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Math Help - algebra based econ - finding a formula involving an excise tax

  1. #1
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    algebra based econ - finding a formula involving an excise tax

    this is based off of Anthony and Brigg's Mathematics For Economics And Finance: Methods And Modeling.

    it's exercise 1.5 on pg 11.

    the question reads, "Find a formula for the amount of money the government obtains from taxing the commodity in the manner described in exercise 1.4. Determine this quantity explicitly when T=0.5."

    i'll give you the required equations:

    qS = 6p - 12
    qD = 40 - 2p

    the excise tax = pT = (13/2)+(3/4)T

    the answer = 27T - (3/2)T^2

    i have no clue how they came up with that answer. i got 27 + (9/2)T.

    my process was to substitute the value of pT into qS.

    i also tried putting pT-T into qS, which gets me 27 + (3/2)T, close but not exactly the answer.

    also, i just followed the example in the book so i don't really have a conceptual understanding of the why, so can someone explain the logic behind inserting pT-T vs pT into qS?
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  2. #2
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    Re: algebra based econ - finding a formula involving an excise tax

    Sorry, too confusing (to me, anyway).
    Can you supply a site where we can see this problem in its original form?
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  3. #3
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    Re: algebra based econ - finding a formula involving an excise tax

    thanks for the reply.

    here's the link for the book Mathematics for Economics and Finance: Methods and Modelling - Martin Anthony, Norman Biggs - Google Books

    the question's on page 11.
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