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First fundamental proposition of marginal reasoning

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A program for patrolling a U.S region for illicit activities using aircraft is being assessed. An associated estimate of the total economic benefits of the interdiction vs. the number of patrol aircraft is shown below. Apply the first fundamental proposition of marginal reasoning to determine the optimal number of patrol aircraft.

# Patrol Aircraft Benefit ($M)
1-> 1995
2-> 3458
3-> 4522
4-> 5320
5-> 5852
6-> 6155
7-> 6358
8-> 6517
9-> 6610
10-> 6677

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Solution Summary

This solution demonstrates how to use marginal analysis to determine the optimal number of patrol aircraft to deploy against illicit activities.

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The first fundamental proposition of marginal reasoning is that any action whose marginal benefit exceeds its marginal cost should be taken. In this example, the marginal benefit is the change in total benefit from adding one more patrol aircraft. The marginal cost is the cost of putting one more aircraft in the air. The attached spreadsheet illustrates several possible scenarios.
The optimal number of aircraft is the largest number at which marginal benefit exceeds marginal cost. If the cost of one aircraft is 800, the maximum net benefit is 2122, achieved with 3 aircraft. If the cost of one aircraft is 500, the maximum net benefit is 3352, achieved with 5 aircraft. If the cost of one aircraft is 300, the maximum net benefit is 4355, achieved with 6 aircraft.

Aircraft Total Benefit Marginal Benefit ...

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