# Theorems of the Elasticity of Demand

Theorems of the elasticity of demand present different attributes and specific conditions of the price elasticity of demand. It also describes how the elasticity and slope of the demand curve interact with each other.

The elasticity of demand refers to the quantitative measurement of the movement between price and quantity demanded. It measures if there is some percentage change in the price of a commodity then by how much percentage its quantity demanded will change. Therefore it differs from the law of demand as latter only talk about the direction of the price-quantity relationship.

Followings are some theorems of the elasticity of demand that has been developed with its attributes.

**Theorem I. Elasticity of the demand curve may be same for different slopes of the curve**

Although the slope of the two demand curves differs with each other the elasticity of the curve will be same at a given price.

**Proof:** Suppose we have two demand curve namely LM and LN with different slope and OP is the price and it intersects LM at E and LN at S.

The slope of LM curve at point E will be E_{p} = ME/EL and the elasticity of LN curve at point S will be E‘_{p} = NS/SL

For right-angled triangle MOL

ME/EL = OP/PL

For right-angled triangle NOL

OP/PL = NS/SL

thus, ME/EL = NS/SL

therefore, E_{p} = E’_{p}

Hence, although the slope at E and S point of the two demand curve differs but their elasticities are same.

**Theorem II. The elasticity of the downward sloped straight demand curve will increase from 0 at x-axis to infinity at the y-axis. **

**Proof:** Measure the elasticity of a demand curve by point elasticity method at different point of the demand curve.

**Theorem III. If two demand curve has the same slope but one is close to origin while other is comparatively far from the origin then the price elasticity of demand for more distant demand curve at the different price will be less than the demand curve close to the origin.**

**Proof:** As the elasticity of demand (Ep) = P/Q*ΔQ/ΔP, in this case, P and ΔQ/ΔP will be same for both curve but Q will differ as Q1< Q2 or Q2>Q1 so P/Q will be lower for far from origin demand curve hence its elasticity will be comparatively less.

**Theorem IV. If two straight-line demand curve with different slope intersect each other at a particular point then elasticity of the steeper curve will be lower than the elasticity of the less steep demand curve. **

**Proof:** As the elasticity of demand (Ep) = P/Q*ΔQ/ΔP, in this case, P and Q or P/Q will be same for both curve but ΔQ/ΔP will differ and ΔQ/ΔP will be lower for steeper demand curve hence its elasticity will be comparatively less.

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Author: Alok Aditya Post Graduate Student Central University of South Bihar

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