Suppose that an intermediary faces a certain number of buyers and sell- ers. The intermediary sets usage prices P, and P, to be paid, respectively, by sellers and buyers whenever there is an interaction between a particular seller and buyer. Interaction can only take place on the platform owned by the in- termediary. (The exact nature of this interaction is not specited. It is simply postulated that a buyer's gross surplus can be expressed in a reduced form that depends only on the number of sellers, and that a seller's surplus can be ex- pressed in a reduced form that depends only on the number of buyers; that is, positive indirect network e/ects are present). Let nb and n, denote the number P and of buyers and sellers who decide to interact on the platform. Suppose that the intermediary does not incur any cost. Hence, the intermediary chooses P, to maximize total revenues, R= non, (Pb+ Ps), where non, is the total number of transactions conducted on the platform and (P+ Ps) is the sum of usage fees paid per transaction. 1. Suppose +rst that there are 3 buyers and 3 sellers (so nin, 2f0; 1; 2; 3g) and that the net surplus of buyers and sellers are as follows: all buyers enjoy a net surplus of ub= (2 Pb)ns; seller i (i=1;2;3) enjoys a net surplus of u = (i Ps) no (a) Find the price P, that maximizes revenues on the buyersside. (b) Given your answer at (a) and the corresponding buyers participation, +nd the price P, that maximizes revenues on the sellers side. (c) Show that the intermediary can increase its revenues by setting a P and lower price than the one you found at (b) and nd the prices P that maximize total revenues.