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 r denote the join set auction commission rate, D;(r) represent 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 denote its average variable cost of auctioning an object. At the agreed-upon commission rate r, the profit of an auction house i is 1 = rpD; (r) - [F + vD; (r)]. What is the sum of the profits of Christie's house (C) and Sotheby's house (S)? The sum of profits, It, is O A. It= p[Dc(r) + Ds(1)] - [F + v(Dc(r) + Ds())]. O B. It= 2rp[Dc(r) + Ds(1)] -[2F + v(Dc(r) + Ds())]. O C. It= 2rp[Dc(r) + Ds(1)] -[2F + 2v(Dc(r) + Ds())]. O D. I= p[Dc(1) + Ds(1)] -[2F + 2v(Dc(r) + Ds(r))]. E. It= P[Dc(1) + Ds(1)] -[2F + v(Dc(r) + Ds(0))]. Characterize the commission rate that maximizes the sum of profits. That is, show that the commission rate that maximizes the sum of profits satisfies an equation that looks something like the monopoly's profit-maximizing condition. The commission rate that maximizes the sum of profits is that value for r as a function of &, such that X p - v -= 2). (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the _ character.) That's incorrect. rp If the auction houses maximize the sum of profits with respect to r, then dD(r) dD(r) - = rp- dr + pD(r) -v dr =0 where D(r) = Dc(r) + Ds(r). That is dD(r) (rp - V) dr + PD(r) = 0 dD(r) (rp - v) d - = - PD(r). dD(r) Dividing both sides by rp and by dr Then, substitute & for the price elasticity of demand. OK