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Thread: Excise Tax?

  1. #1
    May 2010

    Excise Tax?

    Can anyone help me with this?

    Suppose that the market for cigarettes in a particular town has the following supply and demand curves: QS = P;QD = 50 − P, where the quantities are measured in thousands of units. Suppose the town council needs to raise $300,000 in revenue anddecides to do this by taxing the cigarette market. What should the excise tax be in order to raise the required amount of money?
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  2. #2
    Junior Member
    May 2010
    The tax revenue will be $\displaystyle P_{tax}*Q$, with $\displaystyle Q$ determined by the intersection of the Inverse Demand Curve and the New Inverse Supply Curve, which is shifted upward from the original by $\displaystyle P_{tax}$.

    Prior to the imposition of the excise tax, the equilibrium price $\displaystyle P_{E} = 25, Q_{E} = 25$. However, when the tax is implemented, demand will fall, thus you need to find:

    You have Four Equations and Four Unknowns:
    $\displaystyle Q - P_{S} = 0$
    $\displaystyle Q + P_{D} = 50$
    $\displaystyle P_{tax} + P_{S} - P_{D} = 0$
    $\displaystyle Q*P_{tax} = 300,000$

    From the above, you can write $\displaystyle 2Q^2 - 50Q + 300,000 = 0$, which has complex roots for Q. Thus it will not be possible to raise 300,000.

    Perhaps you meant 300? If so, Q = 10 units or 15 units. Substituting Q=15 into the above yields $\displaystyle P_{tax}=20$, i.e

    $\displaystyle P_{S}=15, P_{D}=35, P_{tax}=20$
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