# Contrast with the Pigouvian approach

The Pigouvian approach to negative externalities is to levy a tax which is equal to the marginal damage, where this is evaluated at the efficient level of activity. Applying this approach to the unilateral model of accidental harm is straightforward. What tax rate induces efficient behaviour? The tax must be designed in such a way as to induce the injurer to take the efficient level of care. Therefore, it must be conditioned on the injurer's actual level of care. So let the injurer's tax bill be *t _{i} *

*=*

*t*

*(*

*x*). The injurer's costs are now:

_{{}

whereas total social costs are *w _{i}x*

_{i}+*H*(

*x*). To induce the injurer to behave efficiently, we simply set

_{{}*t*(

*x*

_{t}) =

*H*(

*x*

_{t}) , so that the injurer chooses

*x*

*with the property that*

_{i}*w*

_{{}=-*H*

*'(*

*x*

_{t}), which is the efficiency condition. The expected revenue from such a tax is simply

*H*(

*x**

*). This is a non-linear tax, which requires knowledge of the entire shape of the expected harm function, but in expected terms is identical to a rule of strict liability.*

_{i}