Two Sided Markets - Monopoly Platform

. Consider a monopoly platform serving two distinct groups of users. Each group i = a, b comprises a unit mass of users who interact on the platform. The platform charges (possibly different) membership fees for the two groups, M. and My. The constant marginal cost of attracting users on the platform is normalized to zero. A user of group i enjoys the following net utility when interacting on the platform with users of the other group U1= uit yin; - Mi where u is the intrinsic value of being on the platform, y, measures the indirect network effect provided by an additional member of side j on each member of side i, n, is the number of members of side j on the platform. We assume that u is drawn from a uniform distribution on [0, v;]. As for indirect network effects, we assume that they are positive on both sides (yo b> 0). (a) Derive the number of participating users on side i as a function of the number of participating users on the other side. (b) Solve for the system of equations that you derived in the previous question so as to express the number of participating users on the two sides as a function of the two membership fees. Why is it legitimate to assume that Ya Yb