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Homework answers / question archive / Suppose a city releases 16 million gallons of raw sewage into a nearby lake
Suppose a city releases 16 million gallons of raw sewage into a nearby lake. The table below shows the total costs of cleaning up the sewage to different levels, together with the total benefits of doing so. (Benefits include environmental, recreational, health, and industrial benefits.) Using the information in the table, calculate the marginal costs and marginal benefits of reducing sewage emissions for this city. What is the optimal level of sewage for this city?
| Total Cost (in thousands of dollars) | Total Benefits (in thousands of dollars) | |
| 16 million gallons | Current situation | Current situation |
| 12 million gallons | 50 | 800 |
| 8 million gallons | 150 | 1300 |
| 4 million gallons | 500 | 1850 |
| 0 gallons | 1200 | 2000 |
Answer: 4 million gallons
| Total Cost | Total Benefits | Marginal Cost | Marginal Benefit | |
|---|---|---|---|---|
| 16 million gallons | Current situation | Current situation | - | - |
| 12 million gallons | 50 | 800 | 50 | 800 |
| 8 million gallons | 150 | 1300 | 100 | 500 |
| 4 million gallons | 500 | 1850 | 350 | 550 |
| 0 gallons | 1200 | 2000 | 700 | 150 |
Above is the table that is given in the question but with two columns for marginal cost and benefit. The optimal amount of sewage is 4 million gallons because marginal benefit is always greater than marginal cost when decreasing sewage until that point. As long as marginal benefit of an action is greater than marginal cost, then the action should occur. In this case we continue to reduce sewage until marginal benefit is no longer greater than marginal cost.
