Results 1 to 7 of 7

Math Help - marginal analysis

  1. #1
    Junior Member
    Joined
    Mar 2006
    Posts
    40

    marginal analysis

    At a factory, the daily output is Q(K) = 600K^1/2 units, where K is the capital investment measured in units of $1,000. The current capital investment is $900,000. Estimate the effect that an additional capital investment of $800 will have on the daily output.

    I'm not sure I am setting this up correctly.

    Q'(K) = 300K^-1/2
    K=900,000/1,000
    Change in K=0.8

    Is the problem set up by finding Q'(900) and Q'(900.8) and then subtracting the two totals?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Close but not completely right. You can use the slope of the output graph to estimate how much each additional unit(s) will cost close to 900. The more units you add/subtract the worse the estimate gets. This is where you use Q'(K).

    Let's think of linearization.

    L(x)=f'(a)(x-a)+f(a)

    So our "a" value is 900, and our "x" value, our estimate, is 900.8. Take it from here.
    Last edited by Jameson; August 9th 2006 at 03:03 PM. Reason: error
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2006
    Posts
    40

    Need explaination please

    You put the x value at 908. I thought it would be 900.8. I rationalized it as 900,000/1,000 = 900, then if you add 800 it would be 900,800/1,000 = 900.8. Please help me see your way...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Ooops. My mistake. Didn't convert. You are correct. 900.8
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2006
    Posts
    40

    Then - here I go...

    L(x) =2/3(900.8-900)+270,000
    L(x) = 2/3(.8) +270,000
    L(x) = 1.6/3 +270,000
    L(x) =270,000.533

    I still don't feel confident with this answer. Any chance it's right?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by becky
    At a factory, the daily output is Q(K) = 600K^1/2 units, where K is the capital investment measured in units of $1,000. The current capital investment is $900,000. Estimate the effect that an additional capital investment of $800 will have on the daily output.

    I'm not sure I am setting this up correctly.

    Q'(K) = 300K^-1/2
    K=900,000/1,000
    Change in K=0.8

    Is the problem set up by finding Q'(900) and Q'(900.8) and then subtracting the two totals?
    <br />
\Delta Q\approx \frac{dQ}{dK} \Delta K= 300K^{-1/2} \Delta K<br />

    So here K=900, \Delta K=0.8, hence:

    <br />
\Delta Q\approx  300\times 900^{-1/2}\times 0.8=8 \mbox{ units}<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Sorry I misread your question a bit. My linearization formula gave you the change plus the original value to give the new estimated value. If you want just the change, use this part of the linearization formula.

    \Delta(x) \approx f'(a)(x-a)

    which is what CaptainBlack told you to do.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. marginal p.d.f
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 23rd 2010, 08:44 AM
  2. Marginal pdf's
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 28th 2009, 11:30 PM
  3. Marginal pdf's
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 4th 2009, 10:20 PM
  4. Marginal revenue and the marginal cost
    Posted in the Business Math Forum
    Replies: 1
    Last Post: November 28th 2008, 05:22 PM
  5. Replies: 3
    Last Post: May 30th 2006, 02:59 AM

Search Tags


/mathhelpforum @mathhelpforum