MATH 1K03 Lecture 27: elasticity of demand
31 Jan 2019
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Suppose demand q is given as a (di erentiable) function of unit price: that is, q = q(p). If p increases by 1%, then the price will go from p to 1. 01p. From section 2. 5, we know that q(p + 0. 01p) q(p) q (p)(0. 01p). We interpret the left side of this formula, q(p+0. 01p) q(p), as the change in demand as p increases by 1%. The percent decrease in q as the price increases from p to p + 0. 01p is. 100(cid:18)q(p + 0. 01p) q(p) q(p) (cid:19) . By the above approximation, this percent decrease is approximately. 100(cid:18)q (p)(0. 01p) q(p) (cid:19) = q (p) p q(p) In general, q (p) will be negative - demand decreases when price rises. So we multiply the above by 1 to get a positive percentage. Thus, the percentage that demand decreases by when price is raised by 1% will be approximately q (p) p q(p) which is e(p).
