Cell World and Phones R US are two stores in a small town that sell used cell phones. Cell World sells only high-quality used cell phones. Each phone costs Cell World $90 to buy and repair. Phones R US sells low-quality used cell phones and each phone costs them $70 to buy and repair. Consumers are willing to pay $85 for a low-quality used cell phone and $110 for a high-quality used cell phone. However, consumers don't know which store sells high-quality cell phones and which store sells low-quality cell phones. Therefore, they are willing to pay $95 for an used cell phone.
Cell World would like its customers to know that it sells high-quality cell phones. So, to send such a signal, Cell World wants to offer a warranty that covers all necessar repairs for the cell phones. Such a warranty would cost Cell World $5 per year per cell phone (cost of warranty = $5 x years of warranty), while it would cost Phones R US $9 per year per cell phone (cost of warranty = $9 x years of warranty). Consumers will assume that the store offering the longer warranty sells high-quality cell phones. If both stores offer the same warranty, consumers will be willing to pay only $95 per cell phone.
A. Without offering a warranty, Cell World would make a profit of ($5, $9, $10, $15, $20, $25) per cell phone, and Phones R US would make a profit of ($5, $9, $10, $15, $20 $25) per cell phone.
B. Suppose that Cell World commits itself to a two year warranty (Y = 2). Then Phons R US's best response is to (offer no warranty, offer a one-year warranty, offer a two-year warranty, offer a three-year warranty) so Cell World's profit will be (-$10, $0, $5, $10, $15, $20) per cell phone, and Phones R US's profit will be ($7, $10, $13, $15, $16, $22, $25) per cell phone.
C. If Cell World commits itself to a one year warranty (Y = 1), what would maximize Phones R US profit? (offering a one year warranty or offering no warranty)
D. Suppose that Cell World offers a warranty and Phones R US does not. It is then discovered that consumers that bought their cell phones at Cell World mistreat their cell phones compared to owners of Phones R US cell phones. This is a problem of (a lemons market, adverse selection, asymmetric information, moral hazard).