There is a summer party at Kilyos beach club and the capacity of the club is 8,000 people. Customers can be segmented into members and non-members. We assume the price-response curves for each of these segments are:

Members: d_m(p_m) = (6,000 - 200p_m)⁺

Non-members: d_n(p_n) = (10,000 - 200p_n)⁺

where p_m is the price charged to the members and p_n is the price charged to the non-members.

Assume incremental cost per admission is $0.

a) What will be the optimal single price, p^*, to be charged to the members and non-members? Calculate corresponding demands from members and non-members and also the total revenue.

b) If members and non-members can be charged different prices, what will be the optimal separate prices for members and non-members? Calculate the demands from members and non-members and also the total revenue.How does this total revenue compare to the case with single price?

c) How does the optimal separate prices change when capacity decreases to 6,000? What is the "opportunity cost" for the 2,000 unavailable capacity?