The basic insight of the analysis in this chapter - that changes in consumer willingness to pay for quality will induce firms to offer greater quality levels - is due to Rosen (1974), who examines product quality and variety in competitive markets. The analysis of product liability rules in Cournot oligopoly follows Polinksy and Rogerson (1983), although they do not consider the case where consumers overestimate expected harm. The condition for the superiority of the negligence rule in equation (6.23) is stated by Polinksy and Rogerson (1983), although the proof provided here which directly compares triangle deadweight losses, is to my knowledge, new. Spulber (1989) contains an excellent analysis of product liability rules.
This appendix shows how welfare changes in a competitive market under a no liability rule when consumer perceptions of risk, A, change. Welfare is given by equation (6.6):
The change in welfare as A changes is:
This expression has two components. Let us consider the first. The term n'(A) is negative. The term u'[n(A)q0]q0 - C(q0) - q0[wx(A) + H(x(A))] is the difference between marginal social consumption benefits and marginal social costs. It is negative when l < 1 (since consumers purchase too many units of the good in that case) and positive when l > 1 (since consumers consume too few units in that case). The product of these two terms together is therefore positive if l < 1, and negative if l > 1.
The next term, -n()q0x'()[w + H'(x)], is the change in the social costs of care as l changes. The term x'(l) is positive. The term w + H'(x) is negative when l < 1 (since care is underprovided in this case), and is positive when l > 1 (since in that case care is overprovided). Hence the term -n(A)q0x'(A)[w + H'(x)] is positive if l < 1, and negative if l > 1.
Thus, the two components of dW have the same sign, and so dW is positive if l < 1, and negative if l >1. d^ d^