Under a rule of no liability, firms in industry i do not have to compensate firms in industry v. This rule is inefficient for the same reasons as discussed in the unilateral care model. Firms in industry i do not take any care. Their marginal costs are c + wx, and so to minimise marginal costs firms choose xt = xfL = 0. The competitive equilibrium price in industry i is therefore PNL = c . The competitive quantity in industry i is QN = u,-i (c) > Q*.
On the other hand, marginal costs in industry v are equal to:
To minimise these costs, firms in industry v choose a level of care which obeys:
Since Qnl > Q*, the marginal benefit of care by firms in industry v is higher. This would be the case even if firms in industry i were to choose the efficient level of care. In addition, firms in industry choose an inefficiently low level of care, which further increases the marginal benefit of care for firms in industry v. Therefore, xNL > x*, and H(0,xN) > H(x*,x*), which, together with the fact that xNL > x*, means that the competitive equilibrium price in industry v must be higher than the efficient price:
which also means that QN < Q*. The competitive equilibrium under no liability is illustrated in Figure 5.4.2.
What is the welfare loss from a no-liability rule here? Producers in industry i still earn zero profits, with all price reductions being passed on to
Figure 5.4.2 Competitive equilibrium under a no liability rule consumers. For each additional unit of good i that is consumed, marginal social cost exceeds the price, and since consumers equate marginal benefits with price, it must be the case that the marginal social cost of each additional unit consumed in market i exceeds the social marginal benefit of each unit. Hence we get a welfare loss from overconsumption in market i.
Similarly, producers in industry v still earn zero profits in equilibrium, with all price increases being passed on to consumers. For each unit of good v that is not consumed, marginal social cost is less than the price, and since consumers equate marginal benefits with price, it must be the case that the marginal social cost of each additional unit consumed in market v is less than the social marginal benefit of each unit. Hence there is also a welfare loss from under-consumption in market v. The total welfare loss is the sum of the triangle welfare losses in each market as shown in Figure 5.4.2 above.