Question

The following information concerns energy drinks sold in a city.

Price Qd (thousand) Qs (thousand)

$1.50 20 0

$2.00 15 6

$2.50 10 10

$3.00 7 13

$3.50 5 15


a) What is the equilibrium price?

b) What is the equilibrium quantity?

c) What is the total revenue at this price and quantity?

d) Calculate the price elasticity of demand for a proposed price change from $3.00 to $3.50.

e) Is the price elasticity of demand elastic, inelastic, or unit elastic in this range?

Answer 1

a) What is the equilibrium price?

Price Demand Supply Revenue

$1.50 20 0 $30.00

$2.00 15 6 $30.00

$2.50 10 10 $25.00

$3.00 7 13 $21.00

$3.50 5 15 $17.50

b) What is the equilibrium quantity?

The equilibrium quantity is 10 units

c) What is the total revenue at this price and quantity?

The total revenue at the equilibrium price and quantity is $25.00

d) Calculate the price elasticity of demand for a proposed price change from $3.00 to $3.50.

At P = $3.00, the quantity demanded is Q = 7. At P = $3.50, the quantity demanded is Q = 5. Thus, the elasticity of demand is:

$$E_d = \dfrac{5 - 7}{3.50 - 3.00}\cdot \dfrac{(3.50 + 3.00)/2}{(5 + 7)/2}$$

$$E_d = \dfrac{-2}{0.5}\cdot \dfrac{3.25}{6}$$

$$E_d \approx -2.167$$

$$\color{red}{|E_d| \approx 2.167}$$

e) Is the price elasticity of demand elastic, inelastic, or unit elastic in this range?

The demand is elastic since the elasticity is greater than 1.