# Answer in Microeconomics for She3er #111626

- 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 = -20Delta 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.}}”