versatilities you don't have to worry about which point is the starting point and which point is the ending point since the arc elasticity gives similar value at elasticity whether costs rise or fall. Subsequently, the arc elasticity is more valuable than the price elasticity when there is a significant change in price.

Features

The arc elasticity is more helpful for bigger price changes and gives similar elasticity outcome whether price falls or rises.
In the concept of arc elasticity, elasticity is estimated over the arc of the demand curve on a graph.
Arc elasticity estimations give the elasticity utilizing the midpoint between two points.