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5) Consider the production function q = 41.5 + 5K. a. Starting from the input combination...
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...
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.
2. Consider a firm producing pizza with production function q = KL, that faces input prices...
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
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.
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function:...
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function: q=8LK + 5L2 - L. Assume capital is fixed at K = 25. (a) At what level of employment does the marginal product of labor equal zero? (Hint: To answer this question mathematically, you will have to use the quadratic formula.) (b) Illustrate the above production function for values of L € [1,30] (Note: Your graph does not necessarily have to be precise at...
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...
(a) Consider the production function, q = 100K2L1.5 Calculate the marginal product of labor, MPL, and...
(a) Consider the production function, q = 100K2L1.5 Calculate the marginal product of labor, MPL, and the marginal product of capital,MPK. (c) Suppose that in the short run, the level of capital is fixed at K = 15. Write out the total product of labor curve. What is the marginal product of labor when L = 100? (d) Now consider two input combinations, (K = 5, L = 100) and (K = 20, L = 25). Which of the two...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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.
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%?
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function: q=8LK + 5L2 - L. Assume capital is fixed at K = 25. (a) At what level of employment does the marginal product of labor equal zero? (Hint: To answer this question mathematically, you will have to use the quadratic formula.) (b) Illustrate the above production function for values of L € [1,30] (Note: Your graph does not necessarily have to be precise at...
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...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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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