Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is p​q, where q is the number of rounds of golf that he plays per year. The manager of the Northlands Club negotiates separately with each person who joins the club and can therefore charge individual prices. This manager has a good idea of what​ Joe's demand curve is and offers Joe a special​ deal, where Joe pays an annual membership fee and can play as many rounds as he wants at ​$​, which is the marginal cost his round imposes on the Club. Joe marries​ Susan, who is also an enthusiastic golfer. Susan wants to join the Northlands Club. The manager believes that​ Susan's inverse demand curve is pq. The manager has a policy of offering each member of a married couple the same​ two-part prices, so he offers them both a new deal. What​ two-part pricing deal maximizes the​ club's profit?
Will this new pricing have a higher or lower access fee than in​ Joe's original​ deal?
How much more would the club make if it charged Susan and Joe separate​ prices?
The club maximizes profit subject to the policy by charging a per round price of: