1. For each of the following production functions,(a) F(L, K) = LK³(b) F(L, K) = L+3K(c) F(L, K) = (min{L, K})³i. Sketch a representative isoquant.ii. Calculate the marginal product for each input, and indicate whether each marginal productis diminishing, constant, or increasing.iii. Calculate the marginal rate of technical substitution for each function.iv. Also indicate whether the function exhibits constant, increasing, or diminishing returns toscale.

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Answered: 1. For each of the following production…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Table: Production Function for Soybeans Quantity of labor (workers) Quantity of soybeans (bushels) 1 25 45 3 60 4 70 75 Look at the table Production Function for Soybeans. Assume that the fixed input, capital, is 10 acres of land and a tractor, which have a combined cost of $150 per day. The cost of labor is $100 per worker per day. The total cost of producing 70 bushels of soybeans is: None of these options is correct. $1,024. $550. $250. $400.
Solve the exercise with a production function with diminishing returns: In this case, production increases as workers are added, but it increases less and less. a) Calculate the amount of production for each worker and add it to the table, taking into account the production function K 10 1 9. 2 8 3 7 4 6. 4 7 3 8 2 9 10 b) Explain why the production function exhibits diminishing returns to scale.
Consider the following production functions• F(L,K) = LK^3 For each for these production functions: (a) Draw the corresponding graph (b) Calculate the marginal product of labor and capital (c) Discuss if each marginal product is diminishing, constant or increasing (d) Calculate the marginal rate of technical substitution (e) Calculate if the function exhibits constant, increasing, or diminishing returns to scale*Just solve d and e
Please see the attached photo, and Only solve part d, e, and f
Consider a short run production function q = cL+ K where the value for c = 3, using L units of labour and K units of capital. a) Compute the marginal product of labour. b) Does the production function exhibit decreasing, increasing or constant returns to scale? With a diagram. Note: The writing is clear and abbreviations are not allowed.
A firm has the production function f(x, y) = x®y0.3, where a>0.7. This firm has Select one: a. decreasing returns to scale and increasing marginal product for factor x and y. b. None of the above. c. increasing returns to scale and diminishing marginal product of factor x. d. constant returns to scale. e. decreasing returns to scale and diminishing marginal products for factor y.
Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a) Type of returns to scale and the marginal products of labor and capital. b) The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c) The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d) The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.
If the production function is f(x1,x2) = x1,x2.a. Show whether this production function exhibits increasing, decreasing or constant returns to scale.b. Show whether the average cost is increasing, decreasing or constant.
In the following production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. What is the marginal product of input 1?
Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.
1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
Q = a,H + a,L +a,H² +a¸L² +a‚HL , where a,>0 2. Q = aH " L, where a, a, y> 0 a) Derive the equation of the relevant Isoquant. b) Find out whether the production function is well behaved.

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