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Math Help - Excise Tax?

  1. #1
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    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
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    The tax revenue will be P_{tax}*Q, with Q determined by the intersection of the Inverse Demand Curve and the New Inverse Supply Curve, which is shifted upward from the original by P_{tax}.

    Prior to the imposition of the excise tax, the equilibrium price 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:
    Q - P_{S} = 0
    Q + P_{D} = 50
    P_{tax} + P_{S} - P_{D} = 0
    Q*P_{tax} = 300,000

    From the above, you can write 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 P_{tax}=20, i.e

    P_{S}=15, P_{D}=35, P_{tax}=20
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