Yet again we tread the dusty streets of Charlie Plopp’s home town. Everything is as in the previous problem. Professional bulldozer operators are willing to pay $6,000 for a bulldozer and recreational users are willing to pay $C. Charlie is just about to sell his bulldozer when a third potential buyer appears. Charlie believes that this buyer, like the other two, is equally likely to be a professional bulldozer operator as a recreational bulldozer operator and that this probability is independent of the types of the other two.
(a) With three buyers, Charlie’s expected revenue from using method 1 is _______, his expected revenue from using method 2 is _______ , and his expected revenue from using method 3 is __________
(b) At which values of C would method 1 give Charlie a higher expected revenue than either of the other two methods of selling proposed above?
(c) At which values of C (if any) would method 2 give Charlie a higher expected revenue than either of the other two methods of selling proposed above?
(d) At which values of C would method 3 give Charlie a higher expected revenue than either of the other two methods of selling proposed above?