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Math Help - Help with calculus question in economics

  1. #1
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    Help with calculus question in economics

    Hi guys... Not sure if this is the right forum to post my question in but i'll give it a go anyways.
    Here's the question:
    Total Revenue is price times quantity. Suppose the demand curve for a good is
    given by Q = A BP . Find the e ect of a price change on revenue, i.e., take the
    derivative of revenue with respect to price. When is it positive? When is it negative?
    What role does elasticity play?

    Here is the answer:
    Q = A - BP . So, R = PQ = AP - BP^2. This is total revenue. Taking
    derivatives with respect to price, dR/dP = A -2BP = Q - BP (since Q = A-BP ).
    Note that elasticity is E = (dQ/dP )(P=Q) = B(P/Q). So, EQ = BP .
    Substituting this in the expression obtained earlier, we have, dR/dP = Q
    BP = Q + EQ = Q(1 + E) = Q(1- absolute value of E).
    The RHS is positive if demand is inelastic and negative if demand is elastic.
    So, if demand is inelastic an increase in price will increase revenue and if demand is
    elastic an increase in price will decrease revenue


    Now the part im stumped with is if dR/dP = A-2BP, how does that = Q-BP (since Q = A-BP)? Any help would be greatly apreciated. Thanks!
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  2. #2
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    Re: Help with calculus question in economics

    Quote Originally Posted by russellmania79 View Post
    Hi guys... Not sure if this is the right forum to post my question in but i'll give it a go anyways.
    Here's the question:
    Total Revenue is price times quantity. Suppose the demand curve for a good is
    given by Q = A BP . Find the eect of a price change on revenue, i.e., take the
    derivative of revenue with respect to price. When is it positive? When is it negative?
    What role does elasticity play?

    Here is the answer:
    Q = A - BP . So, R = PQ = AP - BP^2. This is total revenue. Taking
    derivatives with respect to price, dR/dP = A -2BP = Q - BP (since Q = A-BP ).
    Note that elasticity is E = (dQ/dP )(P=Q) = B(P/Q). So, EQ = BP .
    Substituting this in the expression obtained earlier, we have, dR/dP = Q
    BP = Q + EQ = Q(1 + E) = Q(1- absolute value of E).
    The RHS is positive if demand is inelastic and negative if demand is elastic.
    So, if demand is inelastic an increase in price will increase revenue and if demand is
    elastic an increase in price will decrease revenue


    Now the part im stumped with is if dR/dP = A-2BP, how does that = Q-BP (since Q = A-BP)? Any help would be greatly apreciated. Thanks!
    dR/dP = A - 2BP = (A - BP) - BP = Q - BP
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  3. #3
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    Re: Help with calculus question in economics

    Thanks for getting back to me. I'm still a little confused though. What happens to the 2 in front of the BP?
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  4. #4
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    Re: Help with calculus question in economics

    Quote Originally Posted by russellmania79 View Post
    thanks for getting back to me. I'm still a little confused though. What happens to the 2 in front of the bp?
    -2bp = -(bp + bp)
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