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# 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
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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