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Math Help - marginal propencity to consume

  1. #1
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    marginal propencity to consume

    The consumption function is given by where is the total national income and the total national consumption, both expressed in billions of dollars.
    The marginal propensity to consume is defined as the rate of change of consumption with respect to income:


    The marginal propensity to consume for the consumption function C given above when equals??? (billions of dollars)/(one billion of dollars of change of the income).
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  2. #2
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    Quote Originally Posted by pourcarlos View Post
    The consumption function is given by where is the total national income and the total national consumption, both expressed in billions of dollars.
    The marginal propensity to consume is defined as the rate of change of consumption with respect to income:


    The marginal propensity to consume for the consumption function C given above when equals??? (billions of dollars)/(one billion of dollars of change of the income).
    C = 6 \cdot \frac{2 \cdot I^{\frac{3}{2}} + 5}{I+10}

    \frac{dC}{dI} = 6 \cdot \frac{(I+10)(3 \cdot I^{\frac{1}{2}}) - (2 \cdot I^{\frac{3}{2}} + 5)(1)}{(I+10)^2}

    sub in 100 for I and evaluate
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  3. #3
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    so therefore

    6 ( 16500 - 1000005 / 12100 )

    which gives me -487.6884298

    however, it is telling me that this answer is wrong.....
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  4. #4
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    Quote Originally Posted by pourcarlos View Post
    so therefore

    6 ( 16500 - 1000005 / 12100 )

    which gives me -487.6884298

    however, it is telling me that this answer is wrong.....
    "it" is telling you the truth ... you did not evaluate the value of the derivative correctly.

    put away the calculator and try it by hand.
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  5. #5
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    im sorry, but i still dont seem to understand.....

    could you please help explain the correct way to plug in 100 for I to figure out the marginal propensity to consume
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  6. #6
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    Quote Originally Posted by pourcarlos View Post
    im sorry, but i still dont seem to understand.....

    could you please help explain the correct way to plug in 100 for I to figure out the marginal propensity to consume
    You have been told what to do. Your trouble is that you haven't done the basic arithmetic properly. Substitute I = 100. Do the calculation more carefully!!
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