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1. (24 points) 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.