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S.2.2 Negligence rule

Under a negligence rule where the due standard is set at x*, each firm's profits are:

The firm can again minimise its costs by choosing the efficient level of care, so xt = x*. Therefore, the firm's profits are:

The first-order condition is:

Adding up across all n firms yields:

Or:

Under a negligence rule, each firm will produce more and the market price will be lower than under a rule of strict liability. Again, if the marginal cost of care wi rises, there can be cost overshifting.

A no liability rule

Under a no liability rule, the firm's profits are:

The monopolist can again minimise its costs by choosing to provide no care. Therefore, the firm's profits are:

And we get the usual Cournot outcome. Under a no liability rule, the industry will produce more and will charge a lower price than under a rule of strict liability or a negligence rule.

Discussion and comparison with perfect competition

The usual result in economic theory is that a monopolist or oligopoly that chooses a single price always produces an inefficiently low quantity. This is also true here if we fix the legal rule, and compare outcomes under various market structures: a monopolist facing the same legal rule will always still produce a lower amount than a Cournot industry, which in turn will produce a lower amount than a perfectly competitive industry.

There are two important points to note here, however. First, because firms restrict output under monopoly or imperfect competition, this may be welfare improving relative to the outcome under perfect competition when output may lead to accidental harm. The reason is straightforward: in the previous section we saw that under perfect competition under a negligence rule, even though individual firms chose the efficient level of care, market output is inefficiently high. But under our assumptions a monopolist or oligopolist under a negligence rule also chooses the efficient level of care - but both restrict output. Therefore, with a negligence rule, welfare may be higher under monopoly than under perfect competition - even though in both cases firms choose the efficient level of care.

This is illustrated for the case of monopoly in Figure 4.5.1 below, which assumes constant marginal costs of c > 0 (so that marginal costs are also equal to average costs). Consider a negligence rule with the due standard of care set at x*. Under perfect competition, firms minimise costs by choosing the efficient level of care, and so the market price is equal to c + wx*. The competitive quantity is Q, but the efficient quantity is QNR < Q, where price equals c + wix*+H(x*), which is marginal production costs plus the costs of care per unit, plus the harm per unit.

If the efficient level of care is chosen, the change in welfare as Q changes is:

For a small change in Q, this is the shaded area in Figure 4.5.1. The change in the area is zero at the efficient quantity.

A monopolist facing a negligence rule

Figure 4.5.1 A monopolist facing a negligence rule

Now consider a monopolist facing the same negligence rule. The monopolist chooses a level of output that is less than the level under perfect competition, but chooses the same level of care. This means that welfare may be higher under monopoly. Figure 4.5.1 shows the special case where the monopolist's pursuit of profit induces him to choose exactly the efficient quantity. This happens if the monopolist's profit- maximising price under the negligence rule happens by accident to be equal to c + wix* + H (x*), which is marginal production costs plus the costs of care per unit, plus the harm per unit of output:

This holds if demand for the good is sufficiently elastic at the monopolist's profit-maximising point:

This can also happen with a no liability rule. The monopolist chooses a level of output that is less than the level under perfect competition. Again, this means that welfare must be higher under monopoly. Figure 4.5.2 shows the special case where the monopolist's pursuit of profit again induces him to 'accidentally' choose exactly the efficient quantity. This happens if the monopolist's price happens to be equal to c + wtx* + H (x*), which happens if:

This holds if demand for the good is sufficiently elastic at the monopolist's profit-maximising point:

However, although in this case the efficient quantity is chosen, the efficient level of care is not. The efficiency loss in this case is equal to the (efficient) quantity multiplied by the social cost per unit of the good that is in excess of the optimal social cost:

The second point to note is that the standard result of a monopolist always producing less than the outcome under perfect competition no longer holds if the monopolist faces a different legal rule to that

A monopolist under a no liability rule, producing the efficient quantity

Figure 4.5.2 A monopolist under a no liability rule, producing the efficient quantity

A monopolist under a no liability rule producing an inefficiently high quantity

Figure 4.5.3 A monopolist under a no liability rule producing an inefficiently high quantity

which might prevail under perfect competition. For example, consider a monopolist facing a rule of no liability, and compare this against the efficient outcome. Suppose that the costs of care and harm are very high, relative to production costs. Efficiency requires that the firm internalise these costs and produce a relatively low quantity. However, under a no liability rule, the firm avoids paying these costs, and lower costs boost production - even for a monopolist. As Figure 4.5.3 shows,

it can easily happen that under a no liability rule (or a negligence rule) a monopolist could produce more than the efficient quantity.

 
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