Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (A) and the amount of capital used (C) by the following function: S-20 L0 C07 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 tans of steel at minimum enst. If your answer is sere, enter Min 40 120 s.t. 20 O0. c. S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an intial >o and C0 Do not round intermediate calculatione. Round vour answers to the nearest whole number 2991 2318 Cost S 397448 lide feedback

Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (A) and the amount of capital used (C) by the following function: S-20 L0 C07 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 tans of steel at minimum enst. If your answer is sere, enter Min 40 120 s.t. 20 O0. c. S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an intial >o and C0 Do not round intermediate calculatione. Round vour answers to the nearest whole number 2991 2318 Cost S 397448 lide feedback

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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

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I’m not sure logically if a production function can simultaneously exhibit CRTS and Economies of scale? And I’m also unsure how to draw the isoquants based on the isocost lines I derived ?
A company produces commercials. A 2-minute commercial, for example, needs exactly 5 minutes of filming and 8 minutes of editing. Let x1 denote the minutes of filming and x2 denote the minutes of editing. a) Write down the production function and state whether it has increasing, constant, or decreasing returns to scale b) Suppose that filming costs $45 per minute and editing costs $10 per minute. To produce a 5-minute commercial, how many minutes of filming and how many minutes of editing is needed to minimize cost? c) Suppose that filming costs w1 per minute and editing costs w2 per minute. Let y denote the length (in minutes) of commericals produced. derive the conditional factor demand functions x1(w1,w2,y) and x2(w1,w2,y) and its cost function c(w1,w2,y)
Marginal cost is the one more unit of a good and opportunity cost of producing increases as production O price that must be paid to consume; decreases as consumption O opportunity cost of producing: decreases as production O price that must be paid to consume; increases as consumption of the good increases.
I am having trouble understanding how to answer the last part of this question. I am providing the work I did on the remainder of the problem to provide context, but the multiple choice question is what I'm stuck on. If you see an error in my previous work that would cause me to have trouble with this last question, please let me know and I will fix it. Thank you!
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Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
Please answer fast please arjent help please
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.
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13. Suppose you have a production technology given by f(x1, x2) = min{2x₁, x2} and you are producing at the point where x₁ = 10 and x₂ = 20. (a) Explain in words what we mean (generally) by the ‘marginal product' of an input in production. (b) For the production technology in this question and the initial point x₁ = 10 and x2 = 20, what is the marginal product of a small increase in input 1? (c) Suppose input 2 increases and you are now at the initial point x₁ = 10 and x2 = 30. Relative to your answer in part (b), does the marginal product of input 1 decrease, increase, or stay constant? Explain briefly.
QUESTION 1 For the production function Qs = K0.6L0.7 find the returns to scale, recall that a doubling of inputs that doulbes output is a CONSTANT returns to scale = 1.0 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…