Extending the unilateral care model to other market situations: Liability rules in imperfectly competitive markets

This section reconsiders some of problems analysed in previous sections, but we now assume that markets are not perfectly competitive.

Monopoly

Strict liability

Consider a firm which is a monopolist in the market. Suppose that it produces Q units. The demand curve is still:

Under a rule of strict liability, the firm's profits are:

The monopolist can minimise its costs by choosing the efficient level of care, so x_i = x* d Therefore, its profits are:

The first-order condition is:

or:

where ? is the elasticity of demand and ? < -1 for a profit-maximising monopolist.

One question of interest here is the degree of 'forward cost shifting', which refers to the degree to which consumer prices change in response to a change in the costs of care or changes in the liability rule. Overshifting is said to occur if the market price rises by more than the change in costs. Under perfect competition the forward shifting of the costs of care and external harm onto consumers in the short run depends on the elasticity of demand and supply curves. As shown earlier in this chapter, in the long run (assuming that the long-run supply curve is flat), the full amount of the increase in producer costs is usually passed on to consumers. Furthermore, under perfect competition unless the supply curve is downward sloping, the costs of care and harm under a strict liability rule can never be 'overshifted' in the sense that consumer prices rise by more than these costs.

The situation under monopoly is not as straightforward, because the monopolist can choose his price level. Consider the monopolist's first-order condition for profit maximisation in the presence of a strict liability rule. Let Z = w_tx* + H(x*) be the per unit costs of care and harm at the optimal level of care. Then:

Suppose that Z increases by a small amount. Then and so or:

Therefore, the change in the monopolist's price is:

d-? P

where E = is the elasticity of the elasticity of demand with respect

dP ?

to price - that is, E tells us how the elasticity of demand changes as we move along the demand curve. The formula tells us that there will be overshifting of the costs of care and expected harm under certain conditions. For example, if the elasticity of demand is constant and if marginal costs are constant (so that C" = 0), then E = 0 and we have:

so that price rises by more than the increase in the sum of the costs of care and the costs of harm that are imposed on the firm under a rule of strict liability.

Intuitively, if the elasticity of demand does not increase much as we move up the demand curve, consumption is not becoming too sensitive to price changes as the price increases. Thus, the monopolist can afford to pass on more of the change in costs under a strict liability rule. Thus, even if marginal production costs are constant, it can easily happen that P'( Z) > 1. Note also that forward cost shifting is less likely if marginal costs are increasing, since then the denominator becomes more negative. Since the numerator is also negative, this means that the absolute value of the right hand side becomes smaller, and so forward cost-shifting is less likely.

Negligence rule

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

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

The first-order condition is: or:

Under a negligence rule, the firm will produce more and will charge a lower price than under a rule of strict liability. Again, however, if the marginal cost of care w_i rises, there may be cost overshifting by a monopolist.

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:

The first-order condition is:

or:

Under a no liability rule, the firm will produce more and will charge a lower price than under a rule of strict liability or a negligence rule.