Question

Consider the following demand function for game consoles: (D): P = 400 - 20Q
1. Assume that the price decreases from 150$ to 100$.
a. Calculate the price elasticity of demand.
b. Is the demand elastic, inelastic or unit elastic?
c. What happens to Total Revenue?


2. Assume that the price decreases from 75$ to 50$.
a. Calculate the price elasticity of demand.
b. Is the demand elastic, inelastic or unit elastic?
c. What happens to Total Revenue?

Answer 1

Consider the following demand function for game consoles: (D): P = 400 - 20Q

1. Assume that the price decreases from 150$ to 100$.

a. Calculate the price elasticity of demand.

Answer

Inverse demand function: P = 400 - 20Q

Demand function q = 10 – 1/20 p

Quantity demanded at price $150 q1 = 10 – 1/20 × 150 = 2.5

Quantity demanded at price $ 100 q2 = 10 – 1/20 × 100= 5.0

Price elasticity of demand using the Midpoint Method for Elasticity

Elasticity =   =   = -1.67

 

b. price elasticity is > 1, the demand is elastic

c. Total Revenue = Price × quantity

           TR= P × Q d

Initial Total Revenue= 150 × 2.5 = $375

Final Total Revenue = 100 ×5.0 = $ 500

When the price is decreased an increase in total revenue is realized.

2. Assume that the price decreases from 75$ to 50$.

a. Calculate the price elasticity of demand.

Inverse demand function: P = 400 - 20Q

Demand function q = 10 – 1/20 p

Quantity demanded at price $75 q1 = 10 – 1/20 × 75 = 6.25

Quantity demanded at price $ 50 q2 = 10 – 1/20 × 50= 7.5

Price elasticity of demand using the Midpoint Method for Elasticity

Elasticity =   =   = -0.455

 

b. price elasticity is < 1, the demand is inelastic

c. Total Revenue = Price × quantity

           TR= P × Q d

Initial Total Revenue= 75 × 6.25 = $468.75

Final Total Revenue = 50 ×7.5 = $ 375

When the price is decreased a decrease in total revenue is realized.