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(60 - SA - SM), or (SA60 - SA² SMSA). The marginal benefit to Alex from planting additional seeds is, therefore, equal to (60 - 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
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(60 - SA - SM), or (SA60 - SA² SMSA). The marginal benefit to Alex from planting additional seeds is, therefore, equal to (60 - 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
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter12: Environmental Protection And Negative Externalities
Section: Chapter Questions
Problem 10SCQ: Suppose a city releases 16 million gallons of raw sewage into a nearby lake. Table 12.8 shows the...
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