Price Elasticity of Demand along a Linear Demand Curve | Constant Elasticity along a demand curve

Horizontal Demand Curve | Vertical Demand Curve | Rectangular Hyperbola

Introduction

In previous session, we discussed in detail regarding the elasticity of demand. The responsiveness of demand i.e., quantity demanded for a good or commodity to a change in any of the factors affecting the demand is known as Elasticity of Demand. Now there are several factors which affect quantity demanded for a good or commodity in a market. Those factors are price of the good itself, income of the consumer, price of related goods as well as taste & preferences of the consumer. Now we can study the responsiveness of demand towards each factors individually. So to say if we study the responsiveness of demand for a good to a change in its price as a deciding factor, we are measuring the Price Elasticity of Demand. And is if we measure the responsiveness of demand for a good to a change in income of the consumer, we are measuring the Income Elasticity of Demand. Although we discussed the Price Elasticity of Demand in detail.

Price Elasticity of Demand along a Linear Demand Curve

Price Elasticity of demand can be defined as the percentage change in quantity demanded of the good divided by the percentage change in price of the good. Thus we are measuring how the demand is responding to a per unit change in price. We can describe the same in formula form as under;

We know that for a linear demand curve, the general equation is q = a - b(p).

In this equation the b is the slope of the demand curve which denotes the change in demand to per unit change in price. So slope in formula form can be written as

As we know there is inverse or negative relation between demand and price, the slope will be negative.

If we substitute the value of slope or –b in the formula for Price Elasticity of demand we get,

As we know the value of q is a-b(p), substituting the same in above equation will give

We will understand the different level of price elasticity with a graph to make it more lucid.

The above graph shows price elasticity of demand at different price levels. When the price(p) = 0, the price elasticity Pe(D) = 0. At quantity (q) = 0, the Pe(D) = ∞. When the price is a/2b, the Pe(D) = 1. This clearly means that, at any price more than 0 but less than a/2b, the Pe(D) is less 1 and at any price higher than a/2b, the Pe(D) will be higher than 1.

Constant Elasticity along a demand curve

In the above scenario of Price Elasticity of Demand along a linear demand curve, we saw that the price elasticity was different at different price levels carrying from 0 to 1 to ∞.

But there are scenarios where the price elasticity of demand remains constant throughout the demand curve, which we call it as Constant elasticity along a demand curve.

1st Scenario – Vertical Demand Curve 

Look at the below graph given.

In the above case, the quantity demanded for the product remains the same given whatever be the price. It simply means, that a change in price will never lead to a change in quantity demanded for the product i.e., demand never responds to whatever be the change in price. Hence in case of a Vertical Demand Curve the price elasticity of demand is always 0 (zero). Thus the Vertical Demand Curve is Perfectly Inelastic. 

2nd Scenario – Horizontal Demand Curve

In the above scenario, the market price remains constant at whatever be the quantity demanded for the product. At any price other than the given p leads to quantity demanded dropping to 0 (zero). Hence in case of a Horizontal Demand Curve, the price elasticity of demand is equal to ∞. Thus the Horizontal Demand Curve is Perfectly Elastic. 

3rd Scenario – Rectangular Hyperbola

In the above scenario, the percentage change in price always results at any point of the demand curve always results in equal percentage change in the quantity demanded. Hence in case of a Rectangular Hyperbola Demand Curve, the price elasticity of demand is equal to 1. Thus the Rectangular Hyperbola Demand Curve is Unitary Elastic. 

Summing up the above 3 cases, we can summarize it as

1) Price Elasticity of Demand at all points along the Vertical Demand Curve is equal to Zero.

2) Price Elasticity of Demand at all points along the Horizontal Demand Curve is equal to Infinity (∞).

3) Price Elasticity of Demand at all point along the Rectangular Hyperbola Demand Curve is equal to 1.

Conclusion 

In this session, we studied in detail the Price Elasticity of Demand along a Linear Demand Curve and Constant Elasticity along a demand curve. Under Constant Elasticity along a demand curve we discussed 3 scenarios where the demand curve is Vertical, Horizontal or Rectangular Hyperbola.