1. Consider the production functions for good X and good Y: X = K? +L ; Y = 20/KL A. Show and discuss which production function(s) exhibit(s) diminishing marginal productivity of labor and capital. (5 pts)
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- production-function-Q=100k^0.5L^0.5.During the last production of tyres .The inputs were 100 and 25 for capital and labor respectively. What is the marginal product of capital and marginal product of labor based on stated rates.Question Establish input demand function in case of multiple variable inputs3. Consider the following production functions along with their corresponding marginal product of labor function. I. Q = 15KL II. Q = 2K0.4L0.6 III. Q = 8K + L. a. In each case, what happens to the marginal product of labor as the firm uses more labor? b. In each case, what happens to the marginal product of labor as the firm uses more capital?
- Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Fish (pounds) 0 0 1 10 2 18 3 24 4 28 5 30 What is the marginal product of the 4th hour spent fishing? Question 8 options: 8 4 6 27 which of the following are examples of fixed-proportions production functions?
- 1.Suppose a chair manufacturer is producing in the short run (with its existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:Number of Workers Number ofChairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to becomenegative.1. Explain production function and illustrate examples. 2. Explain marginal product of input in a production process. 3. Illustrate example of getting the slope of the production function curve.Production function Q=100K^0.5L^0.5 .During the last production of Tyres the following inputs of 100 and 25 for capital and labor were used.What is the marginal product of capital and marginal product of labor based on the stated inputs.
- 4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…Explain the properties of production function? Given a production function of this nature AX1a X2b=Y, determine the Marginal Rate of Technical Substitution.