Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

LeoMessi

What type of returns to scale does the following production function exhibit?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. LeoMessi
    Best Response
    You've already chosen the best response.
    Medals 0

    \[q = 10K^{2/3} + L^{1/2}\] K = # machines, L = # labor units.

    • 2 years ago
  2. dpflan
    Best Response
    You've already chosen the best response.
    Medals 3

    OK, there are (i.) decreasing returns, (ii.) increasing returns, and (iii.) constant returns. Your function is one of K and L so \[q=f(K,L)\]. if we increase K and L by 2, is the quantity produced greater than, less than, or equal to 2 * the production function?

    • 2 years ago
  3. dpflan
    Best Response
    You've already chosen the best response.
    Medals 3

    \[2*F(K,L) versus F(2*K, 2*L)\]

    • 2 years ago
  4. LeoMessi
    Best Response
    You've already chosen the best response.
    Medals 0

    \[F(2*K, 2*L) = 10*(2K)^{2/3} + (2*L)^{1/2} = 10 * 2^{2/3} * K + 2^{1/2} * L\] and \[2*F(K,L) = 2 *(10 * K^{2/3} + L^{1/2}\]

    • 2 years ago
  5. dpflan
    Best Response
    You've already chosen the best response.
    Medals 3

    right, to easily compare the 2 factor out a 2 in \[F(2*K, 2*L)\] \[(2) * (10 * 2^{-1/3} * K + 2^{-1/2} * L)\] given the exponents, that is obviously less than \[2*(10*2^{2/3}*K + 2^{1/2}*L)\]

    • 2 years ago
  6. LeoMessi
    Best Response
    You've already chosen the best response.
    Medals 0

    yep, so decreasing returns to scale

    • 2 years ago
  7. LeoMessi
    Best Response
    You've already chosen the best response.
    Medals 0

    right on, so it seems safe to assume that when the exponents are less than 1, decreasing returns are most likely, and when the exponents are 1 then constant, and if greater than 1 than increasing

    • 2 years ago
  8. LeoMessi
    Best Response
    You've already chosen the best response.
    Medals 0

    cool stuff, thanks man

    • 2 years ago
  9. dpflan
    Best Response
    You've already chosen the best response.
    Medals 3

    yeah, I think you get the idea, try out some more problems

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.