2. Consider a firm with the following production function: Q = 3K2/3L2/3 2a. Calculate the marginal...
2. Consider a firm with the following production function: Q = 3K2/3L2/3
2a. Calculate the marginal product of labor. Show all work.
2b. Is the marginal product of labor increasing, decreasing or constant? Explain how you know.
2c. Calculate the output elasticity of labor. Show all work.
2d. Does the production process for this firm exhibit increasing returns to scale, decreasing returns to scale or constant returns to scale? Explain how you know.
Homework Answers
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2. Consider a firm with the following production function: Q =
3K2/3L2/3
2a. Calculate the marginal...
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...
Consider the following production function: Q = 55⋅K2/3L4/3 A. Determine whether this production function has increasing,...
Consider the following production function: Q = 55⋅K2/3L4/3 A. Determine whether this production function has increasing, decreasing, or constant returns to scale. Explain and show your work. B. Does this production function obey the law of diminishing marginal product in labor? Explain and show your work.
Question 6 For the production function Q = 3L2 + K2, returns to scale: Is constant....
Question 6 For the production function Q = 3L2 + K2, returns to scale: Is constant. Is increasing Can be increasing, decreasing, or constant depending on the values of Land K. is decreasing
3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ???...
3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ??? = 1.8? −0.7? 0.6 and ??? = 3.6? 0.3? −0.4 . a. In the short run assume that capital is fixed at ? = 10. Derive formulas for the short-run Total Product (TP), Average Product (APL), and Marginal Product (MPL). Graph these three functions. b. In the long run, capital is not fixed. Graph the isoquant for ? = 6. Identify and label three...
A firm's production function is Q = 70L0.6 K0:3. Its marginal product of labor is thus...
A firm's production function is Q = 70L0.6 K0:3. Its marginal product of labor is thus MP2 = 42L-0.4 0.3 and its marginal product of capital is MPK = 21L0.6 K-0.7. a. What returns to scale does this production function exhibit: constant, increasing, or decreasing? Show mathematically. b. Suppose the wage rate is $12 and the rental rate for capital is $48. Show that the firm is not minimizing cost when it employs 40 workers (L) per day and 15...
the second question In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4)...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
For the following rice production function: Q = 80 ( K 0.6 L 0.4) Beginning with...
For the following rice production function: Q = 80 ( K 0.6 L 0.4) Beginning with K=5 and L=37, find out if the marginal product of both K and L is decreasing. Show your work. Does the production function exhibit increasing, decreasing, or constant returns to scale? Show your work. Why does it matter to know about what you found in a. and b. above?
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...
A firm has a production function q = KL, where q is the quantity of output,...
A firm has a production function q = KL, where q is the quantity of output, K is the amount of capital and L is the amount of labor. a) Does this production function exhibit increasing, decreasing or constant returns to scale? b) Does the long-run cost function exhibit economies of scale or diseconomies of scale? c) Is the LR Average Cost curve increasing or decreasing with q?
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%?
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...
Question 6 For the production function Q = 3L2 + K2, returns to scale: Is constant. Is increasing Can be increasing, decreasing, or constant depending on the values of Land K. is decreasing
A firm's production function is Q = 70L0.6 K0:3. Its marginal product of labor is thus MP2 = 42L-0.4 0.3 and its marginal product of capital is MPK = 21L0.6 K-0.7. a. What returns to scale does this production function exhibit: constant, increasing, or decreasing? Show mathematically. b. Suppose the wage rate is $12 and the rental rate for capital is $48. Show that the firm is not minimizing cost when it employs 40 workers (L) per day and 15...
the second question
In Example 6.4 wheat is produced according to the production function: q=100(k0.6 0.4) Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing (Round responses to two decimal places.) The MPK at 5 units of capital is 156.12 The MP at 6 units of capital is 144.02 The MP at 50 units of labor is 8.84 The MP...
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...
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%?
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