Answer to Question #111626 in Microeconomics for She3er

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

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

a. Calculate the price elasticity of demand.

We have the demand curve $P = 400 - 20Q$

The price elasticity of demand is computed as:

$E = \dfrac{\Delta Q}{\Delta P}\cdot \dfrac{(P_1 + P_1)/2}{(Q_1 + Q_2)/2}$

From the demand curve:

$\Delta P = -20\Delta Q$

$\dfrac{\Delta Q}{\Delta P }= -\dfrac{1}{20}$

At $P_1=\$150$ , the quantity demanded is:

$150 = 400 - 20Q$

$20Q = 250$

$Q_1 = \dfrac{250}{20} = 12.5$

When the price drops to $P_2 = \$100$ , the quantity demanded increases to:

$100 = 400 - 20Q$

$20Q = 300$

$Q_2 = \dfrac{300}{20} = 15$

Thus, the elasticity of demand is:

$E = -\dfrac{1}{20}\cdot \dfrac{(100 + 150)/2}{(15 + 12.5)/2} \approx -0.45$

$|E| \approx \color{red}{0.45}$

b. Is the demand elastic, inelastic or unit elastic?

$\color{red}{\text{The demand is inelastic since the elasticity is less than 1.}}$

c. What happens to Total Revenue?

$\color{red}{\text{The total revenue will decrease since the demand is inelastic.}}$

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

a. Calculate the price elasticity of demand.

At $P_1 = \$75$, the quantity demanded is:

$75 = 400 - 20Q$

$20Q = 325$

$Q_1 = \dfrac{325}{20} = 16.25$

When the price drops to $P_2 = \$50$, the quantity demanded increases to:

$50 = 400 - 20Q$

$20Q = 350$

$Q_2 = \dfrac{350}{20} = 17.5$

The elasticity of demand is equal to:

$E = -\dfrac{1}{20}\cdot \dfrac{(75 + 50)/2}{(16.25 + 17.5)/2} \approx -0.185$

$|E| \approx \color{red}{0.185}$

b. Is the demand elastic, inelastic or unit elastic?

$\color{red}{\text{The demand is inelastic since the elasticity is less than 1.}}$

c. What happens to Total Revenue?

$\color{red}{\text{The total revenue will decrease since the demand is inelastic.}}$