Question: 1. There is a buyer and a seller. The buyer has a valuation 40 for a usable product. The seller has a cost 0 of producing a bad product and a cost 20 of producing a good product. The sequence of events is as follows. First, the seller decides what price to charge and whether to offer a warranty. Second, the buyer can accept or reject the offer from the seller. Third, if the buyer accepts the offer, then the seller decides whether to produce a good or a bad product. A good product is usable without repair. A bad product needs repair costing 30 to be usable. In this case, the cost of repair must be paid by the buyer if the product does not have a warranty and by the seller if the product has a warranty.

(a) Suppose that the seller offers the product at a price P without a warranty. If the buyer accepts this offer, should the seller produce a good or a bad product? Explain briefly.

(b) Suppose that the seller offers the product at a price P with a warranty. If the buyer accepts this offer, should the seller produce a good or a bad product? Explain briefly.

(c) What is the highest price P that the buyer is willing to pay for a product without a warranty? What is the highest price P that the buyer is willing to pay for a product with a warranty?

(d) Should the seller offer a warranty? Explain briefly.