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Strict liability

A rule of strict liability is also inefficient for the same reasons as discussed in the no liability case. Firms in industry v do not take any care. Their marginal costs are c + wxv, and so firms choose xv = xsvL = 0. The competitive equilibrium price in industry v is therefore P^ = c. The competitive quantity is Qf = u'- (c) > Q*.

The marginal costs in industry i are now:

To minimise these costs, firms choose a level of care which obeys:

Again, since Qf1 > Q*, the marginal benefit of care by firms in industry v is higher, even if firms in industry i chose the efficient level of care. All of the other results discussed above go through, with the role of each industry simply reversed. Moreover, under our special symmetry assumptions the welfare loss under strict liability is identical to the welfare loss under no liability.

A negligence rule

Suppose that each firm in industry i is held liable for harm to firms in industry v if they fail to meet some due standard of care. Suppose that this due standard is set at the efficient level of care, zi = x*. Consider industry v first. Suppose that each firm in industry v believes that all firms in industry i will choose the efficient level of care, and that the industry as a whole will also produce the efficient quantity. Then the profit of the representative firm in industry v is:

Each firm in industry v would then choose the efficient level of care. The first-order condition with respect to Qv satisfies:

and so industry v will produce the efficient quantity.

Consider, on the other hand, firms in industry i. Suppose that they believe that each firm in industry v will supply the efficient levels of care and output. Then each firm's profit is:

Firms can escape liability and minimise costs by choosing to meet the due standard, so that xi = x*. Then each firm's profit is:

The zero profit condition then implies that:

But this implies that QfR > Q*. Going back to industry v, this means that the original conjecture of the firms in that industry about firms in industry i could not have been correct. In other words, the negligence rule cannot produce efficient outcomes.

As in the analysis of the unilateral care model in a market setting, this conclusion once again suggests that traditional legal rules such as strict liability rule or a negligence rule are not efficient once a market setting is introduced. Under a negligence rule, firms in industry i can avoid liability by meeting the due standard of care, and this lowers marginal and average costs, forcing prices below efficient levels. The industry produces too much, even though all firms individually might have an incentive to take the appropriate per unit level of care.

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