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- Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3The engineers at Morris Industries obtained the following estimate of the firm's production function: Q = F(K, L) = min {3K, 4L} How much output is produced when 2 units of labor and 5 units of capital are employed?b) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of output
- Consider the production function: Q = 2K + 3L. The MRTSLK is:Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…The engineers at Morris Industries obtained the following estimate of the firm’s production function Q = F ( K, L ) = min { 3K, 4L } How much output is produced when 2 units of labor and 5 units of capital are employed?
- : Suppose that the production functions be like as (A) i) Y = X15 X20.5 ii)Y= X10.5 + X20.5 Find MRTS of these functionsCompute the MRTS for this production function: Y (K,L) = 2K+5L100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
- Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph T PL, APL, and MPt. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (ii) the maximum value of M PL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…12. Which of the following production function shows decreasing returns to scale? (a) f(r) = min{x1, 12}. 1/4 (b) f(z) = xỉ + x}/2 1/4 1/2 (c) f(x) = r1 + xj"x (d) f(x) = VE +a3.A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a) What is the average product of labor, APL, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MPL, when capital is fixed at 36 units? (c) Suppose capital is fixed at 36 units. If the firm can sell its output at a price of $100 per unit of output and can hire labor at $40 per unit of labor, how many units of labor should the firm hire in order to maximize profits?