Elasticity of Demand

Introduction


Price Elasticity of Demand


It is denoted as: Percentage Change in amount demanded/ Percentage Change in Price

Methods of Measuring Price Elasticity of Demand

• The Percentage Method - It is determined by thee co-efficient of price elasticity (Ep). This co-efficient determines the percentage change in the quantity demanded of an article from a specified percentage price change. It is given by:
  
  Ep = % change in q / % Change in p = (Δq / q) / (Δp / p) = (Δq / Δp) x p / q
  
  Where q refers to quantity demanded, p to price and Δ to change. If Ep > 1, demand is elastic. If Ep < 1, demand is inelastic and if Ep = 1, demand is unity elastic.


• The Point Method - This method has been formulated by Prof. Marshall for measuring elasticity at a point on the demand curve.
  
  
  
  In this diagram, let us see how the point method works out. AB being straight line demand curve, if the price falls from PG(=OC) to FH(=OE), the quantity demanded is augmented from OG to OH. Elasticity at Point P on the AB demand curve as per the formulae is Ep = (Δq / Δp) x p / q, where Δq represents change in quantity demanded, Δp change in price level whereas p and q are prime price and quantity levels. From the pictorial representation. We derive the following. Δq = GH = QH, where, Δp = PQ.
  
  P = PG and q = OG. Substituting these parameters in the specified elasticity formulae, we acquire: Ep = (QF / PQ) x (PG / OG). Besides, (QF / PQ) x (GB / PG). [ ∠PGB being right angles and PQF and PGB are similar Δb]. Hence, (GB / PG) x (PG / OG) = GB / OG.


• The Arc Method - When elasticity is calculated between two points on the same demand curve, it is termed as Arc elasticity. Prof. Baumol defines as "Arc elasticity is a measure of the average responsiveness to price change exhibited by a demand curve over some finite stretch of the curve." Any two points in the demand curve is an arc which measures elasticity over a definite array of the price and quantity demanded. The formula for computing elasticity under this method is as below.
  
  Ep = [Δq / (q1+q2)^∧1/2] / [Δp / (p1+p2)^∧1/2] = (Δq / (q1+q2) ^∧1/2) x [(p1+p2)^∧1/2 / Δp) = (Δq / Δp) x [(p1+p2) / (q1+q2)]


• The Total Outlay Method - Prof. Marshall has derived the total outlay method of ascertaining the elasticity of demand. It is also termed as total revenue or total expenditure method as a measure of elasticity. By contrasting the total outlay of a purchaser both before and after the change in price, it can be known whether his demand for a good is elastic, unity or less elastic. Total outlay is denoted as price proliferated with the quantity of an article purchased that is denoted as below.
  
  Total outlay = Price x Quantity Demanded
  
  Demand is elastic, whilst with the drop in price, the sum of outlay augments and with the mount in price, the total outlay diminishes. The demand is unity when with the drop or mount in price, the total outlay stays invariable. Demand is less elastic with the consequence of drop in price drops total outlay and mount in price, mounts total outlay.
  

Elasticity and Slope of the Demand Curve

The slope of the demand curve is different from its price elasticity. This fact is evidenced by measuring price elasticity on two demand curves of the same or different inclines.

• Two straight line demand curve originating from the same point
  
  
  
  There are two straight line curves PQ and PR in this representation. PR is flatter than PQ and hence it appears that its price elasticity is higher than the other curve. But this is not actuality. If we further draw another line TS, passing through these curves and touching the vertical axis at point T, the elasticity at point U on the PQ curve as per the point formula is (QU/UP) = (OT/OP). Similarly, elasticity at point S on the PR curve is (RS/SP) = (OT/OP) and hence, (QU/UP) = (RS/SP) = (OT/OP) = 1.
  
  Thus the elasticity is equal on both the points U and S of the two curves. We may conclude that if two linear demand curves originate from the vertical axis at the same point, such as P, they have exactly equal elasticity at every single price.


• Two straight line demand curves originating from Different points which are neither parallel nor intersecting -
  
  
  
  This picture shows two demand curves PQ and XR. Of these, the curves XR is flatter and so it looks more elastic in price. But this is incorrect. To prove it, we shall draw another line from point T of the vertical axis which passes through these curves at points V and W respectively. Thus price elasticity of point V on the PQ curve is QV/VP = OT/TP and at point W on the XR curve is RW/WX = OT/TX. Since OT/TP > OT/TX, hence QV/VP > RW/WX.
  
  It means that price elasticity of demand is less than 1 at point W on the demand curve XR and greater than 1 at point V on the PQ curve.


• Two parallel straight line demand curve -
  
  
  
  Two parallel straight line demand curves appear to have the same slope and hence the same price elasticity. Again this view is incorrect. To evidence this, let PQ and XR be two parallel straight line demand curves. We shall draw a line TU which passes through these straight lines at point Y and U correspondingly. As per the formula, elasticity of point Y on the curve PQ is QP/YP = OT/TP. Likewise, elasticity of point U on the XR curve is RU/UX = OT/TX. Since OT/TP > OT/TX, OT/TP > RU/UX. It means greater elasticity at point Y on the line PQ than at point U on the line XR.


• Two points on a curved demand curve -
  
  
  
  Let us consider the points IJ on a curved demand curve K. Elasticity at point J is QJ/JP and at point I, RI/IX. Since RI/IX is greater, elasticity at point I is greater than unity and at point J, it is less than unity. The above cases evidence that the price elasticity of demand cannot be computed by merely looking at the incline of a demand curve.

Exceptions:

However, there are three exceptions to this and they are (1) When price and quantity are identical, it can be said by looking at the inclines of the two intersecting demand curves which one is more or less elastic. This is described in the nearby picture, where the incline of XQ curve shows that it is flatter and that of the PR curve shows it to be steeper. Both intersect at point C so that they have identical price OT and identical quantity OZ. If the demand curve is vertical, its price elasticity is zero and if the demand curve is horizontal, its price elasticity is infinite.

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Other topics under Consumption Theory:

• Cross Elasticity of Demand, Income Elasticity of Demand
• Demand and Law of Demand
• Exceptions to the Law of Demand
• The Concept of Customer's Surplus
• The Indifference Curve Theory - PART I
• The Indifference Curve Theory - PART II
• Price Earnings Line or Budget Line
• Revealed Preference Theory of Demand
• Superiority of Hicks' gauge of CS over Marshall's
• Superiority of Revealed Preference Theory
• Uses or Application of Indifference Curve Study