Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
LeoMessi
Group Title
What type of returns to scale does the following production function exhibit?
 2 years ago
 2 years ago
LeoMessi Group Title
What type of returns to scale does the following production function exhibit?
 2 years ago
 2 years ago

This Question is Closed

LeoMessi Group TitleBest ResponseYou've already chosen the best response.0
\[q = 10K^{2/3} + L^{1/2}\] K = # machines, L = # labor units.
 2 years ago

dpflan Group TitleBest ResponseYou've already chosen the best response.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

dpflan Group TitleBest ResponseYou've already chosen the best response.3
\[2*F(K,L) versus F(2*K, 2*L)\]
 2 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.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

dpflan Group TitleBest ResponseYou've already chosen the best response.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

LeoMessi Group TitleBest ResponseYou've already chosen the best response.0
yep, so decreasing returns to scale
 2 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.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

LeoMessi Group TitleBest ResponseYou've already chosen the best response.0
cool stuff, thanks man
 2 years ago

dpflan Group TitleBest ResponseYou've already chosen the best response.3
yeah, I think you get the idea, try out some more problems
 2 years ago
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
 Engagement 19 Mad Hatter
 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.