Can someone pls help with this homework question?

Consider the market for a good called Chico that is sold by a monopolist that faces a downward sloping demand curve. The production of Chico causes a negative externality of $1 per unit produced. In addition, all consumes are subject to biases in making decisions such that they perceive their marginal benefit of consumption as being higher than it truly is. Specifically, their perceived marginal benefit is $2 more than their true marginal benefit.

a. True or False: Any corrective tax on Chico will lead to a second-best outcome (i.e., some deadweight loss will remain).

b. What is the optimal tax rate on Chico? (Less than $3; Exactly $3; More than $3;It is impossible to tell whether any of the listed answers are correct without further information)