Suppose that firm uses 3 units of labor (L) with 4 proportion. Which of the following is correct? Inits of capital (K) in The law of diminishing MRTSLK holds and thus Lagrange multiplier method is applicable MRTSLK is not well defined and thus Lagrange multiplier method is applicable The law of diminishing MRTSLK holds and capital and labor are perfect complements. MRTSLK is not well defined and thus Lagrange multiplier method is not applicable
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![Suppose that firm uses 3 units of labor (L) with 4 units of capital (K) in fixed
proportion. Which of the following is correct?
The law of diminishing MRTSLK holds and thus Lagrange multiplier method is applicable
MRTSLK is not well defined and thus Lagrange multiplier method is applicable
The law of diminishing MRTSLK holds and capital and labor are perfect complements.
MRTSLK is not well defined and thus Lagrange multiplier method is not applicable](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd17ceb30-ae45-4cc2-b4bd-b11b3998c402%2Fd9b7d19d-060e-4bb5-89d5-cf707df091a3%2Ffsnrwwb_processed.jpeg&w=3840&q=75)
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- Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used () and the amount of capital used () by the following function: S- 20 L0 C0.7 In this formula L represents the units of labor input and Cthe units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zere, enter "p" Min 40 120 s.t. 20 S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial >oand C0 Do not round intermediate calculations. Round your answers to the nearest whole number 2991 2318 Cost S 397448 ide Feedback
- Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. 2040.30 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. min s.t. S = $ L, C≥ 0 = 55,000 (b) Solve the optimization problem you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5,000 for both L and C before solving. (Round your answers to three decimal places.) at (L, C) =You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
- Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?Consider the following production function: Q = (6L + 3K)¹/2 1. What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital (MPK)? Are they diminishing? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)? 3. What is the TRSL,K? Is the absolute value of TRSLK diminishing in L or K? 4. Are there constant, decreasing, or increasing returns to scale?For each of the following production functions, compute the marginal product of capital (MPK) and the marginal product of capital (MPL). a. Q = 3K0.4 + 4L0.3 b. Q = K²/5[3/5
- Consider the production function: Q = L1/4 K 3/4 Does this production show increasing, decreasing, or constant returns to scale? Show your work. I. II. Derive an expression for the marginal product of labor. Ш. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased. IV. Derive the average product of labor. Explain whether the average product of labor is increasing, decreasing, or constant, as the labor input is increased.Please don't copy ans Economics You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 . a. What are costs as a function of output for each individual factory? b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory? c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions? d. It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay…Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L0.30c0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. Min s.t. = 60,000 L, C 20 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest integer.) $ at (L, C) =
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