Homework Help is Here – Start Your Trial Now!
Business
Economics
The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital c. and labor. It has the form f(L,C) = c_L" C² where co, c₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c₁ = 5, c₁ = 0.25, and c = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $80,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. 25L +75C 80000 L,C>0 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 L3,000 and 0 C1,000. Round your answers to the nearest integer when necessary.) units at (L,C) = (x)

The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital c. and labor. It has the form f(L,C) = c_L" C² where co, c₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c₁ = 5, c₁ = 0.25, and c = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $80,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. 25L +75C 80000 L,C>0 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 L3,000 and 0 C1,000. Round your answers to the nearest integer when necessary.) units at (L,C) = (x)

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
See similar textbooks
icon
Related questions
Question
The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital c. and labor. It has the form f(L,C) = c_L" C² where co, c₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c₁ = 5, c₁ = 0.25, and c = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $80,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. 25L +75C 80000 L,C>0 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 L3,000 and 0 C1,000. Round your answers to the nearest integer when necessary.) units at (L,C) = (x)
Transcribed Image Text:The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital c. and labor. It has the form f(L,C) = c_L" C² where co, c₁, and c₂ are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c₁ = 5, c₁ = 0.25, and c = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $80,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. 25L +75C 80000 L,C>0 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 L3,000 and 0 C1,000. Round your answers to the nearest integer when necessary.) units at (L,C) = (x)
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS