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Question

# The economic advisor of a large tire store proposes the demand function D(p)=$\frac { 1800 } { p - 40 }$, where D(p) is the number of tires of one brand and size that can be sold in one day at a price p. For what prices is the demand elastic? Inelastic?

Solution

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$E(p)=\dfrac{p}{40-p}$

Elasticity is interpreted as the percentage change in the demand that results for every $1\%$ change in the price.

We have:

$E(60)=\dfrac{60}{40-60}=-3$

So, for every $1\%$ change in the price, demand drops for $3\%$. Since the change $\dfrac{\Delta p}{p}=\dfrac{62-60}{60}=3.33\%$, demand drops for $-3\cdot 3.33\%=-10\%$.

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