Why is it possible that negative externalities lead to inefficient overproduction?
With negative externalities, private marginal cost distorts resource allocation by understating true social cost.
In the graph note that true marginal social cost is above private marginal cost. This is pretty much the definition of a negative externality. Some cost related to production or consumption of the good involves a cost that is not internalized by the market -- such as pollution. The truly efficient outcome in this graph would be an equilibrium at P() and Q(), which is the point where the marginal social cost equals the marginal social benefit (which is measured by the demand curve).
Unfortunately, because this market does not internalize all social costs, the market equilibrium is at P(e) and Q(e). However, at every quantity above Q(*), this market has inefficiently high production and consumption, because the marginal social cost is above the marginal social benefit for each additional unit of the good. At the market equilibrium quantity, Q(e), the true marginal social cost is P(High), not P(e), but the externalities prevent the private market from responding to the proper incentives for efficient resource allocation. In this case, production is too high.
For positive externalities, private markets provide inefficiently low production, because positive externalities have a marginal social benefit that is higher than the marginal benefit measured by the private demand curve.