Extending the unilateral care model to a market setting: Liability rules in competitive markets
In most discussions of the unilateral care model, market exchanges are kept in the background. However, the goal of this book is to put markets front and centre. Therefore, this section extends the unilateral model to a market framework.
Consider a perfectly competitive market for a good, and suppose that the production of the good causes external harm to those who do not consume the good (the case where the good causes harm to consumers or purchasers of the good is dealt with in the next chapter). Consumer utility is equal to u(Q). Suppose that there are n identical firms (where n is determined endogenously in the long run), each with a total cost function of C(q). The efficiency conditions and the long-run equilibrium outcome were discussed in Chapter 1.
In contrast to the situation examined in Chapter 1, now suppose that production of the good causes total expected harm of nqH( xt), where q is the quantity produced by each firm, xi is the level of care taken by each firm, and H(xi) is the expected harm per unit of the good produced. Finally, let each firm's per unit cost of care be equal to w. Welfare is given by the difference between benefits and costs:
Welfare maximisation now requires three conditions. First, for a given number of (identical) firms, it must not be possible to increase welfare by having each firm produce more. This means that:
This equation states that the marginal consumption benefits from consuming the last unit of the good must equal the full marginal costs of consumption, where those costs now include the marginal expected harm that occurs as a result of producing the good, as well as the cost of care. In contrast, if the good was harmless, the efficiency condition with respect to q would be u'(nq) = C'(q*). Thus, when the good causes harm, the efficiency condition with respect to q implies that overall consumption and production should be less than it would if the good was not harmful.
Second, for a given quantity, it must not be possible to increase welfare by changing the number of firms. This means that:
This condition states that the marginal consumption benefits must also equal average expected costs, where these costs again include the expected harm that occurs as a result of the good being produced. Since the consumer equates marginal benefits with price P, welfare maximisation again requires price = marginal cost = average cost.
Finally, efficiency requires that it must not be possible to increase welfare by altering the level of care:
This states that for the last unit of care that is provided, the reduction in expected harm (which is the marginal benefit of care) should be equal to the marginal cost providing that last unit of care.