The demand price for a monopolistic firm’s product is a function of quantity q and quality s: P(s,q) = s(a – bq) , while the firm’s production cost is a function of quality s only: C(s, q) =0.5s^2 .
a) Find all critical points (s,q) of the monopolist’s profit maximization problem.
b) Use the second order conditions to find the firm’s (local) maximum.