Solution: Price elasticity of demand = Percentage change in quantity demanded Percentage change in price of the commodity = 20 ( )8 ± = (–) 2.5 [This is to be noted that price elasticity of demand is always a negative number because of inverse relationship between price and quantity demanded. However, minus sign is often ignored while writing the value of elasticity.]
Notes ECONOMICS MODULE - 6 Price Elasticity of Demand Consumer's Behaviour 70 Illustration 2 When price of a commodity is ` 10 per unit, its demand is 100 units. When the price falls to ` 8 per unit, demand expands to 150 units. Calculate price elasticity of demand. Solution: e d = Percentage change in quantity demanded Percentage change in price of the commodity Percentage change in quantity demanded = ² ³ 150 100 100 50% 100 ± u Percentage change in price = ( )2 100 ( )20% 10 ± u ± So, e d = 50 ( )2.5 ( )20 ± ± We can also use the simplified formula for percentage change method. e d = ǻ Q P × ǻ P Q = ² ³ 150 100 10 8 10 100 ± u ± = 50 10 ( )2 100 u ± = (–) 2.5 Illustration 3 Price elasticity of demand of a commodity is (–) 2. A consumer demands 50 units of this commodity when its price is ` 10 per unit. At what price he will demand 40 units of this commodity? Solution: e d = ǻ Q P × ǻ P Q
Notes 71 Price Elasticity of Demand ECONOMICS MODULE - 6 Consumer's Behaviour (–)2 = 40 50 10 50 ± u ' P –2 = ( )10 10 P 50 ± u ' ' P = Re 1 per unit New price = 10 + 1 = ` 11 per unit 16.3.2 Geometric Method This method is also known as ‘point method’. Geometric method is used to measure the elasticity at a point on the straight line demand curve. Elasticity of demand is different at different points on the same straight line demand curve. According to the geometric method, elasticity of demand at any point of a straight line demand curve is measured as a ratio of lower segment of the demand curve and upper segment of the demand curve e d = Lower segment of the demand curve Upper segment of the demand curve Let us consider a straight line demand curve AB at which elasticity of demand is to be measured at point C, D, M, N, and P (Fig. 16.5). Quantity demanded Price 0 Y X C D M N P ed = ¥ ed = 1 ed > 1 ed = 1 ed < 1 Fig. 16.6
Notes ECONOMICS MODULE - 6 Price Elasticity of Demand Consumer's Behaviour 72 M is the mid- point of the demand curve AB. So, e d at point M = Lower segment of the demand curve Upper segment of the demand curve = MP 1 MC (Because MP= MC) e d at point N = NP NC Point N is below point M so NP is less than NC and elasticity will be less than one. e d at point P = 0 0 PC (Here lower segment is 0) e d at point D = DP DC Point D is above point M. So, DP is more than DC. Elasticity at this point will be more than one. e d at point C = CP 0 f (Upper segment is 0) So, we can conclude that elasticity at mid- point of a straight line demand curve will be 1, elasticity at every point below the mid- point will be less than one and elasticity at every point above the mid- point will be greater than one.
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