Who wants to be a Millionaire: Are simple questions optimal?

A TV channel designs a revenue maximizing interactive quiz show by using two instruments: the questions' degree of difficulty and the cost per phone call which callers have to make to answer the question. A question is asked, spectators knowing the answer make a costly phone call and the winner is randomly selected among all those who know the answer. The TV channel's revenue is the expected number of callers times the cost for the phone call. Simple questions increase the number of phone calls. On the other hand, spectators' extractable rents decrease in the number of other callers due to negative externalities through an additional caller. I analyze the TV channel's decision problem in a Bayesian setting and find that the most simple questions are optimal indeed. The optimal price per phone call extracts fully spectators' rents and is decreasing in the number of spectators