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Math Help - could you please correct these two problems?

  1. #1
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    could you please correct these two problems?

    marginal cost for a determined product is MC=3x+50 and the production of 20 units results in a total cost of $2,000, what is the total cost function?

    Integrate MC to get
    3/2 + 50x + c

    Substitute to find c:
    2(400) + 2(20) + c = 2,000

    800+40 = 2,000
    c= 1,160
    3/2 + 50x + 1,160

    2- If consumption is $5.8 billion when disposable income is 0, and if the marginal propensity to consume is dc/dy = 1/√(y+9) +0.8


    (in billions of dollars) find the national consumption function.


    If "y" is disposable income [not national] then:
    C = (y)
    MPC = ∂C/∂y
    C = ∫ [∂C/∂y] ∂y = ∫ [0.8+1/√(y+9)] ∂y = X + 0.8y + 2√(9+y)
    C [billions] = X + 0.8y + 2√(9+y)

    C[y=0] =5.8 billion
    5.8 = X + 0.80 + 2√(9+0)
    5.8 = X+6
    X = 5.8-6 = -0.2

    C [billions] = 0.8y + 2√(9+y) - 0.2

    thank you.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by jhonwashington View Post
    marginal cost for a determined product is MC=3x+50 and the production of 20 units results in a total cost of $2,000, what is the total cost function?

    Integrate MC to get
    1) 3/2 + 50x + c

    Substitute to find c:
    2) 2(400) + 2(20) + c = 2,000
    800+40 = 2,000
    c= 1,160

    3) 3/2 + 50x + 1,160
    I numbered your equations for convenience.

    1) Where did the 'x' go?
    1) Should this be an equation or function defintion? It's just an expression.

    2) Where did the '3' go?
    2) Why is the '2' in the numerator?
    2) You did square '20', but there is nothing in your equation #1 to indicate that you should have done that.
    2) The equation did come back!

    3) Where did the 'x' go?
    3) Where did the equation go again?

    Use very careful and consistent notation.
    Last edited by TKHunny; December 13th 2009 at 03:25 AM.
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