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 = K2/5L3/5
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Answer:
Marginal product: marginal product of input refers to the additional output produced by that input when an additional unit of that input is employed.
(a).
To find the marginal products of inputs let us partially derivate the production function with respect to the inputs.
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- 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?Suppose the productionfunction is given by Q = 5K + 3L. What is the average product of capital when10 units of capital and 10 units of labor are employed? 5 8 3 30Suppose the production function is given by O = 5K - 3L What is the average product of capital when 10 units of capital and 10 units of labor are employed? 8 30
- Q(K, L) = 4K²L2 Type your answers in all of the blanks and submit The production function of good x is as follow: a. What is the marginal production of capital with 16 labor and 4 capital? Type your answer her b. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 10 labors and 400 units of capital. Slope = Type your answer her (absolute value.) c. If we increase the amount of labor we use in our production process from 10 to 1000 units, how much change in capital is needed for us to stay on the same isoquant? Change in K= Type your answer here (Actual value, negative if decrease and positive if increase) d. Is diminishing return a characteristic of this production function? For labor? (yes/no) Type your answer her ;For Capital (yes/no)? Type your answer hereConsider 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?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) =
- Suppose a soap-manufacturing production process is described by the following equation: Y = a + b log K + с log L Where, Y= Output (number of soaps produced) K=Capital L=Labor a, b and c are constants Suppose 0<a<1, 0< b<1 a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital (MPK) in the production of soap b. Is MPL diminishing, increasing or constant as L increases? c. Is MPK diminishing, increasing or constant as K increases?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.
- A firm can manufacture a product according to the production function: Q = F(K, L) = K3/4L1/4.a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. (Enter your responses rounded to three decimal places)(Part of A): What is the average product of labor when the firm uses 256 units of labor?Answer:b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. (The second response is the exponent on L in the expression. Enter your responses rounded to two decimal places).MPL = × L ^ Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. (Enter your responses rounded to three decimal places).MPL when L = 16: MPL when L = 81: c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at…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) =Assume the production function is given as Y = 4X + 3X ² - 0.2X 3 %3D Where Y is amount of output produced and X is levels of input used, Then, A. Calculate the APx, MPx and Ep B. Determine the value of X that maximize APx and MPx and calculate Ep when APy and MPx maximum value of X X
