Question 19
Two used car dealerships compete side by side on a main road. The first, Hamid’s Cars, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Hamid’s $7000 to buy and service each car that it sells. The second dealership, Latif’s Motors, always sells lower-quality cars. On average, it costs Latif’s only $4000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would pay $9,000 on average for Hamid’s cars and only $6000 on average for Latif’s cars.
Without more information, consumers do not know the quality of each dealership’s cars. In this case, they would figure that they have a 50-50 chance of ending up with a high quality car, and are thus willing to pay $7500 for a car.
Hamid has an idea: He will offer a bumper-to-bumper warranty for all cars he sells. He knows that a warranty lasting Y years will cost $500Y on average, and he also knows that if Latif tries to offer the same warranty, it will cost Latif $1000Y on average.
Suppose Hamid offers a one-year warranty on all of the cars he sells.
Based on the above data, answer the given subquestions.
What is Latif’s profit (per car in $) if he offers a one-year warranty? ________________