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Unformatted text preview: Math 006 (Lecture 23) Elasticity of Demand
Deﬁnition 1. The relative rate of change of a function f (x) is given by f (x) . f (x) Deﬁnition 2. Let x = f (p) be a demand function. The elasticity of demand is deﬁned by f (p) relative rate of change of demand pf (p) f (p) =− 1 =− . − relative rate of change of price f (p) p Let us consider the revenue function R(p) = pf (p). We see that the marginal revenue is given by pf (p) + 1 = f (p)[1 − E (p)] R (p) = pf (p) + f (p) = f (p) f (p) where E (p) is the elasticity of demand. Deﬁnition 3. We call the demand is inelastic if E (p) < 1 and the demand is elastic if E (p) > 1. 1. When demand is elastic, that is E (p) > 1, R (p) < 0. (a) A price increase will decrease revenue. (b) A price decrease will increase revenue. 2. When demand is inelastic, that is E (p) < 1, R (p) > 0. (a) A price increase will increase revenue. (b) A price decrease will decrease revenue. 1 Example 1. A sunglass manufacturer currently sells one type of sunglass for $4 a pair. The price p and the demand x for these glasses are related by x = f (p) = 7, 000 − 500p. If the current price is increased, will revenue increase or decreased? Example 2. Use the following price-demand equation x = f (p) = 10(p − 20)2 to ﬁnd the values of p for which demand is elastic and the values for which demand is inelastic. 2 ...
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