Question

Suppose 50 bottles of beer are demanded at a price of $1 per bottle. Reducing the price at happy hour to $0.20 per bottle increases the quantity demanded to 70 bottles. 1. What is the price elasticity of demand (using the mid-point formula discussed in class)? 2. Is the demand elastic, inelastic, or unit elastic? 3. What happens to the total revenue of the firm if they lower their price from $1 to $0.20.

Answer 1

Answer

1.
The elasticity of demand =0.25

Given
Qd=50
Qd'=70
P=1   
P'=0.20
The elasticity of demand=(change in quantity/average quantity)/(change in price/average price)
Change in quantity=50-70=-20
average quantity=(50+70)/2=60
change in price=1-0.20=0.8
average price=(1+0.20)/2=1.20/2=0.6
Elasticity of demand=(-20/60)*(0.6/0.8)=-0.25
The elasticity of demand =0.25
The negative sign is an indicator of the negative relationship between the price and quantity demanded.

2.
The demand is inelastic since the absolute value of elasticity is less than 1.

3.
Since the demand is inelastic therefore a fall in the price would decrease the total revenue since the quantity effect is less.