Suppose that the following production fnction is given: Q-4KL For the above production function, find the elasticity of substitution? Find the Retuns to Scale.
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A: Given: MPK=42K-1/2=2K-1/2MPL=42L-1/2=2L-1/2MRTSLK=MPLMPKMRTSLK=2L-1/22K-1/2MRTSLK=KL Formula for…
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Q: The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L =…
A: (Note: Since, the question has multiple parts, the first three have been solved. Please resubmit the…
Q: Suppose we are given a production function: q = [alº + (1 – a)kP]P a. Please show that MP;= (1–…
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can you do part b, c, d and e i can hse 4 questions for it
- Consider a Cobb-Douglas production function:f(l, k) = Alα k1−α,where A is the total factor of productivity (a constant greater than 1), 0 < α < 1, lrepresentslabor, and k represents capital. The following sub-questions will guide you through showing thatthe elasticity of substitution is constant.a) Find the marginal product of labor. Verify that this production function exhibits diminishingmarginal productivity of labor. b) Find the marginal product of capital. Verify that this production function exhibits diminishingmarginal productivity of capital. c) Find the marginal rate of technical substitution. Write your answer as MRT S = . . . d) In part (C), you should’ve found the MRTS as a function of the input ratio, kl. Take theabsolute value of both sides and solve for the input ratio, so that the expression gives theinput ratio as a function of MRTS (i.e. kl = . . .). Take the log of both sides, then take thederivative with respect to the log of MRTS. Is the elasticity of…Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit 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?Consider the following production functions, to be used in this week’s assignment:(A) F(L, K) = 20L^2 + 20K^2(B) F(L, K) = [L^1/2 + K^1/2]^2For each of production functions (A) and (B) given above, do the following steps.(i) Calculate the marginal product of labor MPL(L, K) = ∂F(L, K) / ∂L.(ii) Calculate the marginal product of capital MPK(L, K) = ∂F(L, K) / ∂K.(iii) Calculate the absolute value of the technical rate of substitution as the ratio of marginal products andsimplify as far as possible: |TRS(L, K)| = MPL(L, K) / MPK(L, K). PLEASE SHOW ALL WORK
- please sir solve these 3 questions 33- If an increase in the price of one good leads to a fall in the quantity demanded of other than these goods are complementry good A- True B- False 34- the production function is a purely technical relationship between input and output A- True B- False 35- marginal proudact is defined as the change in TP resulting from the employment of an additional unit of a varibal factor: A- True B- FalseQ5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.a. In which direction will the substitution effect change the firm’s employment and capital s tock?b. In which direction will the scale effect change the firm’s employment and capital stock?c. Can we say conclusively whether the firm will use more or less labor? More or less c apital?
- The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt)a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if L=12 and K=20 .b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and 30. c) Determine factor intensity and returns to scale of this production function. d) Prove that the elasticity of labour is 0.8 and elasticity of capital is 1.8 .The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt)a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if L=12 and K=20 b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and 30. c) Determine factor intensity and returns to scale of this production function. d) Prove that the elasticity of labour is 0.8 and elasticity of capital is 1.8 a) According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). Tohire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In the study of…The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt)a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if L=12 and K=20 b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and 30. c) Determine factor intensity and returns to scale of this production function. d) Prove that the elasticity of labour is 0.8 and elasticity of capital is 1.8 a)According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In the study of…
- Given a constant elasticity of substitution (CES) production function as follows:y = [a1x1ρ + a2x2ρ]1/ρ 1. Find the marginal rate of technical substitution (MRTS)2. Derive the expression for Elasticity of SubstitutionSuppose a firm has a production function with two inputs, capital (K) and labor (L). The production function takes the form: Q = L2K2. Further, let the wage be given by w, the rental rate of capital be given by r, and suppose that the firm wishes to produce Q0 units of output. Determine the elasticity of substitution for this production function. Explain your answer. Determine the returns to scale for the production function. Solve for the long-run optimal input demand functions for capital and labor as a function of exogenous variables only. Derive an expression for long-run total cost as a function of the exogenous variables. Let w=16, r=25, and Q0 = 10,000. Solve for the long-run cost-minimizing input combination.Suppose a huge scientific breakthrough doubles the output that an additional houra huge scientific breakthrough doubles the output that an additional hour of U.S. labor can produceof U.S. labor can produce. As a result, there is ______ in the U.S. production function. A. an upward shiftan upward shift B. no shiftno shift C. a downward shifta downward shift There is ______ in the U.S. demand for labor and ______ in the U.S. supply of labor. A. a decreasea decrease; a decreasea decrease B. an increasean increase; a decreasea decrease C. no changeno change; an increasean increase D. an increasean increase; no changeno change