Assuming that the price of a pack of cigarettes is $5 before the tax and if the actual price elasticity of demand for california-taxed cigarettes is 0.8, c. by how much will the quantity demanded decrease with the new tax? d. how much additional revenue will the state take in?

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                     $

Price of a cigarette pack after an increase in taxes          $

Change in Prices (ΔP)                                    $

Price Elasticity of demand  (PED)                                    0.8  

% change in Price                

% Change in Price                                    34.07155%

% Change in quantity demanded 

% 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                

New demand for cigarette packs          

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

Previously it used to get

Hence the additional revenues the state will take in is            

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 :

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:

Working note 5:

Calculate the change in quantity demanded:

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

2.Demand and supply of goods

3.  Elasticity of demand

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.

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