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.}}”
