Question

A beverage company works out a demand function for its sale of soda and finds it to be x = D(p) = 3100 - 20p where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?

Answer 1

Answer with Step-by-step explanation:

We are given that a demand function

$x=D(p)=3100-20p$

Where x=The quantity of sodas sold

p=Per can price (in cents)

We  have to find the price p for which  the demand inelastic.

Differentiate the demand function w.r.t p

$D'(P)=-20$

Price elasticity of demand=$E(p)=\frac{-pD'(p)}{D(p)}$

Price elasticity of demand=$E(p)=\frac{-p(-20)}{3100-20p}$

When demand  is inelastic then

E(p)<1

$\frac{20p}{3100-20p}$ <1

Multiply by (3100-20p) on both sides

$20p$

Adding 20p on both side of inequality

$40p$

Divide by 40 on both sides

$p$

When the value of price is less than 77.5 then the demand of elasticity is inelastic.