Assume the Backwoods Shoe Company hires three inputs: labor (L), capital (K), and land (A) to produce shoes (X). Which of the following conditions must be met so that the firm is using the optimal, or least costly, combination of inputs? OMPLIPL MPK/PK = MPA/PA O MPL = MPK = MPA = 1/PX O MPL = MPK = MPA O PL = PK = PA
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- What is the difference between a fixed input and a variable input?Sam Malone is considering renovating the bar stools at Cheers.The production function for new bar stools is given byq = 0.1k 0.2l0.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stoollathes used during the week, and l represents the number ofworker hours employed during the period. Sam would like toprovide 10 new bar stools, and he has allocated a budget of$10,000 for the project.a. Sam reasons that because bar stool lathes and skilled barstool workers both cost the same amount ($50 per hour),he might as well hire these two inputs in equal amounts.If Sam proceeds in this way, how much of each input willhe hire and how much will the renovation project cost?b. Norm (who knows something about bar stools) arguesthat once again Sam has forgotten his microeconomics.He asserts that Sam should choose quantities of inputs sothat their marginal (not average) productivities are equal.If Sam opts for this plan instead, how much of…Suppose a firm is planning to replace a labor intensive production process with an automated robot production line. Calculate the marginal rate of technical substitution (MRTS) using the following information. Labor Intensive Production: 24 workers / 3 machines Automated Robot Production: 10 workers / 30 machines Assume both production process can produce the same level of output.
- 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?Suppose that aKC = 5, capital used to produce one yard of cloth. aLC = 8, labor used to produce one yard of cloth aKF = 4. capital used to produce one calorie of food aLF = 6. labor used to produce one calorie of food. Which of the following is True? a. Cloth is labor intensive. b. Food is labor intensive. c. Both food and cloth are labor intensive. d. Both food and cloth are capital intensive.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?
- Consider 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?Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is $20 per unit. Complete the following table, and then answer the accompanying questions. (1) (2) (3) (4) 5 6 L K Q MPL P VMPK 0 5 0 1 5 10 2 5 30 3 5 60 4 5 80 5 5 90 6 5 95 7 5 95 8 5 90 9 5 80 10 5 60 11 5 30 b. Which inputs are fixed inputs? Which are the variable inputs?c. How much are your fixed costs?According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In thestudy of production process and markets where capital is procured, suppose that Mitsubishi determine that its marginal productivity of capital is 0.5 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is US$ 9500. Determine the rate at which Mitsubishi can rent capital and marginal productivity of labour at its new targeted level of output. To minimize…
- If the economy uses inputs efficiently, then (pls select all that applies) Group of answer choices a) MRTS = 1. b) MRTS must be equal to the slope of a firm’s isoquant curve. c) the ratio of input marginal products must be equal to the ratio of input prices. d) the quantity of one output cannot be increased without decreasing the quantity of the other. e) every firm’s MRTS is equal to every consumer’s MRS. f) every firm’s MRTS is equal to the ratio of input prices. g) MRTS = MRT. h) outputs are on PP5 Supposing that a single consumer works for a firm, the quantity of labor input for the firm, N, is identical to the quantity of hours worked by the consumer, h - l. Graph the relationship between output produced, Y on the vertical axis and leisure hours of the consumer, l, on the horizontal axis, which is implied by the production function of the firm. (In Chapter 5, we refer to this relationship as the production possibilities frontier.) What is the slope of the curve you have graphed? PLEASE DO NOT COPY OTHER PEOPLE'S WORK AND GRAPHAnswer the Constrained Optimization: Cobb-Douglas Production Function:3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the 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