A firm produces its output using the following production function: f(x₁, x₂) = √√√x₁ - 1 + 4x2 where x₁ denotes the amount of factor 1 and x2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market price of factor 2 is $10. (a) To produce y = 8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost.
A firm produces its output using the following production function: f(x₁, x₂) = √√√x₁ - 1 + 4x2 where x₁ denotes the amount of factor 1 and x2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market price of factor 2 is $10. (a) To produce y = 8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
(b) Now, suppose the price of factor 2 has increased to $40, and the price of factor 1 is still $4. To produce ?=1 unit of output with the lowest cost, how much of factor 1 and factor 2 should the firm use? Find the optimal bundle of inputs and calculate the minimal cost.
Transcribed Image Text:A firm produces its output using the following production function:
f(x1, x₂) = √√√x₁ −1+ 4x₂
where x₁ denotes the amount of factor 1 and X2 denotes the amount of factor 2. The market price of factor 1 is $4, and the market
price of factor 2 is $10.
(a) To produce y =
8 units of output with the lowest cost, how much factor 1 and factor 2 should the firm use? Find the optimal
bundle of inputs and calculate the minimal cost.
Transcribed Image Text:(c) Suppose the firm utilizes a new technology to produce output. According to the new production function, factors 1 and 2 must
be combined in fixed proportions. To produce 2 units of output, the firm needs to combine 3 units of factor 1 with a unit of factor
2.
If the price of factor 1 is $2 a unit and the price of factor 2 is $4 a unit, draw an isocost representing the lowest cost of producing 2
units of output.
Expert Solution
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 5 steps with 2 images
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
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 (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