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

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

dpflanBest 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

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

LeoMessiBest 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

dpflanBest 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

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

LeoMessiBest 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

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

dpflanBest ResponseYou've already chosen the best response.3
yeah, I think you get the idea, try out some more problems
 2 years ago
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