Elasticity of Demand- Price Elasticity and Arc Elasticity Methods

Elasticity of Demand

The term 'elasticity of demand' refers to the responsiveness of demand to changes in the price of a given commodity, assuming all other factors remain constant.

To be more specific, the Price Elasticity, or "Elasticity of Demand," is a measure used to determine the percentage change in the quantity demanded of a good or service in response to a one percent change in the price of that good or service.

We are all aware that whenever the price of a commodity increases, we tend to curtail our demand for that commodity. So, the tool of the elasticity of demand tries to measure the magnitude of those changes in demand with reference to the changes in the price of that commodity.

The Elasticity of Demand is also known as the price elasticity of demand.

These terms are expressed in abbreviated form, either as "Ed" or "PED", respectively.

The elasticity of demand is mostly negative in almost all cases except in cases of "status goods" (Veblen goods) or "goods that have no substitutes" (Giffen goods).

Veblen goods are luxurious items that are the status symbols of extremely wealthy people.

Giffen goods are basic, non-luxury goods that have no substitutes. They are necessary for survival when the prices of other staple items rise. Bread, potatoes, and rice are essential for a common man to survive. So, he has to buy them when no food is available, even at higher prices.

How to Measure Elasticity of Demand?

The Elasticity of Demand is measured with the help of formulas just like Elasticity of Supply.

The general equation for Price Elasticity of Demand is expressed as follows:

Price Elasticity of Demand = Percentage change in quantity demanded divided by Percentage change in Price

So, if the original quantity is Q and the price is P, then Ed = (dQ/Q)/ (dP/P)

In the above equation, Ed denotes the elasticity of demand (price elasticity).

DQ refers to the change in quantity, and Q refers to the original quantity demanded.
DP points to the change in price, and P to the original price.

You can express the above equation as (Qd1/Qd) / (P1/P), where Qd1 denotes the changed quantity, and Qd denotes the original quantity. P1 is the new price, and P is the original price.

But we know that when prices increase, demand for those items decreases, and demand increases whenever prices fall. 

So, there is always an inverse relationship in the equation, except in the cases mentioned above. Hence, the equation always gives a negative value.

Two more precise, result-yielding formulas are being used by economists nowadays to measure the elasticity of demand. 

These formulas are as follows:

1) The Arc Elasticity of Demand formula
This method is used when there is no exact equation for demand available or when we are not accustomed to taking derivatives.

2) The Point-Price (or Price-Point) Elasticity of Demand formula
This method is used when we have the exact equation available, or when we are capable of calculating the derivatives of equations.

Now, let us study these two methods of calculation, one by one:

Arc Elasticity of Demand Method

The arc elasticity method gives us the average elasticity of demand between two end points of an arc on a demand curve. So, it gives us the average elasticity of demand for that curve. 

It solves the problem faced by analysts in choosing one point as the original point and the other point as the new point and, thereby, provides great relief from the dilemma faced by economists in calculating the elasticity. 

But it may not provide accurate figures, as you are taking the average of two points on a curve.

The mathematical equation for arc elasticity of demand is as follows:

{(P1+P2)/2} / {(Qd1+Qd2)/2} x (change in quantity demanded/change in price)

So, Elasticity of Demand according to this formula = (the average of prices divided by the average of quantities demanded at each price) x (change in quantity divided by change in price)

You are taking the average of multiple prices on an arc and dividing it by the average of new quantities demanded by consumers at those changed prices. Thereafter, you are multiplying the same by the derivative of (change in quantity divided by the change in price) at any point to decide the elasticity at that point.

Suppose there are two price levels for a commodity, sugar, at Rs. 40 per kg and Rs. 50 per kg.
Let us assume that at price 40, quantity demanded is 10 kg, and at 50, quantity demanded is 8kg.

Now, according to above formula, Ed = {(40 + 50)/2 divided by (10 + 8)/2} x {(10 - 8) divided by (40 - 50)} = (90/2 divided by 18/2) X (2/10) = (45 divided by 9) X (2/10) = 5 X 0.2 = 1
So Ed = 1

1% change in original price is 40 x 1/100 = 0.40 = 40 paise.

According to this formula, for every 40 paise, the quantity is assumed to change by 1%.

Point-price Elasticity of Demand Method

The point-price method is used to determine the elasticity of demand at very small changes in prices. 

It is useful in determining the price elasticity of demand at a specific point on the demand curve. 

It studies the changes in demand at price points very close to each other on a demand curve.

It also uses the same formula: the percentage change in demand divided by the percentage change in price. 

But instead of calculating each equation, we take information from the demand equation to calculate the price elasticity of demand.

Ed = percentage change in demand / percentage change in price = (Qd1/Qd) / (P1/P) = (P/Qd) x (Qd1/P1)

Now, as I mentioned above, this method is applied when we have the exact equation for the demand curve and the derivatives with respect to price.

Let us take an example:

The equation for the elasticity of demand for a demand curve Q = 5000 - 50P

So, in this equation, Qd1/P1 = 50 (per one unit of price, the change in quantity demanded is 50).

Now, suppose we have to find the point-price elasticity of demand at prices of 40 and 25.

The quantity demanded at 40 will be 5000-2000=3000. (multiplying 40 by 50)
The quantity demanded at 25 will be 5000-1250=3750. (multiplying 25 by 50)

So, Ed at 40 is -50 (40/3000) = -2000/3000= -2/3= -0.666
Ed at 25 is -50 (25/3750) = -1250/3750= -1/3= -0.333