We revisit our financially afflicted friend, Charlie Plopp. This time we will look at a slightly generalized version of the same problem. All else is as before, but the willingness to pay of recreational bulldozers is an amount C < $6, 000 which is known to Charlie. In the previous problem we dealt with the special case where C = $4, 500. Now we want to explore the way in which the sales method that gives Charlie the highest expected revenue depends on the size of C.
(a) What will Charlie’s expected revenue be if he posts a price equal to the reservation price of professional bulldozer operators?
(b) If Charlie posts a price equal to the reservation price C of recreational bulldozer operators, what is his expected revenue?
(c) If Charlie sells his bulldozer by method 3, the second-price sealed-bid auction, what is his expected revenue? (The answer is a function of C.)
(d) Show that selling by method 3 will give Charlie a higher expected payoff than selling by method 2 if C < $6, 000.
(e) For what values of C is Charlie better off selling by method 2 than by method 1?
(f) For what values of C is Charlie better off selling by method 1 than by method 3?