Total Revenue Elasticity

Total Revenue Elasticity - percentage change of quantity,...

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Pingkang Yu 09/30/2009 This file is my additional explanation to help you understand the change of total revenue when changing prices in different scenarios of elasticity. (This is the same question discussed on page 7 of the Lecture Notes.) For inelastic demand, which is represented by a steep demand curve, total revenue rises (falls) when price rises (falls), because the percentage change of price is larger than the percentage change of quantity, so when the price rises (falls) for example, the rise (fall) of price is more than enough to compensate the drop (rise) in quantity, as a result, the total revenue, which is a product of price and quantity, increases (drops). For elastic demand, which is represented by a flatter demand curve, total revenue falls (rises) when price rises (falls), because the percentage change of price is less than the
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Unformatted text preview: percentage change of quantity, so when the price rises (falls) for example, the rise (fall) of price leads to a even larger the drop (rise) in quantity, as a result, the total revenue, which is a product of price and quantity, decreases (rises). A mathematic explanation is as following: R: revenue P: price Q: quantity e: elasticity P e R P P P Q R P Q R P dP Q dQ R dR QdP PdQ dR PQ R + = + = + = + = + = = )% 1 ( % % % % % % % % % The last step arrives based on the definition of elasticity: P Q e = % % Therefore, in the last equation, P e R + = )% 1 ( % For inelastic demand, -1< e <0, so (e+1) is positive. Therefore, R % and move towards the same direction. P % For elastic demand, e < -1, so (e+1) is negative. Therefore, R % and move towards the opposite direction. P %...
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