I appreciate a complete handwritten answer.

Consider a situation in which there is a monopolist in a market with inverse demand function p(q). The monopolist makes two choices: How much to invest in cost reduction, I, and how much to sell, q. If the monopolist invests I in cost reduction, his (constant) per-unit cost of production is c(I). Assume that c(I)0. Assume throughout that the monopolist's objective function is concave in q and I. a) Derive the first-order conditions for the monopolist's choices. b) Compare the monopolist's choices with those of a benevolent social planner who can control both q and I (a "first-best" comparison)