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Thread: Economic Mathematical Equation which is constantly decreasing.

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    Economic Mathematical Equation which is constantly decreasing.

    I don't know where this goes so I'll just put this here. It's a question regarding a decreasing value over time.

    If you have an equation B = (1 - R) A + I,

    where A is the value of stock in one period, and B is the value of stock in a next period,
    R is a depreciation rate of 2%, and I is an investment value added upon every period.

    Would the value ever become constant?

    E.G. the Initial value of capital stock is 200, and I = 10, R = 0.02

    where you get the first period formula to be (1 - 0.02)*200 + 10 = 206
    second period (1-0.02)*206 + 10 = 211.88
    third period (1-0.02)*211.88 + 10 = 217.6424

    The difference between each period becomes smaller just by inspecting that 211.88 - 206 > 217.6424 - 211.88.

    However, since it is a depreciation rate, the value becomes continuously smaller. So, does the stock eventually become constant? I assumed it shouldn't, but the answers differ.

    This is a macroeconomics class so I'm unsure if they take mathematical theories as seriously. The answers say that it does, and perhaps this is due to the disregard of dollar value if it reaches a point where it is too miniscule to consider.
    Last edited by ProdigyInspired; 23 Aug 2017 at 3:41 AM.
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    Re: Economic Mathematical Equation which is constantly decreasing.

    Just a wild guess - does the long term value settle at 500? Must be 500.
    Last edited by Drongoski; 24 Aug 2017 at 9:14 PM.
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    Re: Economic Mathematical Equation which is constantly decreasing.

    Quote Originally Posted by Drongoski View Post
    Just a wild guess - does the long term value settle at 500? Must be 500.
    Yes.

    Quote Originally Posted by ProdigyInspired View Post
    I don't know where this goes so I'll just put this here. It's a question regarding a decreasing value over time.

    If you have an equation B = (1 - R) A + I,

    where A is the value of stock in one period, and B is the value of stock in a next period,
    R is a depreciation rate of 2%, and I is an investment value added upon every period.

    Would the value ever become constant?

    E.G. the Initial value of capital stock is 200, and I = 10, R = 0.02

    where you get the first period formula to be (1 - 0.02)*200 + 10 = 206
    second period (1-0.02)*206 + 10 = 211.88
    third period (1-0.02)*211.88 + 10 = 217.6424

    The difference between each period becomes smaller just by inspecting that 211.88 - 206 > 217.6424 - 211.88.

    However, since it is a depreciation rate, the value becomes continuously smaller. So, does the stock eventually become constant? I assumed it shouldn't, but the answers differ.

    This is a macroeconomics class so I'm unsure if they take mathematical theories as seriously. The answers say that it does, and perhaps this is due to the disregard of dollar value if it reaches a point where it is too miniscule to consider.
    "Would the value ever become constant?"

    Yes, it asymptotically approaches a constant.



    Last edited by InteGrand; 25 Aug 2017 at 5:13 AM.
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