A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K.The price of labor, w, is $4 and of capital, r, is $6 per unit.a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it mustemploy to produce Q = 300 units of output.b) How much money is the firm losing by not having the ability to choose its level of capitaloptimally? Hint: Solve the long run cost minimization problem (where the firm canchoose its level of both capital and labor) and compare the cost of the solution with thecost of the inputs used in the answer to part a.

Marginal productivity of capital: It refers to the additional capital that is added for the…

Answered: A plant's production function is Q =…

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

Money cannot serve as a medium of exchange unless it also serves as a store of value. Is this statement true or false? Explain.
12. A firm’s production is represented by the following function: Q = L0.4 K0.6 . The rental rate of capital (r) is $30 and the wage rate (w) is $5. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? How much capital and labor should be used to produce 600 units of output? What is the total cost? What is the short run total cost if output is decreased to 300 units? What would be the optimal choice of capital and labor in the long run in order to produce 300 units of output? What is the long-run total cost? Does this production function exhibit increasing, decreasing, or constant returns to scale? Please answer based on the cost calculations in parts c and d.
Suppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.
A production function for a good Q uses inputs of labor (L) and capital (K) and takes the form Q=LK. The wage is equal to $20 and the rental rate of capital is equal to $80. The firm has to produce a target qo. What is the equation for the firm's long-run total cost curve?
I need help on this question
imagine your firm has total cost function C = 2q3 – q2 + 40q + 60. Suppose it operates with level of production q = 9. What is your firm’s total cost?
The production function has the following form q= K + 2L where q is output, K is capital input and L is labor input. If the prices of inputs are w=5 and v=2 what is the cost minimizing (or efficient) combination of inputs to produce 6 units of output?
Economics A firm has the production function q = K0.25L0.25 , where K is capital, L is labor, and q is output. The price of capital is v = 4 and the price of labor is w = 4. [You may need this result: if Yα = Z. Then Y = Z1/α]. (i) Derive the firm’s short-run cost function if capital is fixed at K = 16. (ii) Derive the firm’s long-run cost function. (iii) Someone claims that the firm’s
A company has a production function Q = (K)0.5 + L. For this production function MP, = 1 and MPK = 0.5(K)-0.5. The firm faces w=$50 and r= $1. Keeping r =1, the price of labor, w, must fall to less than $ in order for the firm to use a positive amount of capital to produce 10 units, or the output Q must increase to over units for the firm to use a positive amount of capital, at w=$50.
A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function: f (L , K) = 6L1/3K1/6 If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.
Suppose you are the production manager of a firm that has a production function: Q = (K )(L^0.5) where Q represents the firm’s level of output, K is the number of units of capital you utilize, and L is the number of units of labour you hire. The rental rate of a unit of capital is given by r = $100, and the wage rate for a unit of labour is given by w = $10. The firm operates in a competitive market where its output can be sold for $100 per unit. (a) Suppose the firm is operating in the short run, with its capital fixed at K = 1. What level of Q will maximize its profits? (b) Now suppose that in the long run, the firm can set its capital to be either K=1 or K=2. What would you recommend in order to maximize profit?
Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in.

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