If no one owns the lake and the government levies a pollution tax, what is the tax

Question:

If no one owns the lake and the government levies a pollution tax, what is the tax that achieves the efficient outcome?

When factories produce pesticide, they also create waste, which they dump into a lake on the outskirts of the town. The marginal external cost of the waste is equal to the marginal private cost of producing the pesticide (that is, the marginal social cost of producing the pesticide is double the marginal private cost).

FIGURE 17.5 Problems 13 to 16 150 125 100 75 50 25 10 30 40 50 Quantity (tons per week) Price (dollars per ton) 20