anonymous
  • anonymous
What type of returns to scale does the following production function exhibit?
OCW Scholar - Principles of Microeconomics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[q = 10K^{2/3} + L^{1/2}\] K = # machines, L = # labor units.
anonymous
  • anonymous
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?
anonymous
  • anonymous
\[2*F(K,L) versus F(2*K, 2*L)\]

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anonymous
  • anonymous
\[F(2*K, 2*L) = 10*(2K)^{2/3} + (2*L)^{1/2} = 10 * 2^{2/3} * K + 2^{1/2} * L\] and \[2*F(K,L) = 2 *(10 * K^{2/3} + L^{1/2}\]
anonymous
  • anonymous
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 \[2*(10*2^{2/3}*K + 2^{1/2}*L)\]
anonymous
  • anonymous
yep, so decreasing returns to scale
anonymous
  • anonymous
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
anonymous
  • anonymous
cool stuff, thanks man
anonymous
  • anonymous
yeah, I think you get the idea, try out some more problems

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