I have a room to sell. There are two types of buyers. P types who will pay 8100 but no more and T type who will pay C <8100. C is known to me so I will hold a sale. Only two people turn up, they dont know each other so collusion is not a problem. I know that the probability that either buyer is an P or T type is independent of the others type. Each of them have probability of 0.5 of being either type. There are two ways of selling the room:

1) Run a sealed bid auction and sell it to the higher bidder at the second highest bid(if tie then choose one of the high bidders at random and sell it to the bidder at price bid by both bidders).

2) Run an ascending auction with reserve price R(choosing randomly if both stop at same price). If no one bids then I get nothing.

a) If I choose 2 I will set R>C. R<-8100. What is probability that neither makes the bid? What will my expected revenue be as function of R? What value of R should I choose as risk neutral?

b)If both bid rationally, what is my expected revenue if i choose method 1, as function of C?

c) When should I choose method 2 over method 1? If i am risk neutral, is either method effecient?

d) How would answer in c change if i was risk averse? Use calculations.