5. (Perloff 13.37) In October 2002, the European Union fined Sotheby's auction house more than 20 million euros for operating, along with rival auction house Christie's, a price-fixing cartel. The two auction houses were jointly setting commission rates that sellers must pay. Let denote the jointly set auction commission rate, D. (r) the demand for auction house i's services by sellers of auctioned items, p denote the average price of auctioned items, F represent an auction house's fixed cost, and v represent its average variable cost of auctioning an object. At the agree upon commission rate, the profit of an auction house i is A; = rpD, (r) -(F + vD;(r)). a) What is the sum of the profits of the houses i and j? (2 points) b) Characterize the commission rate that maximizes the sum of the profits. (4 points) c) Do the auction houses have an incentive to cheat on their agreement? And what if one considers the problem in a dynamic perspective? (2 points)