Respuesta :
Answer:
c. The quantity demanded will decrease by approximately 218 million units to 582 million units.
d. The state will take in $468 million in additional revenues.
We follow these steps to arrive at the answer
Current Price of a cigarette pack with taxes $[tex]5.87 = 5+0.87[/tex]
Price of a cigarette pack after an increase in taxes $[tex]7.87 = 5+2.87[/tex]
Change in Prices (ΔP) $[tex]2 = 7.87 - 5.87[/tex]
Price Elasticity of demand (PED) 0.8
% change in Price [tex]\mathbf{\frac{\Delta P}{P_{0}}*100}[/tex]
[tex]\mathbf{\frac{2}{5.87}*100}[/tex]
% Change in Price 34.07155%
% Change in quantity demanded
[tex]\mathbf{{% change in price}* PED}}[/tex]
[tex]\mathbf{34.07155 * 0.8}[/tex]
% change in quantity demanded 27.5724%
Since price of a commodity and the quantity demanded share an inverse relationship, this means that when the price of cigarettes increases by 34.07155%, the demand for cigarettes will fall by 27.25724%.
Current demand for cigarette packs 800 million
Fall in demand for cigarette packs [tex]218.0579216=800*0.2725724[/tex]
New demand for cigarette packs
[tex]581.9420784 = 800-218.0579216[/tex]
The state will gain from an increase in price by $2, since all of the price increase is due to an increase in taxes. So, the state will take in [tex]2 * 582 = 1164[/tex]
Previously it used to get [tex]0.87 * 800 = 696[/tex]
Hence the additional revenues the state will take in is [tex]1164 - 696 = 468[/tex]
c.
The quantity demanded decreased by 27.25%.
d.
The state will get an additional revenue of $974 million.
Further Explanation:
Price Elasticity of Demand: It refers to the measure which represents the change in the demand of quantity of goods when there is a change in price of goods. The elasticity of price can be calculated as :
[tex]{\text{Price elasticity of demand = }}\dfrac{{{\text{Percentage change in quantity demanded}}}}{{{\text{Percentage change in price}}}}[/tex]
c.
Calculate the decrease in quantity demanded:
The fall in quantity demanded = 800,000,000 × .2725
= 216,000,000 or 218 million
The quantity demanded decreased by 27.25% or 218 million.
Working note 1:
Compute the current price of cigarette pack:
Current Price of a cigarette pack before increase in taxes = $5 + $0.87
= $5 + 0.87
Working note 2:
Compute the price of cigarette pack after increase in taxes:
Price of cigarette pack after increase in taxes = $5 + $2.87
= $7.87
Working note 3:
Compute the change in price of cigarettes:
Change in price = $7.87 - $5.87
= $2
Working note 4:
Compute the percentage change in the price:
[tex]\begin{aligned} {\text{Percentage change in price}} &= \dfrac{{{\text{\$2}}}}{{\$5.87}} \times 100 \\ &= 34.07\% \\ \end{aligned}[/tex]
Working note 5:
Calculate the change in quantity demanded:
[tex]\begin{gathered} {\text{Price elasticity of demand = }}\dfrac{{{\text{Percentage change in quantity demanded}}}}{{{\text{Percentage change in price}}}} \\ 0.8 = \dfrac{{{\text{Percentage change in quantity demanded}}}}{{34.07\% }} \\ {\text{Percentage change in quantity demanded = 27}}{\text{.256\% }} \\ \end{gathered}[/tex]
d.
Calculate the additional revenue to be taken by state:
The state will earn $2 per cigarettes pack as the tax has increased from $0.87 to $2.87 and the demand has fallen from 800 million to 582 million .
Additional revenue = Increase in revenue – Decrease in revenue due to fall in demand
= ($2 × 582 million) – (218 × $0.87)
= $974 million
The state will get an additional revenue of $ 974 million by imposing a higher tax of $2.87.
Learn more:
1. Demand and type of goods
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2. Demand and supply of goods
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3. Elasticity of demand
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Answer details:
Grade: Middle School
Subject: Economics
Chapter: Elasticity of demand
Keywords: Elasticity of demand, quantity demanded, Price elasticity of demand, the state will get additional revenue, , California taxed cigarettes, assuming that the price of a pack, actual price elasticity of demand.
