1.(5 points) All used cars are "lemons" (poorly maintained, poor quality) or "peaches" (well-maintained, high quality). Owners know whether or not their car is a lemon, but buyers do notthat is, the quality of a car is private information. There are many more buyers than sellers. Buyers value a peach at $5,000 and a lemon at $400; owners value a peach at $3,000 and a lemon at $200. Owners can have their cars inspected for $100. If they do have their cars inspected, they will receive a certificate that shows whether the car is a lemon or a peach. Show that owners of peaches will have their cars inspected and will sell those cars for $5,000. Show also that the owners of lemons will not obtain a certificate and will sell their cars for $400.