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ch04_End-of-chapter-question - Chapter 4 Elasticity 29 May...

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Unformatted text preview: Chapter 4 Elasticity 29 May 2011 1. On the accompanying demand curve, calculate the price elasticity of demand at points A, B, C, D and E. Answer: Roughly speaking price elasticity measures the responsiveness of quantity demanded to change in price. Price elasticity of demand refers to the percentage change of quantity demanded relative to the percentage change of price. In other words, price elasticity of demand indicates how much (in percentage) will the quantity demanded change with respect to a 1% change in price. Price elasticity of demand is always a negative index, as the demand curve is downward sloping (i.e., on the same demand curve, an increase in price is associated with a decrease in quantity demanded). Sometimes, for convenience and without confusion, we take absolute value of a price elasticity of demand. • Elastic price elasticity of demand: The quantity demand is strongly responsive to a change in price. It happens when the percentage change in quantity demanded is greater than the percentage change in price. The price elasticity of demand is less than negative 1 (i.e., -1). The absolute value of a price elasticity of demand is greater than one (i.e., 1). • Inelastic price elasticity of demand: The quantity demand is weakly responsive to a change in price. It happens when the percentage change in quantity demanded is smaller than the percentage change in price. The price elasticity of demand is larger than negative 1 (i.e., -1). The absolute value of a price elasticity of demand is smaller than one (i.e., 1). • Unitary elastic price elasticity of demand: The quantity demand is mildly responsive to a change in price. It happens when the percentage change in quantity demanded is equal to the percentage change in price. The price elasticity of demand is exactly negative 1 (i.e., -1). The absolute value of a price elasticity of demand is equal to one exactly (i.e., 1). General formula for Price Elasticity of Demand ξ = Change of quantity demanded / Original quantity demanded Change of price / Original price 1 Let the original price and quantity pair be ( P , Q ) and the new one be ( P 1 , Q 1 ). ξ = ( Q 1- Q ) /Q ( P 1- P ) /P = Δ Q/Q Δ P/P = Δ Q Δ P P Q where Δ Q ≡ Q 1- Q and Δ P ≡ P 1- P . One can easily recognize that Δ Q/ Δ P is just the reciprocal of slope of the demand curve. ξ = 1 slope P Q Of course, for a linear demand curve, the slope stays the same for all price-quantity pairs. Now consider Δ Q very close to zero (but not zero). We must also have Q 1 ≈ Q . Or imagine Q 1 = Q = Q . Hence, we ξ = Δ Q Δ P P Q ≈ Δ Q Δ P P 1 Q 1 ≈ Δ Q Δ P P Q = 1 slope P Q Using this formula, we can derive price elasticity of demand at any point along the demand curve....
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