Figure 16.3 shows that an emissions fee can be chosen that attains the same level of pollution

Question:

Figure 16.3 shows that an emissions fee can be chosen that attains the same level of pollution reduction as does direct control. Explain why firms would make the same choices under either control method. Would this equivalence necessarily hold if government regulators did not know the true marginal costs of emissions control?
Figure 16.3
Optimal Pollution Abatement