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Math Help - Calculus applied to Cost Value Analysis

  1. #1
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    Calculus applied to Cost Value Analysis

    Hi anyone,

    I need help in attaining the relationships between Fixed Costs and Variable Costs (this is for accounting). I hope someone will know what I'm taling about as thsi applies to business, not science.

    I can easily derive the relationship of Variable Costs and I get:

    Total Variable Costs= y= Ax + B
    Variable Costs per Unit= y'= A

    so: VCU= d/dx(TVC)

    But I cannot see the relationship between Total Fixed Costs and Fixed Costs per Unit.

    I can see that their graphs are:

    TFC= A

    and

    FCU= A/x

    How are the derived from each other? I am puzzled. Any help would be appreciated. Thanks.
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  2. #2
    Member Mentia's Avatar
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    Bellingham, WA
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    Okay so your equation implies that each unit costs a certain amount, A, but also there is some overall associated cost (perhaps startup costs or setup costs or something) which is B.

    To my understanding it should be something like this:

    TOTAL cost = y = Ax + B
    Total Fixed costs = B (this value is the same no matter how many units are made)
    Total Variable costs = Ax (this value varies depending on how many units are made)

    Then the variable cost per unit is just the Total Variable cost divided by the number of units:

    VCU = TVC/x = Ax/x = A =  \frac{dy }{dx }

    The fixed cost per unit is the total fixed cost divided by the number of units:

    FCU = TFC/x = B/x

    Seem logical?
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  3. #3
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    Thanks Mentia

    Yes, it would seem logical if A = B, but that is exactly what threw me off. A doesn't have to equal B!

    Yes, this is correct. The y = Ax + B is the Total Cost function made up of fixed and variable costs! I didn't need calculus at all, I was just "over engineering" it all.

    Thanks
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