Under a rule of no liability, firms do not have to compensate consumers for any losses that are incurred when the good is consumed.
Assuming that consumers can observe the level of care that is provided, risk-neutral consumers reduce their marginal willingness to pay by the perceived marginal expected harm:
Note that the price that consumers are willing to pay is a function of the level of care provided by firms, as well as the perception parameter A. Notice that we have written the demand curve as a function of x. This is deliberate: even if consumers cannot perfectly perceive harm, an increase in x will increase their marginal willingness to pay for the good, and so also shift the demand curve.
Each producer's profit is equal to P(x)q - qwx - C(q), and so for any number of firms, each price-taking profit-maximising firm chooses q by equating price with marginal cost. Therefore:
In a long-run equilibrium we have
Once again, the quantity that minimises C(q) will also minimise wx + C(q ). In other words, qNL = q*.
What level of care will firms provide? Since firms are not obligated to take care, it is tempting to conclude that they will choose x = 0. However, in general this conclusion is incorrect. To see why, suppose that A = 1 and consider a candidate long-run equilibrium in which each firm provides an inefficiently low level of care, x < x*. Each firm continues to produce q* units since the minimum of the average cost curve still occurs at q*. The market price in this candidate equilibrium is:
and consumers' perceived net benefit is:
This situation cannot be sustained as a competitive equilibrium. To see why, suppose that all firms chose a slightly higher level of care, x', for all units supplied, with x < x' < x*. This increases each firm's average cost and marginal cost. Suppose that each firm continued to supply q* units, but that each of them charged a price which was greater than their new average costs. Since we have assumed that l = 1 here, consumers can perfectly observe this new higher level of care. For each unit of the good they are willing to pay H(x) - H(x') > 0 for such a change, since this is the reduction in expected harm per unit of the good.
But the increase in cost per unit from providing the higher level of care is w(x' - x) < H(x) - H(x'), where the inequality holds as long as x < x' < x*. This means that there is a price that each firm could charge which would more than cover the increase in cost from greater care, and the price increase would be less than the consumer increase in willingness to pay. In other words, starting from a position where x < x*, all firms could make a profit by providing a greater level of care than the initial level x. In other words, even though firms are not legally obligated to take greater care, the profit motive would drive them to do so.
Moreover, if l = 1 and since x above was arbitrary, such a profit opportunity always exists as long as x < x*. The gain to consumers (that is, their willingness to pay) for an additional unit of care per good is -H'(x). The marginal cost to producers is w. Hence, no further profit opportunities will exist when:
But this is just the same condition as the efficiency condition in equation (6.3). In other words, in contrast to the results in Chapter 4, if l = 1 the no liability rule is efficient.
Since profits get bid down to zero in a competitive equilibrium, the price under a rule of no liability when l = 1 is:
which is lower than the price under strict liability. A legal rule of no liability produces the same level of care, output and welfare as a rule of strict liability and is efficient because the market price adjusts in response to all of the costs and benefits that are incurred by each party. With a rule of strict liability, consumers are fully insured against and potential risks, but this simply drives up the costs of firms and is reflected in a higher price for the good. With a no liability rule, consumers bear the full costs of all accidents, which lowers their marginal willingness to pay for the good. However, firms are forced to charge a lower price under competitive conditions since damages no longer form part of their cost base.
The effect of each legal rule on the market outcome is shown in Figure 6.4.2.
Figure 6.4.2 Equilibrium under no liability
If consumers misperceive the harmfulness of the product, then the previous result breaks down. To see why, note that if l Ф 1, the consumer's willingness to pay for a change in the level of care provided by firms, x, is -XH'(x) Ф -H'(x). Firms still have an incentive to provide some care under a no liability rule (unless l = 0), but their incentives no longer align exactly with efficient incentives.
Suppose, for example, that consumers underestimate the expected harmfulness of the product, so l <1. Then in the competitive equilibrium firms will provide care up to the point where consumer perceived marginal willingness to pay equals the marginal cost of care, so that:
in the equilibrium, where x^L is the equilibrium level of care. But X <1, so:
This series of equalities and inequalities shows that the actual marginal benefit of care at the equilibrium, x^L, exceeds the marginal benefit at x*, which implies that x^L < x*. In other words, in the competitive equilibrium, firms underprovide care. In the limit, if consumers completely misperceive the product's harm, then x^L = 0, and no care would be provided.
On the other hand, if consumers overestimate the harmfulness of the product (so l >1), then the above argument is reversed. In the competitive equilibrium firms will still provide care up to the point where consumer marginal willingness to pay, so that:
But now 1 > 1, so:
The actual marginal benefit of care at x1 is less than the marginal benefit at x*, which implies that x1 > x*, and firms overprovide care. The reason is straightforward: consumers believe that the good is very dangerous, and are willing to pay a relatively high amount at the margin, -1H' (x) > -H' (x) for firms to reduce care. Firms are willing to provide care as long as there is a profit opportunity for doing so, which is the case as long as -1H' (x) > w. This provides firms with an incentive for overprovision of care.
The aggregate competitive equilibrium quantity under no liability when 1 < 1 is greater than the efficient level, and when 1 > 1 it is inefficiently low. To see this, note that each firm produces the same output, q0, but that the number of firms in the industry varies with 1. To see how n changes with 1, note that the competitive equilibrium quantity is determined where the demand curve (which is determined by consumer misperceptions) meets the long-run market supply curve, or where:
Taking the total derivative yields:
where we have used the fact that w + 1H'(x(1)) = 0 in the competitive equilibrium. Total welfare is:
W = u[n(1)q*] - n(1)C(q*) - n(1)q*[wx(1) + H(x(1))] (6.6)
As shown in the Appendix, the change in welfare with respect to 1 has the following pattern:
In other words, under a no liability rule, welfare is at a maximum when consumers accurately perceive risk, and then falls away as consumers either underestimate or overestimate risk.
To summarise, in cases where there are consumer misperceptions and l Ф 1, there will be a welfare loss which consists of two parts:
- • First, there is a price effect: firms' marginal and average costs (and therefore the market price) are either inefficiently low (in the case where l < 1) or inefficiently high (in the case where l > 1). Since price equals marginal and average costs, this means that even if consumers could accurately perceive risk, they would consume either too many units of the good (in the case where l < 1) or two few units of the good (in the case where l > 1).
- • Second, there is a harm misperception effect: there is a welfare loss because consumers incorrectly estimate the expected harm in each unit of the good, leading them to consume the wrong amount of the good for the level of care that is provided in equilibrium. In the case where l < 1, this effect induces consumers to consume too many units, and in the case where l < 1 it induces them to consume too little.
In other words, both effects tend to reinforce one another.