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2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...
SHOW ALL WORK!!! 2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for m...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
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 =...
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. Given a Cobb-Douglas production function Q = 25020602. 1) Derive expressions for the average and...
4. Given a Cobb-Douglas production function Q = 25020602. 1) Derive expressions for the average and marginal products of labour and capital; 2) Derive the partial elasticity w.t.r (with respect to) labour and capital.
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where...
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where Yis equal to total production, K is equal to the capital input of production and L is equal to the labour input of production. The constant, A, represents technology in the economy and a the elasticity of capital. function exhibits, decreasing, increasing or constant returns to scale. [ 10 Marks A2. Carefully derive the marginal product of labour and explain how this might be...
Please show all your work step by step 1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (...
Please show all your work step by step
1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (a) Write an expression for the marginal product of xy at the point (21,22). (b) Holding a fixed, for small increases in 31, will the marginal product of increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in x2? (d) Does an increase in the amount of...
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant...
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant when Q=4,000 16.000.000 (Property format your expression using the tools in the palette. Hover over fools to see keyboard shortcuts. Eg, a fraction can be created with the character.) The marginal rate of technical substitution (MRTS) when Q ) 4,000 and L - 100 (with capital measured on the vertical axis and labor measured on the horizontal 2 MRTS - (Enter a numeric response...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
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. Given a Cobb-Douglas production function Q = 25020602. 1) Derive expressions for the average and marginal products of labour and capital; 2) Derive the partial elasticity w.t.r (with respect to) labour and capital.
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where Yis equal to total production, K is equal to the capital input of production and L is equal to the labour input of production. The constant, A, represents technology in the economy and a the elasticity of capital. function exhibits, decreasing, increasing or constant returns to scale. [ 10 Marks A2. Carefully derive the marginal product of labour and explain how this might be...
Please show all your work step by step
1. Suppose the production function is Cobb-Douglas and f(x1,22) = x122. (a) Write an expression for the marginal product of xy at the point (21,22). (b) Holding a fixed, for small increases in 31, will the marginal product of increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in x2? (d) Does an increase in the amount of...
Consider the following Cobb Douglas production function, where =0.5 Q=KLP Find the equation for the isoquant when Q=4,000 16.000.000 (Property format your expression using the tools in the palette. Hover over fools to see keyboard shortcuts. Eg, a fraction can be created with the character.) The marginal rate of technical substitution (MRTS) when Q ) 4,000 and L - 100 (with capital measured on the vertical axis and labor measured on the horizontal 2 MRTS - (Enter a numeric response...
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