A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2. Explain briefly why the profit function is given by π(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22 Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.
A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2. Explain briefly why the profit function is given by π(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22 Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2.
Explain briefly why the profit function is given by
π(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22
Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.
![A firm manufactures two goods labelled 1 and 2. It sells Q; items of good i for a fixed
price per unit of p. The total cost of producing good i is c,Q}.
Explain briefly why the profit function is given by
T(Q,, Q2) = P,Q, + p,Q2 – c,Qi –
Find the values of Q, and Q, which maximise T and verify that the second-order condi-
tions for a maximum are satisfied. Find an expression for the maximum profit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fede84d0a-7492-4d8c-aee1-553d23268c48%2F8c7a1174-b529-4489-b1c4-b6e58f61bf39%2Fcho31oj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A firm manufactures two goods labelled 1 and 2. It sells Q; items of good i for a fixed
price per unit of p. The total cost of producing good i is c,Q}.
Explain briefly why the profit function is given by
T(Q,, Q2) = P,Q, + p,Q2 – c,Qi –
Find the values of Q, and Q, which maximise T and verify that the second-order condi-
tions for a maximum are satisfied. Find an expression for the maximum profit.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
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)](https://www.bartleby.com/isbn_cover_images/9781305585126/9781305585126_smallCoverImage.gif)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Managerial Economics: A Problem Solving Approach](https://www.bartleby.com/isbn_cover_images/9781337106665/9781337106665_smallCoverImage.gif)
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-…](https://www.bartleby.com/isbn_cover_images/9781259290619/9781259290619_smallCoverImage.gif)
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education