Restaurant offers a buffet lunch. There are two types of potential customers in its neighborhood, rich and poor, with respective individual monthly demands Q^d_ h(p) =21p and Q^d_n (p) = 120.5p, where q is the number of buffet visits and p the price(euros). The neighborhood has 100 rich people and 200 npoor. The cost of serving one buffet visit is 3 euros. Restaurant has a fixed cost of 10000euros/per month for organizing the buffet.

(a) What is the profit-maximizing simple price for the buffet?

(b) Exclusive Card gives members access to the buffet at a price that is not available to non-members. Design the profit-maximizing pricing scheme.

(c) Continued from 3b. Compared to simple pricing, what is the impact of exclusive Card on the consumer surplus of rich and poor espectively?

(d) Turns out that poor consume so much salsa that the cost of serving them is 8euros/per visit. How does this affect the optimal pricing scheme in part 3b?