Whoville Marble Works (WMW) produces Bespoke Marble Kits (BMKs) for discerning marble connoisseurs. To produce their BMKS, WMW uses raw materials, labor and energy, and their production function is given by q=2070.410.25 m 0.35, where
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- What is the difference between a fixed input and a variable input?The Whoville Marble Collective (WMC) makes fancy marbles for picky Whos. WMC's output is given by Q = 20K0.75L0.25, where Q is WMC's annual output (measured in 1000s of marbles), K is their annual capital input and L is their annual labor input. WMC's capital input costs PK = $8000 per unit and their labor input costs PL = $25000 per unit. Assuming that WMC's annual production budget is B = $800,000, their maximum annual output is ... = = 412,891 marbles. 726,085 marbles. 578,634 marbles. = 857,232 marbles.The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt)a) Calculate Marginal Product of Labour (MPL) and Marginal Product of Capital (MPK), if L=12 and K=20 b) Derive the equation for Isoquent and graphically show it by assuming L= 10, 15, 20 25 and 30. c) Determine factor intensity and returns to scale of this production function. d) Prove that the elasticity of labour is 0.8 and elasticity of capital is 1.8 a)According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In the study of…
- 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 production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…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 .
- Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital‑labor decisions. Q = 500L0.6K0.8, where Q = annual output measured in pounds, L = labor measured in person hours, K = capital measured in machine hours. The marginal products of labor and capital are: MPL = 300L-0.4K0.8 ; MPK = 400L0.6K-0.2 Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars. Determine the firm's optimal capital‑labor ratio, given the information above. Show your working. How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm's output. Davy is currently negotiating with a newly organized union. The firm's personnel manager indicates that the wage…I am having trouble finding out the formulas to complete this question: The production function for a firm is q = -0.6L3 + 18L2K + 10L where q is the amount of output, L is the number of labor hours per week, and K the amount of capital. The wage is $100 and the rental rate is $800 per timeperiod. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. You will not be able to solve the total product curve for L as a function of output. So, instead construct a table. Headings: L q(L) APL MPL VC TC AVC AC MC w/APL w/MPL