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Math Help - Business calc/applications. Marginal costs and such.

  1. #1
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    Business calc/applications. Marginal costs and such.

    alright problem #1

    If a question gives you the MC (marginal cost) function c'(q), and asks you to find the cost to increase production from a to b units, then is it simply c'(b) - c' (a)? or do we need to know the TC (Total cost) function for this?

    problem #2

    If and investment increases by 500% over a 15 year period under a constant periodic interest rate of r% monthly, the annual interest rate is approximately...

    a) 10.78 %
    b) 11.32 %
    c) 12.69 %
    d) 12.00 %

    Um, so here i am not sure whether this question is pertaining to interest compounded continuously or compound interest. I tried using the compound interest formula for this, it should start off like this i think:

    5P = P(1+r/180)^180
    5 = (1+r/180)^180
    180 sqrt 5 = 1 + r/180
    (180 sqrt 5 - 1) x 180 = r

    Cant seem to get the right answer though...
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  2. #2
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    Business calc/applications. Marginal costs and such.

    1. I think you need to integrate the MC function to determine the total cost (TC) function. Then your answer should be TC(b) - TC(a). The marginal costs are per-unit costs; you seemed like you wanted the total cost change.

    2. If the amount increases by 500%, it means you're going to end up with 600% of what you started with. So I think the formula you want is:
    (1+r/12)^180 = 6, which, if I did the math right, works out to about 12.0% for r. (You want to divide r by 12, not 180, because it's an annual interest rate compounded monthly.)

    - Steve J
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  3. #3
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    Quote Originally Posted by Steve_J View Post
    1. I think you need to integrate the MC function to determine the total cost (TC) function. Then your answer should be TC(b) - TC(a). The marginal costs are per-unit costs; you seemed like you wanted the total cost change.

    2. If the amount increases by 500%, it means you're going to end up with 600% of what you started with. So I think the formula you want is:
    (1+r/12)^180 = 6, which, if I did the math right, works out to about 12.0% for r. (You want to divide r by 12, not 180, because it's an annual interest rate compounded monthly.)

    - Steve J
    Thx for that

    But just wondering, why does a 500% increase yield a 6x increase?
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  4. #4
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    Business calc/applications. Marginal costs and such.

    It doesn't. If you start (for example) with $100, and you increase it by 500%, you're adding $500, which leaves you with a total of $600. Hence the 6 instead of the 5. You're working with the total sum of money available, not the incremental increase.

    - Steve J
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