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 rom to grow 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 as follows: sA(90sAsM), or 90sAsA2sAsM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 902sAsM. Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should 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 plosterse function (assuming his total benefit is given by sM(90sAsM), and thus he responds to alex in the same way alex responds to him), with 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. When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of If, instead, each farmer plants 20 seeds, each farmer will get a benefit of Suppose Alex discovers a new method of fertilizing his seeds, such that his best-response function is now given by sA=500.5(sM). Use the green line (triangle symbol) to plot Alex's new best-response function after this change on the original graph. As a result of this change, the optimal number of seeds for Alex to plant , and the optimal quantity for Mitch to plant 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 rom to grow 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 as follows: sA(90sAsM), or 90sAsA2sAsM. The marginal benefit to Alex from planting additional seeds is, therefore, equal to 902sAsM. Assuming the marginal cost of planting is zero, the best-response function that gives the optimal number of seeds Alex should 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 plosterse function (assuming his total benefit is given by sM(90sAsM), and thus he responds to alex in the same way alex responds to him), with 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. When each farmer plants the Nash equilibrium number of seeds, each farmer gets a benefit of If, instead, each farmer plants 20 seeds, each farmer will get a benefit of Suppose Alex discovers a new method of fertilizing his seeds, such that his best-response function is now given by sA=500.5(sM). Use the green line (triangle symbol) to plot Alex's new best-response function after this change on the original graph. As a result of this change, the optimal number of seeds for Alex to plant , and the optimal quantity for Mitch to plant
