Consider a buyer who, in the upcoming month, will make a decision about whether to purchase a

Question:

Consider a buyer who, in the upcoming month, will make a decision about whether to purchase a good from a monopoly seller. The seller "advertises" that it offers a high-quality product (and the price that it has set is based on that claim.) However, by substituting low-quality components for higher-quality ones, the seller can reduce the quality of the product it sells to the buyer, and in so doing, the seller can lower the variable and fixed costs of making the product. The product quality is not observable to the buyer at the time of purchase, and so the buyer cannot tell, at that point, whether he is getting a high-quality or a low-quality good. Only after he begins to use the product does the buyer learn the quality of the good he has purchased. The payoffs that accrue to the buyer and seller from this encounter are as follows:

The buyer's payoff (consumer surplus) is listed first; the seller's payoff (profit) is listed second. Answer each of the following questions, using the preceding table.
a) What are the Nash equilibrium strategies for the buyer and seller in this game under the assumption that it is played just once?
b) Let's again suppose that the game is played just once (i.e., the buyer makes at most one purchase). But suppose that before the game is played, the seller can commit to offering a warranty that gives the buyer a monetary payment W in the event that he buys the product and is unhappy with the product he purchases. What is the smallest value of W such that the seller chooses to offer a high-quality product and the buyer chooses to purchase?
c) Instead of the warranty, let's now allow for the possibility of repeat purchases by the buyer. In particular, suppose that if the buyer purchases the product and learns that he has bought a high-quality good, he will return the next month and buy again. Indeed, he will continue to purchase, month after month (potentially forever!), as long as the quality of the product he purchased in the previous month is high. However, if the buyer is ever unpleasantly surprised-that is, if the seller sells him a low-quality good in a particular month-he will refuse to purchase from the seller forever after. Suppose that the seller knows that the buyer is going to behave in this fashion. Further, let's imagine that the seller evaluates profits in the following way: a stream of payoffs of $1 starting next month and received in every month thereafter has exactly the same value as a one-time payoff of $50 received immediately this month. Will the seller offer a low-quality good or a high-quality good?