Consider first the following strict liability rule: irrespective of the level of care taken by firms 1 and 2, if there is an accident, firm 1 will be liable for a pre-specified fraction s1 of the victim's losses, and firm 2 will be liable for a pre-specified fraction s2 of the victim's losses, where s1 + s2 = 1.
Assuming that the firms cannot collude, does this rule induce either of the firms to take an efficient level of care? To answer this, we first need to work out the efficient levels of care. Expected total social costs are:
Social costs are minimised when, for both firms, the marginal cost of an extra unit of care is equal to the marginal benefit. So the efficient levels of care, x* and xf, must satisfy the following two marginal conditions:
We will assume that x* and xf are unique, so that: for all (x1,x2) Ф (xf,xf).
Now consider the strict liability rule. Firm 1's expected costs are: and firm 2's expected costs are:
Firms choose x1 and x2 non-cooperatively, to minimise their own individual expected costs. The Nash equilibrium levels of care, (x°, x°) satisfy:
for firm 1, and:
To investigate the efficiency properties of this Nash equilibrium, suppose that x° = x*. Then firm 1 would face a private marginal benefit that is less than the social marginal benefit of its actions, since
by virtue of the fact that s1 < 1. Therefore, firm 1 would choose x° < x*. Hence x1* cannot be a best response to x2*. Similarly, x2* cannot be a best response to x*. These two facts suggest that (x*, x*) is not a Nash equilibrium under this legal rule, so (x°,x°) Ф (x*,x*) and so:
That is, (x°, x°) is not efficient.
The gains from merging under strict liability
Note that if firms were to merge, collude or act cooperatively, then they would jointly choose x1 and x2 to minimise their joint expected costs under the legal rule. Their joint costs under strict liability are:
since s1 + s2 = 1. Therefore, if the firms were to merge, the legal rule would effectively induce them to internalise all of the social costs of their actions. The gains from the merger would simply be:
Another way of stating this result is that a rule of strict liability provides significant incentives for firms to merge. Alternatively, for mergers not to occur under this rule, transaction costs must be at least as large as the gains in (10.1).