1)Q=K+L+KL
For determining returns to scale, we need to multiply the constant with both the inputs and the output.
If f(xK,xL)> xf(K,L) then it is increasing returns to scale.
If f(xK,xL)< xf(K,L), then decreasing returns to scale
If f(xK,xL)= xf(K,L)., then constant returns to scale
f(xK,xL)= xK+xL+x2KL> x(K+L+KL)=xQ
Hence this would be the case of increasing returns to scale
2) Q=2K2+3L2
f(xK,xL)= 2(xK)2+3(xL)2= x2(f(K,L)>xf(K,L)= xQ
Hence it is also giving increasing returns to scale
3)Q=KL
f(XK,xL)= (xK)(xL)= x2KL> xQ
This also displays increasing returns to scale
4)min(3K,2L)
f(xK,xL)= min(3xK,2xL)= xmin(3K,2L)= Qx
This displays constant returns to scale.
Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:...
Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale: Q = 10K0.75L0.25 Q = (K0.75L0.25)2 Q = K 0.75L0.75 Q = K 0.25L0.25 Q = K + L + KL Q = 2K2 + 3L2 Q = KL Q = min(3K, 2L)
3. Determine whether each of the following production functions below displays constant, increasing, or decreasing returns to scale: (a) Q = 10(K0.75 0.252 (b) Q = 2K2 +312 (c) Q=K+L+KL (d) Q = min(3K, 2L) (e) Q = 10K0:250.25
For each of the following production functions, determine whether returns to scale are decreasing , constant, or increasing when capital and labor inputs are increased from K = L = 1 to K = L = 2 Q = 25K0.5 L0.5 Q = 2K + 3L + 4KL Q = 100 + 3K + 2L
5. Determine whether each of the following production functions displays constant, increasing, or decreasing returns to scale. Show workings. a) Q= 10K 0.75, 0.25 b) Q = 2K+ + 3L c) Q = (Kº75 0.25 2 d) Q=K+L+KL
Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale. L, K, and H are inputs and Q is the output in each production function. Initially, set each input = 100 and determine the output. Then increase each input by 2% and determine the corresponding output to see if constant, increasing, or decreasing returns to scale occur. (a) Q = 0.5L + 2K + 40H (b) Q = 3L + 10K +...
Briefly show whether the following production functions exhibit increasing, decreasing, or constant returns to scale: Y = K2/3 + L2/3 Y = min {2L+K, 2K+L} Y = 20*L1/5*K4/5
2) Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale (or none of these) a) Y=K+L^1/3 b) Y= aln(L) + bIn(k)
Do the following production functions exhibit increasing, constant, or decreasing returns to scale? (show your work to illustrate the answer), where Q is quantity of output, K is the amount of capital used, and L is the amount of labor used. a) Q=K^1/3 L^2/3 b) Q=7K^1/5 L^3/5 c) Q=4K+8L d) Q=3k^5 L^4
1. Below are production functions that turn capital (K) and labor (L) into output. For each of the production functions below, state and PROVE whether it is Constant/Increasing/or Decreasing Returns to scale. That is, you want to see how production changes when you increase all inputs (KL) by a factor of a, where a > 1: (3 points each) (a) F(K.L) = (b) F(KL)= min (4K, 2L + 20 (c) F(K,L) = 5K+ 10L
Given the following production functions, determine if they exhibit increasing, decreasing, or constant returns to scale. Be sure to mathematically prove your answer and show your work. Y = K + L Y = 4(K + L)0.5 Y= 10(KL0.5)