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Math Help - Why Use Marginals In Economics?

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    Member pflo's Avatar
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    Why Use Marginals In Economics?

    I believe I have this straight:

    The differential (dy) is a good approximation for the change in y (delta-y) when delta-x is small. Therefore, you can use dy to approximate the change in a function (say the cost, revenue, or profit function) that occurs when there is a small change in x (the quantity of a product).

    It is not difficult to come up with the equation for dy - simply take the derivative of the function and multiply it times delta-x (which must be small for this to work since dx would 'be' zero if delta-y were to actually equal dy).

    In economics, a 'marginal' essentially answers the question "If I were to produce one more or one less, how would that affect my cost, revenue, and/or profit?". Thus, delta-x = 1 when determining the formula for dy.

    My question is: Why do this at all? Why not actually use delta-y? You could get a formula for this quite easily and it would be an exact answer, not an approximation. Is there a flaw in my interpretation of a marginal? Am I not seeing the bigger picture somehow?
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    Super Member Aryth's Avatar
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    Quote Originally Posted by pflo View Post
    I believe I have this straight:

    The differential (dy) is a good approximation for the change in y (delta-y) when delta-x is small. Therefore, you can use dy to approximate the change in a function (say the cost, revenue, or profit function) that occurs when there is a small change in x (the quantity of a product).

    It is not difficult to come up with the equation for dy - simply take the derivative of the function and multiply it times delta-x (which must be small for this to work since dx would 'be' zero if delta-y were to actually equal dy).

    In economics, a 'marginal' essentially answers the question "If I were to produce one more or one less, how would that affect my cost, revenue, and/or profit?". Thus, delta-x = 1 when determining the formula for dy.

    My question is: Why do this at all? Why not actually use delta-y? You could get a formula for this quite easily and it would be an exact answer, not an approximation. Is there a flaw in my interpretation of a marginal? Am I not seeing the bigger picture somehow?
    Your definition is the basic definition. \Delta{Q} = 1 because it is discussing what happens to cost with a unit change in production. A unit would force it to be 1.

    In all actuality however, the equation for marginal cost is:

    MC = \frac{dTC}{dQ}

    This says that the marginal cost is the change in total cost over the change in quantity.

    You're right, it could be more exact. However, in most basic classes you are only interested in unit changes.
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