Question

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. (Round your answer to three decimal places.)x=-3/4p + 29; p= 9E(9)=________???

Answer 1

Answer:

Demand is inelastic at p = 9 and therefore revenue will increase with

an increase in price.

Step-by-step explanation:

Given a demand function that gives q in terms of p, the elasticity of demand is

$E=|\frac{p}{q}\cdot \frac{dq}{dp} |$

• If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
• If E > 1, we say demand is elastic. In this case, raising prices decreases revenue.
• If E = 1, we say demand is unitary.

We have the following demand equation $D(p)=-\frac{3}{4}p+29$; p = 9

Applying the above definition of elasticity of demand we get:

$E(p)=\frac{p}{q}\cdot \frac{dq}{dp}$

where

• p = 9
• q = $-\frac{3}{4}p+29$
• $\frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)$

$\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}$

Substituting the values

$E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337$

$|E(9)|=|\frac{27}{89}| < 1$

Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.