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] 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

Principles of Economics 2e
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter2: Choice In A World Of Scarcity
Section: Chapter Questions
Problem 11RQ: What does a production possibilities frontier illustrate?
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] 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
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
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