Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal productsassociated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1,and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output.Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantityof capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q.b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average costcurve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of materials depends on the quantity Q. e) Find the equation of the short-run total cost curve whencapital is fixed at a quantity of 50 units (i.e., K 50) and graph it along with the long-run total cost curve.f)Findtheequationoftheassociatedshort-runaverage cost curve.

(a) : 1. Cost-minimizing quantity of labor (L*): MPL = w KM = 5 L* = 5 / K2. Cost-minimizing…

Answered: Consider a production function of three…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

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.
Please see the attached photo, and Only solve part d, e, and f
A firm's production function is q = 26x^0.33y^0.67, where x and y are the amounts of factors x and y that the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y, the ratio in which the firm will use factors x and y is closest to. A. x/y = 0.08 B. x/y = 0.25 C. x/y = 0.5 D. x/y = 2.4
Suppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?
Suppose that the production function for Hannah and Sam's home remodeling business is Q = F(L,K) Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ .revised jrl 08-11-2011
Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
In the following production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. What is the marginal product of input 1?
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?
Suppose a firm uses a single input to produce a single output according to a production function f(x) = 10√x where x is the number of units of input. The output initially sells for £120 per unit. The input costs £20 per unit. A change in the market causes the product price to increase from £120 per unit to £200 per unit, all else equal. How does this change in product price affect the firm's profit maximizing level of profits? a. Profits increase by £16,000 Ob. Profits do not change Profits increase by £8,000 d. None of the other answers is correct Profits increase by £9,000 f. Profits increase by £18,000 g. Profits increase by £50,000 h. Profits increase by £32,000 C. e.
Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.
Question # 1: Majeda wrote the following answer on her microeconomics examination: “Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So, when all inputs are doubled, output must be less than double." How would you grade Majeda's answer? Question # 2: Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed-portions production function, what would the firm's expansion path be? Question # 3: Suppose that a firm's production function is q = 30√L. In the short run, where there are fixed costs of $2,200, and labor is the variable input whose cost is $6,300 per units. What is the total cost of producing 20 units of output?
Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $ b. What is their long-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $

SEE MORE QUESTIONS

Recommended textbooks for you

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

Principles of Economics (MindTap Course List)

Economics

ISBN:

9781305585126

Author:

N. Gregory Mankiw

Publisher:

Cengage Learning

Managerial Economics: A Problem Solving Approach

Economics

ISBN:

9781337106665

Author:

Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:

Cengage Learning

Managerial Economics & Business Strategy (Mcgraw-…

Economics

ISBN:

9781259290619

Author:

Michael Baye, Jeff Prince

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS