A retailer sells a product that is either of low or high quality, where quality is measured by the likelihood that the product works. Assume that the probability that the high-quality product functions properly is h and the probability that the low-quality product functions properly is l, where 0 c > 112. That is, only the high-quality product generates a social surplus. Also, $12 > c. That is, the average quality of a product generates an expected utility that is higher than the cost. a. Consider the following game. First, nature selects the quality of the product (according to the above probabilities). Next, the retailer sets a price p, and nally the consumer decides whether or not to purchase the product. Find a perfect Nash-Bayes equilibrium in which both types of retailer select the same price. ' b. Suppose now that firms have the option of offering a money-back warranty: in case the product does not work then consumer gets her money back. That is, the consumer's payoff if she purchases a high-quality product is h(v p), and if low quality l(p 17). Whereas prots for the high and low- quality firm would be hp c and (p c, respectively. The game is now the following. First, nature selects the quality of the product (according to the above probabilities). Next, the retailer sets a price p, and chooses whether or not to offer the money-back warranty. Finally, the consumer decides whether or not to purchase the product. Find a perfect Nash-Bayes equilibrium in which the retailer chooses a warranty only when he has a high-quality product