Suppose you own a car worth an unknown amount between $0 and $1000. You can make a single bid to buy the car. If your bid exceeds the car's value, you pay your bid and receive the car; if your bid is less than the value, you do not get the car. 1) What should your optimal bid be? 2) If you win, how much do you stand to lose? 3) If you have a mechanic who can increase the value of the car by a constant multiple of the car's current value, what should this constant be to make bidding worthwhile?