Pollution Abatement

Q:

Wondered if you might clarify the chart on p. 5 of Tony's hand-out notes for Class 22. I don't understand the "source of last ton" column, nor the relationship between the Total Costs of the individual plants and the Combined Least Cost.

A:

I will try my best to clarify. If your goal is to clean up tons of pollution at least cost, as in this problem, you can think of this as answering the questions: For whom is it cheapest to clean up the first ton? Okay, have them clean up one ton...now, given that, for whom is it cheapest to clean up the second ton? Okay, have them clean up a ton, and so on.

In this example, it is cheapest to have A clean up the first ton. Given that, the relevant costs for cleaning up the second ton are the marginal costs of the first ton for B (since it hasn't cleaned up at all yet) and the marginal cost of the second ton for A (since it has already cleaned up one ton). A is still cheaper, so it cleans up the second ton and the process repeats. Eventually it becomes cheaper for B to start cleaning up. Tou can get the total cost by just adding up the marginal costs for each ton based on which plant cleans it up.