] Alex and Mitch are two farmers who grow vegetables on common land. Each farmer gets a benefit from the seeds that he plants, but the overall size and quality of the individual vegetables decreases as the number of seeds planted increases (since each vegetable has less room to grow and gets a smaller share of nutrients from the soil). If SA represents the total number of seeds planted by Alex and SM is the total number planted by Mitch, then the total benefit to Alex will be as follows: SA (90-SA-SM), or 90SA SA2-SASM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 90 - 2SA - SM- Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should plant, as a function of the number of seeds Mitch chooses to plant, is represented by • Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total number of seeds he plants on the vertical axis as a function of the total number Mitch plants (horizontal axis). Then, use the orange line (square symbol) to plot Mitch's best-response function (assuming his total benefit is given by SM (90-SA-SM), and thus he responds to Alex in the same way Alex responds to him), with the total number he plants (horizontal axis) as a function of the total number Alex plants (vertical axis). Finally, place the black point (plus symbol) on the graph to indicate the Nash equilibrium number each farmer plants, given the other's equilibrium choice. Note: Dashed drop lines will automatically extend to both axes. SEEDS PLANTED BY ALEX 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 SEEDS PLANTED BY MITCH Alex's BRF Mitch's BRF +. Nash Equilibrium Alex's BRF When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of seeds, each farmer will get a benefit of If, instead, each farmer plants 20
] Alex and Mitch are two farmers who grow vegetables on common land. Each farmer gets a benefit from the seeds that he plants, but the overall size and quality of the individual vegetables decreases as the number of seeds planted increases (since each vegetable has less room to grow and gets a smaller share of nutrients from the soil). If SA represents the total number of seeds planted by Alex and SM is the total number planted by Mitch, then the total benefit to Alex will be as follows: SA (90-SA-SM), or 90SA SA2-SASM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 90 - 2SA - SM- Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should plant, as a function of the number of seeds Mitch chooses to plant, is represented by • Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total number of seeds he plants on the vertical axis as a function of the total number Mitch plants (horizontal axis). Then, use the orange line (square symbol) to plot Mitch's best-response function (assuming his total benefit is given by SM (90-SA-SM), and thus he responds to Alex in the same way Alex responds to him), with the total number he plants (horizontal axis) as a function of the total number Alex plants (vertical axis). Finally, place the black point (plus symbol) on the graph to indicate the Nash equilibrium number each farmer plants, given the other's equilibrium choice. Note: Dashed drop lines will automatically extend to both axes. SEEDS PLANTED BY ALEX 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 SEEDS PLANTED BY MITCH Alex's BRF Mitch's BRF +. Nash Equilibrium Alex's BRF When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of seeds, each farmer will get a benefit of If, instead, each farmer plants 20
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![]
Alex and Mitch are two farmers who grow vegetables on common land. Each farmer gets a benefit from the seeds that he plants, but the overall size
and quality of the individual vegetables decreases as the number of seeds planted increases (since each vegetable has less room to grow and gets a
smaller share of nutrients from the soil).
If SA represents the total number of seeds planted by Alex and SM is the total number planted by Mitch, then the total benefit to Alex will be as
follows: SA (90-SA-SM), or 90SA SA2-SASM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 90 - 2SA - SM-
Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should plant, as a function of
the number of seeds Mitch chooses to plant, is represented by
• Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total number of seeds he plants on the
vertical axis as a function of the total number Mitch plants (horizontal axis). Then, use the orange line (square symbol) to plot Mitch's best-response
function (assuming his total benefit is given by SM (90-SA-SM), and thus he responds to Alex in the same way Alex responds to him), with the total
number he plants (horizontal axis) as a function of the total number Alex plants (vertical axis). Finally, place the black point (plus symbol) on the
graph to indicate the Nash equilibrium number each farmer plants, given the other's equilibrium choice.
Note: Dashed drop lines will automatically extend to both axes.
SEEDS PLANTED BY ALEX
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30 40
50
60
70
80
90
100
SEEDS PLANTED BY MITCH
Alex's BRF
Mitch's BRF
+.
Nash Equilibrium
Alex's BRF
When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of
seeds, each farmer will get a benefit of
If, instead, each farmer plants 20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F978f58bf-51f2-4cdd-a0b9-0346ad3c311f%2F65e17fcc-9126-40ca-bbf5-00761933f5bb%2Fqgzlzta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:]
Alex and Mitch are two farmers who grow vegetables on common land. Each farmer gets a benefit from the seeds that he plants, but the overall size
and quality of the individual vegetables decreases as the number of seeds planted increases (since each vegetable has less room to grow and gets a
smaller share of nutrients from the soil).
If SA represents the total number of seeds planted by Alex and SM is the total number planted by Mitch, then the total benefit to Alex will be as
follows: SA (90-SA-SM), or 90SA SA2-SASM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 90 - 2SA - SM-
Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should plant, as a function of
the number of seeds Mitch chooses to plant, is represented by
• Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total number of seeds he plants on the
vertical axis as a function of the total number Mitch plants (horizontal axis). Then, use the orange line (square symbol) to plot Mitch's best-response
function (assuming his total benefit is given by SM (90-SA-SM), and thus he responds to Alex in the same way Alex responds to him), with the total
number he plants (horizontal axis) as a function of the total number Alex plants (vertical axis). Finally, place the black point (plus symbol) on the
graph to indicate the Nash equilibrium number each farmer plants, given the other's equilibrium choice.
Note: Dashed drop lines will automatically extend to both axes.
SEEDS PLANTED BY ALEX
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30 40
50
60
70
80
90
100
SEEDS PLANTED BY MITCH
Alex's BRF
Mitch's BRF
+.
Nash Equilibrium
Alex's BRF
When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of
seeds, each farmer will get a benefit of
If, instead, each farmer plants 20
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 2 steps with 2 images
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