Wednesday, 16 November 2016

Elasticity of demand- Price elasticity and Arc elasticity methods

Meaning and Definition of Elasticity of Demand

The term 'elasticity of demand' refers to the responsiveness of demand to changes in the price of a given commodity assuming that all other factors are remaining the same.

To be more specific, the Price Elasticity or Elasticity of Demand is a measure or tool employed in finding out the percentage change in 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 gets increased, we tend to curtail our demand for that commodity. So, the tool of the elasticity of demand tries to measure the quantum of those changes in demand with reference to the changes in prices of that commodity.

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

These terms are expressed in abbreviated terms 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).

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
ie. Ed = (dQ/Q)/ (dP/P)
In the above equation, Ed denotes elasticity of demand (price elasticity).
DQ refers to the changed quantity and Q refers to the original quantity demanded.
DP refers to changed price and P refers to the original price.
You can express the above equation as (Qd1/Qd) / (P1/P) where Qd1 denotes changed quantity and Qd original quantity. P1 is new price and P is original price.
But, we know that the demanded quantity decreases whenever the price increases and the demanded quantity increases whenever the price falls. So, there is always an inverse ratio in the equation excepting in the cases as 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 mentioned below.

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 with us or when we are capable of calculating the derivatives of equations.

Now, let us study these two methods of calculation.

Arc Elasticity of Demand method
The arc elasticity method gives us the average elasticity of demand between the 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 thus provides a great relief from the dilemma faced by the economists in calculating the elasticity. But, it may not provide the 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 sum total of prices divided by the sum total of quantities demanded at each price) x (change in quantity divided by change in price)
You are taking the average of different prices on an arc and dividing it with the average of new quantities demanded by consumers at those changed prices. Then, 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 Sugarat Rs.40 per kg and Rs.50 per kg.
Let us assume that at price 40, quantity demanded is 10kg and at price 50, quantity demanded is 8kg.
Now, according to above formula, Ed = {(40 + 50) divided by (10 + 8)} x {(10 - 8) divided by (40 - 50)} = (90/18) x (-2/10) = 5 x (-1/5) = -1 or 1%
ie. Demand changed by 1% per each percentage change in the price.

1% change in original price is 40 x 1/100 = 0.40 = 40 paise.
So for every 40 paise, it is assumed that the quantity changes by 1% according to this formula.

Point-price Elasticity of Demand method
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 demands at price-points very closer to each other on a demand curve.

It also uses the same formula of the percentage change in demand divided by the percentage change in price. But, instead of calculating each equation, we can 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 demand curve and the derivatives per unit of price cahnge.

Let us take an example.
The equation for 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 demand quantity is 50).
Now, suppose we have to find out the point-price elasticity of demand at a price of 40 and 25.
The quantity demanded at 40 will be 5000-2000=3000.
The quantity demanded at 25 will be 5000-1250=3750.

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