Please answer the following questions and give the explanations.

3. Consider a used car market. There are two types of used cars, orange and lemon. Orange cars owner value their own cars at $10,000. Lemon cars owner value their own cars at $2,000. Buyers are willing pay $13,000 for orange cars and $3,000 for lemon cars. There are limited stocks of both types of cars. Thus, buyers have to compete with each other and pay their full willingness to pay. Owners of used car know the quality of their car, but potential buyers don't. a. Suppose signaling is not available, what is the minimum value of the action of oranges in the population, f, such that the market for oranges does not collapse? (15 pt) b. Suppose now signaling and screening is available. Owners of used car can get certicate to show that their car is orange. For owners of orange cars, the cost of getting the certicate is $x. For owners of lemon cars, the cost of getting the certicate is $x2 (they have to bribe the person). Finding the range of x to achieve separation. (Hint: You need to check both Incentive Compatibility condition and Participation condition in this question. Car Owners' alternative choice is not selling the car and keeping it.) (15 pt)