Question: Consider a case of warranties with moral hazard. The probability that a low-quality good breaks down is constant at l, but the probability of a high-quality good breaking down, p, varies with effort according to ? = h + (1 - e)(l - h), where e is "effort" (maintenance care, etc.). Assume for simplicity that e can take on only two possible values, 0 or 1, and the disutility of effort is v(e) = e. It would not be profitable for the low-quality manufacturer to offer a warranty.
(a) Let V be the consumer's valuation of a perfectly reliable product. If the high-quality man- ufacturer offered a full warranty, show that the individual would choose e = 0 (compare expected utilities). Knowing this, would the manufacturer still offer a warranty?
(b) Now assume that the consumer is required to pay a proportion a of the cost of replacing a broken good. How high must a be (in terms of l, h, V ) to induce the consumer to choose e = 1?