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?

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