Carmakers acknowledge that a small percentage of new automobiles are “lemons.” In the early 1980s, Chrysler Corporation succeeded in winning back lost market share by offering buyers the chance to return their new cars for up to 30 days if they were not satisfied. In this way, the “new” Chrysler sought to demonstrate its confidence in product quality. Suppose Chrysler made the following estimates for the program:
(1) 4 percent of its new cars were lemons;
(2) One-half of all lemons would be discovered and returned; and
(3) 1 out of every 16 normal-quality cars would be returned because of minor problems, buyer change of heart, and so on.
a. Of all the cars returned, what portion are lemons? For a buyer satisfied after month 1, what is the chance that that person will later find that he or she owns a lemon?
b. How might Chrysler decide whether the program’s benefits in screening for quality are worth its costs?