Find the slope of each of the production functions, y = f(L). Graph the functions and ...
Find the slope of each of the production functions, y = f(L). Graph the functions and their derivative functions. Give the economic significance of the sign of the slope of the derivative function (i.e. whether the derivative is increasing or decreasing in L)
(a)y = 10L
(b)y = 8L1/3
(c)y = 3L4
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Find the slope of each of the production functions, y = f(L). Graph the functions and ...
1. Below are production functions that turn capital (K) and labor (L) into output. For each...
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 (K.L) by a factor of a, where a > 1: (3 points each) (a) F(KL)=KL (b) F(K,L) = min (4K, 22] + 20 (c) F(K,L) = 5K+10L
1. Below are production functions that turn capital (K) and labor (L) into output. For each...
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
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q =...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
4. Below are production functions that turn capital (K) and labor (L) into output. For each...
4. 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 (K.L) by a factor of a, where a > 1: (4 points each) (a) F(K,L) =KİL (b) F(K,L) = min 4K, 2L] + 20 (c) F(K,L) = 4K +3L 5. For this problem you...
Below are production functions that turn capital (K) and labor (L) into output. For each of...
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 (K,L,(M)) by a factor of α, where α > 1: (4 points each) a) F(K,L) = K^1/3*L^1/3+2K+3 b) F(K,L) = sqr(K^3+L^3) c) F(K,L) = (K^2/4+L^2/4)^2 d) F(K,L,M) = min(K,L)*M
1. Graph the short-run total product curves for each of the following production functions if K...
1. Graph the short-run total product curves for each of the following production functions if K is fixed at Ko 4 (a) Q = F(K, L) = 2K + 3L. (b) Q = F(K, L) = K2L2. (c) In the long run, are the above two production functions characterized by constant returns to scale, increasing returns to scale, or decreasing returns to scale?
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
In Problems 7–12, sketch the graph of the given function f. Find the y-intercept and the...
In Problems 7–12, sketch the graph of the given function f. Find the y-intercept and the horizontal asymptote of the graph. State whether the function is increasing or decreasing. 7. f(x) = -5 + 3 9. f(x) = 3 - ()' 11. f(x) = -1 +er-3
1. Below are production functions that turn capital (K) and labor (L) into output. For cach of th...
1. Below are production functions that turn capital (K) and labor (L) into output. For cach 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 (K,L, (M)) by a factor of a, where a > 1: (3 points each) (a) F(K,L)-KİLİ+2K +3L (b) F(K, L)=min/4K, 2L1+20 (d) F(K,L,M) KL3M
1. Below are production functions that turn capital (K) and...
2. for the function f(x)= x+2 cos x on the interval [0,2pi] a. find the first...
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...
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 (K.L) by a factor of a, where a > 1: (3 points each) (a) F(KL)=KL (b) F(K,L) = min (4K, 22] + 20 (c) F(K,L) = 5K+10L
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
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
4. 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 (K.L) by a factor of a, where a > 1: (4 points each) (a) F(K,L) =KİL (b) F(K,L) = min 4K, 2L] + 20 (c) F(K,L) = 4K +3L 5. For this problem you...
1. Graph the short-run total product curves for each of the following production functions if K is fixed at Ko 4 (a) Q = F(K, L) = 2K + 3L. (b) Q = F(K, L) = K2L2. (c) In the long run, are the above two production functions characterized by constant returns to scale, increasing returns to scale, or decreasing returns to scale?
In Problems 7–12, sketch the graph of the given function f. Find the y-intercept and the horizontal asymptote of the graph. State whether the function is increasing or decreasing. 7. f(x) = -5 + 3 9. f(x) = 3 - ()' 11. f(x) = -1 +er-3
1. Below are production functions that turn capital (K) and labor (L) into output. For cach 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 (K,L, (M)) by a factor of a, where a > 1: (3 points each) (a) F(K,L)-KİLİ+2K +3L (b) F(K, L)=min/4K, 2L1+20 (d) F(K,L,M) KL3M
1. Below are production functions that turn capital (K) and...
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...
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