1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework question from economics

  1. Mar 12, 2015 #1
    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

    Hi, I have already delivered the homework so my reason for asking is because I want to/ need to understand it.

    upload_2015-3-12_17-38-42.png

    I am at question d. I have found the two differential equations.

    They are:

    c° = -1/0,5 * ( f'(k) - 0,04)Ct

    and

    k° = f(k)-0,06kt -Ct

    In equilibrium both c° and k° will be zero so both equations can be set equal to zero.

    But how do you proceede from here, to find k* and c*? Can you set f'(k) = 0,25K^-0,75 + 2 since f(k) = k^0,25 and k(0) = 2?

    If I have explained it too bad I can elaborate. I hope someone can help me:)
     
    Last edited: Mar 12, 2015
  2. jcsd
  3. Mar 12, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The posted images are too small on my screen, and I cannot enlarge them. My eyes are not as good as they once were, so your images are unreadable to me, reading glasses and all. If you post larger images or---better still---type it all out (as per PF standards), then I will be willing to help.
     
  4. Mar 12, 2015 #3
    Thanks. I will post a lager picture tomorrow.
     
  5. Mar 13, 2015 #4
    upload_2015-3-13_14-47-51.png


    I have answered until c),

    question d) is:

    d) Find the equilibrium (k* c*).

    And its here I am struggeling. I have my two equations, and all the needed numbers, so all I want to do is solve the two equations for C and K.
     
    Last edited: Mar 13, 2015
  6. Mar 13, 2015 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If ##c^{o}## means ##dc/dt##, etc., and if your two differential equations are correct (I have not checked) then the answer to your questions is YES. You need ##dc/dt = 0##, so if ##c \neq 0## you need ##f'(k^*) = 0.04##. Thus, you can determine ##k^*##. You also need ##dk/dt = 0##, so ## 0 = f(k^*) - 0.06 k^* - c^*##, so you can determine ##c^*##
     
  7. Mar 14, 2015 #6
    Thank you. I found a mistake in my differential equation. It should be:
    c° = -1/0,5 * ( f'(k) - 0,10)Ct

    So this gives:

    f`(k) = 0,10
    0,25k^-0,75=0,10
    k^-0,75=0,4
    k=0,4^(-1/0,75)
    k*= 3,393
    which again gives

    c*= 3,393^0,25-0,06(3,393)
    c*=1,153

    Thanks again for the help. Would you get the same answer if you inserted ct = f(k) - 0,06kt into the first equation?
     
  8. Mar 14, 2015 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Try it for yourself!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Homework question from economics
Loading...