Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.' K0.9 %3D Furthemore, the cost function for a facility is given by the function:C(L, K) = 200L + 100K Suppose the monthly production goal of this facility is to produce 8,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L- (Show your answer is exactly 1 decimal place) Units of Capital K - (Show your answer is exactly 1 decimal place) %3D Also, what is the minimal cost to produce 8,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 8,000 units is S Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate A to get a relationship between L and K. 3. Round your values for L and K to one decimal place (tenths).
Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.' K0.9 %3D Furthemore, the cost function for a facility is given by the function:C(L, K) = 200L + 100K Suppose the monthly production goal of this facility is to produce 8,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L- (Show your answer is exactly 1 decimal place) Units of Capital K - (Show your answer is exactly 1 decimal place) %3D Also, what is the minimal cost to produce 8,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 8,000 units is S Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate A to get a relationship between L and K. 3. Round your values for L and K to one decimal place (tenths).
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
Related questions
Question
Transcribed Image Text:Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.' K0.9
Furthemore, the cost function for a facility is given by the function:C(L, K) = 200L + 100K
Suppose the monthly production goal of this facility is to produce 8,000 items. In this problem, we will
assume L represents units of labor invested and K represents units of capital invested, and that you can
invest in tenths of units for each of these. What allocation of labor and capital will minimize total
production Costs?
Units of Labor L =
(Show your answer is exactly 1 decimal place)
Units of CapitalK =
(Show your answer is exactly 1 decimal place)
Also, what is the minimal cost to produce 8,000 units? (Use your rounded values for L and K from above to
answer this question.)
The minimal cost to produce 8,000 units is $
Hint:
1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function.
2. When finding a relationship between L and K in your system of equations, remember that you will
want to eliminate A to get a relationship between L and K.
3. Round your values for L and K to one decimal place (tenths).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning