The change in the optimal capital-labor ration if both inputs are perfect complements in production and both their prices increase by an identical percentage. Assume the total cost before and after the change in input prices remains the same.
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explain your anwer with clearly and fully labeled graphs.
The change in the optimal capital-labor ration if both inputs are perfect complements in
production and both their prices increase by an identical percentage. Assume the total
cost before and after the change in input prices remains the same.
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- 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 if it the firm decides to triple both the amount of labor and capital?The change in the optimal capital-labor ration if both inputs are perfect complements inproduction and both their prices increase by an identical percentage. Assume the totalcost before and after the change in input prices remains the same.Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimized
- 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?Answer 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 faces21. Find the marginal rate of technical substitution for the Cobb-Douglas production function Q = AL^ak^B. * (B/a) " L/K O (a/B) * K/L
- Please no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.19/ With a production function of if r = $4 and w = $4, how many units of capital and labor will be optimally utilized? All K and no L. All L and no K. Equal amounts of K and L. A combination of K and L not represented above.Fill in the missing parts in the following tables to illustrate the behavior of production and costs in the short-run; then determine the optimal level of production according to the number of inputs you are intending to use. Output Units Land Square Meters Capital Egyptian Pounds Labor Units 0 1000 1600 2100 2500 2600 Output FC VC TC MCL MPL AVC AFC ATC 0 1000 1600 2100 2500 2600 -Hint Consider land and capital as fixed factors, while labor units as variable factors. The cost of land is L.E20 per square meter. The interest rate on capital is 10%. The average wages per unit of labor is L.E1500.
- Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correctFrom the following production functions 1. Q= a1H + a2L + a3H2 + a4 L2 + a5HL, where ai> 0 2. Q = aH@ Ly, where a, @, y > 0 a. Derive the equation of the relevant isoquant. b. Find out whether the production function is well behaved. c. Examine whether the isoquant is well behaved and therefore represents the behaviour of a rational production. d. Derive equation which describes MRTS of 9ne factor. e. For each equation examine whether the production is homogeneous and if so, what is the degree of homogeneity. Is the equation characterized by IRTS, DRTS or CRTS.The number of souvenir coffee mugs (in hundreds) that Ace Novelty can produce monthly is given by the production function where x denotes the amount of labor utilized (measured in thousands of work-hours per month) and y denotes the expenditure on capital investment (in thousands of dollars per month). Find the marginal productivities if 10,000 work-hours per month are utilized and a capital investment of $5000/month is made. Interpret your results.
