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1. For the following production functions, find the marginal rate of technical substitu- tion (MRTSLK). Does the produc...
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...
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
1. A production function is given by f(K, L) = L/2+ v K. Given this form,...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
For the production function F(L,K)=(L+K)^2 find whether the firm has constant, increasing or decreasing returns to...
For the production function F(L,K)=(L+K)^2 find whether the firm has constant, increasing or decreasing returns to scale. . A firm has monthly production function F(L,K) = L+√1+K, where L is worker hours per month and K is square feet of manufacturing space. A. Does the firm's technology satisfy the Productive Inputs Principle? B. What is the firm’s MRTSlk at input combination (L, K)? Does the firm’s technology have a declining MRTS? C. Does the firm have increasing, decreasing, or constant...
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...
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?
(c) What is marginal rate of technical substitution? (d) What do we mean by returns to...
(c) What is marginal rate of technical substitution? (d) What do we mean by returns to scale? Give examples of Cobb-Douglas production functions exhibiting increasing, decreasing and constant returns to scale. [A Cobb-Douglas production function takes the following form: Q = AKalpha Lbeta, ; A > 0, Alpha > 0, Beta> 0:
3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of...
3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital (MRTS ) is diminishing, constant, increasing, or none of these. a. Q=LK b. Q=LVK c. Q=L*K13 d. Q = 3L +K e. Q = min{3L, K}
Show transcribed image text 3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital...
Briefly show whether the following production functions exhibit increasing, decreasing, or constant returns to scale: Y...
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
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)...
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...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
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...
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?
3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital (MRTS ) is diminishing, constant, increasing, or none of these. a. Q=LK b. Q=LVK c. Q=L*K13 d. Q = 3L +K e. Q = min{3L, K}
Show transcribed image text 3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital...
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