Consider a monopolist who cannot price discriminate. she has total cost function C(q)=q^2 an faces inverse demand function p=a-q where a is a positive parameter.

1: Solve for her optimal choice of q

2: Solce 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)