In the case of a production function with TFP A and constant returns to scale, which...
In the case of a production function with TFP A and constant returns to scale, which of the following, all other things held constant, does not lead to a lower marginal product of capital (MPK)?
- A. None of the choices is correct.
- B. Higher I
- C. Higher depreciation rate
- D. Lower A
- E. Lower L
Homework Answers
E. Lower L
Lower the level of input higher is the productivity. So when L or labor decreases its productivity increases leading to increase in marginal product.
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In the case of a production function with TFP A and constant
returns to scale, which...
Returns to scale. A production function has constant returns to scale with
Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z > 0: F(z · K, z ·L) = zF(K, L), For example, for a production function with constant returns to scale, doubling the amount of each input (i.e., setting z = 2) will lead to a doubling of the output from the production function. A production function has increasing returns to scale if for any z >1: F(z ·...
A production function exhibits constant returns to scale if: Doubling all inputs delivers exactly twice the...
A production function exhibits constant returns to scale if: Doubling all inputs delivers exactly twice the output. Doubling all inputs delivers exactly more than twice the output. Doubling all inputs delivers exactly less than twice the output. none of the above The marginal product of capital (MPK) is: The additional unit of output that is produced when both labor and capital are increased by one unit. The additional output that is produced when there is technological improvement. The additional output...
1. For a constant returns to scale production function: a. marginal costs are constant but the...
1. For a constant returns to scale production function: a. marginal costs are constant but the average cost curve as a U-shape b. both average and marginal costs are constant c. marginal cost has a U-shape, average costs are constant d. both average and marginal cost curves are U-shaped 2. The production function q = 10K +50L exhibits: a. increasing returns to scale b. decreasing returns to scale c. constant returns to scale d. none of the above
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...
All other things constant, which of the following will make MPK rise and MPL fall? A....
All other things constant, which of the following will make MPK rise and MPL fall? A. Higher K B. Higher A. C. Higher L D. None of the choices is correct. E. Lower L
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...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...
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%?
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%?
The production function -k0 4710.5. Oa exhibits constant returns to scale and diminishing marginal productivities for...
The production function -k0 4710.5. Oa exhibits constant returns to scale and diminishing marginal productivities for k and 1. Ob. exhibits constant returns to scale and constant marginal productivities for k and 1. c.exhibits diminishing returns to scale and diminishing marginal productivities for k and 1. o d. exhibits diminishing returns to scale and constant marginal productivities for k and I.
Consider production function f(l, k) = l2 + k2 (a) Evaluate the returns to scale. (b)...
Consider production function f(l, k) = l2 + k2 (a) Evaluate the returns to scale. (b) Calculate the marginal product of labor and the marginal product of capital. (c) Calculate the MRTS. (d) Does the production function exhibit diminishing MRTS? (e) Plot the isoquant for production level q = 1. Hint: Notice that the input mixes (1; 0) and (0; 1) are on this isoquant.
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. 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...
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%?
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%?
The production function -k0 4710.5. Oa exhibits constant returns to scale and diminishing marginal productivities for k and 1. Ob. exhibits constant returns to scale and constant marginal productivities for k and 1. c.exhibits diminishing returns to scale and diminishing marginal productivities for k and 1. o d. exhibits diminishing returns to scale and constant marginal productivities for k and I.
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