Answer to Question #111626 in Microeconomics for She3er

Question #111626
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?
1
Expert's answer
2020-04-23T11:51:13-0400


  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:



"\n150 = 400 - 20Q\n\n"

"20Q = 250\n"

"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.}}"


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