Consider a monopolist who cannot price discriminate. she has total cost function c(q) = q 2 and faces inverse demand function p = a − q where a is a positive parameter. (a) solve for her optimal choice of q. (b) solve for the socially optimal level of q. (c) if a government regulator requires that the monopolist produce at the socially optimal level, will a lump sum subsidy be needed to keep the monopolist in the industry? show graphically the deadweight loss associated with the monopolization of this industry (in the absence of a subsidy).