6. (20 points) A country club has two types of members. Serious golfers each have demand given by Q = 350 10P, while casual golfers have demand Q = 100 10P. In each case, P is the price per round of golf and Q is the number of rounds played per year. Suppose that the marginal cost to the club of another round played is $5 regardless of the type of golfer. (a) Find the price per round that the country club should charge each type of golfer if it can engage in third-degree price discrimination. (b) Suppose the club wants to charge a membership fee and a per-round fee, but it cannot price discriminate i.e., all golfers pay the same amount. Assume there are equal numbers of serious and casual golfers; nd total demand for golf and then nd the amounts the club should charge for the annual membership and per round played